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Quantum Physics

Quantum theory cannot consistently describe the use of itself

  • Quantum theory cannot consistently describe the use of itself | Nature Communications

  • [1604.07422] Single-world interpretations of quantum theory cannot be self-consistent

  • 新版薛定諤貓或證明量子理論自相矛盾 | 大紀元

    【大紀元2018年09月27日訊】（大紀元記者张妮編譯報導）「薛定諤的貓」（Schrödinger's cat）可能是世界上最著名的思想實驗，也是量子理論的重要基礎。如今兩位物理學家設計了一個「多貓」版本的實驗，其結果讓所有物理學家大惑不解，並引發了激烈的爭論。

    據《自然》雜誌報導，最近的這個「多貓」版實驗構想發現，如果量子力學的通用論述是正確的，那最新版實驗就會得到兩種完全相反的結論。這說明，量子理論是自相矛盾的。

    新實驗的設計者、瑞士聯邦理工學院（ETH）的Daniela Frauchiger和Renato Renner於2016年4月首次發佈他們的設計。之後至今兩年里，該理論讓物理界炸開了鍋。最終版論文9月中旬發表在《自然-通訊》上。

    奇異的量子世界

    量子物理學目前為止能解釋幾乎所有的近代物理現象，但是其不能得到確定結果的特性仍讓研究者們入迷地尋找答案。量子學物體，比如電子，其位置處於不斷運動中，可以用數學的波函數來表達，就像海上的波浪。但當其位置被測量的時候，其位置就是一個確定的值。

    上世紀20年代量子物理學先驅Niels Bohr和Werner Heisenberg對此做了一種可通用的解釋，人們把他們的理論以Bohr居住過的城市命名為哥本哈根詮釋（Copenhagen interpretation）。該理論說，觀測量子系統的行為使得波函數從一個彌散狀態「坍塌」為一個數據值。

    然而，最新的這個實驗構想挑戰了包括哥本哈根詮釋在內的多個量子學理論。

    薛定諤實驗的幾個版本

    -1935年：盒子里關著一隻貓，和一個與隨機性事件，比如由核衰變觸發釋毒的機關相連。在這種情況下，貓的生死只有在打開盒子查看後才是確定的，而在此之前貓處於生與死的疊加狀態。

    -1967年：匈牙利物理學家維格納（Eugene Wigner）提議，把貓和毒氣機關換成一位物理學家（維格納的朋友）和一個測量儀，測量儀能返回某種隨機事件的結果，比如一枚硬幣哪面朝上的結果。問題是，當那位朋友知道了硬幣哪面朝上的結果時，波函數是否坍塌？一個學派認為是這樣的，認為意識在量子領域之外。但如果把量子學應用到物理學家身上，那在維格納打開盒子之前，這位朋友以及硬幣應該處於兩種結果的疊加狀態。

    -2016年：Frauchiger和Renner的實驗更為複雜。他們設想有兩位維格納一起做實驗，把兩位朋友Alice和Bob分別關在兩個盒子里。Alice投擲一枚硬幣，並把其結果通過量子信息的方式傳遞給Bob。Bob也用量子原理偵測Alice傳來的信息，並猜測硬幣哪面朝上。當兩位維格納打開盒子時，在某些情況下，他們兩得出的哪面朝上的結論是一樣；而在某些情況下，兩位維格納得出的結果是不一樣的。

    對最新版實驗的不同解釋

    這個實驗公佈後，量子學基礎理論領域的很多專家反響熱烈。很多人都在捍衛自己的理論。「有的爭辯甚至很情緒化，」Renner說，「多數人說這個實驗證明他們的詮釋是唯一正確的。」

    位於加利福尼的查普曼大學（Chapman University）的理論物理學家Matthew Leifer認為，得到不一致的結果不是大問題。他說量子學的一些理論本來就允許不同的觀察角度，有著不同的結果。他覺得這樣的解釋比認為量子學不適用於人體這樣的說法要「好受」的多。

    至今，物理學家們對這個最新實驗意味著什麼，如何解釋，仍無統一的答案。Leifer說：「我認為我們還沒找到合理的解釋。」 ◇

Quantum physicists achieve entanglement record

Quantum 'spooky action at a distance' becoming practical

  • Quantum 'spooky action at a distance' becoming practical

  • 量子技術再突破 超越時空正在變成現實？ | 量子學 | 量子糾纏 | 光子 | 大紀元

    【大紀元2018年01月15日訊】（大紀元記者張秉開編譯報導）量子學研究不斷取得突破，澳洲科學家最近找到檢測量子超距作用的可靠方法，距離實現真正的量子計算機又邁進一步。

    據《科學》近日報導，澳大利亞格里菲斯大學（Griffith University）的量子學家找到可靠的方法，測量一對光子發生的量子超距作用。

    光子可用於諸如「量子糾纏」這樣的量子超距作用。在兩個光子之間發生量子糾纏作用時，一個位置的光子可即時影響處於其它任何位置的另一個光子狀態，而不受空間距離限制。

    目前，科學家正在利用「量子糾纏」等超距作用開發量子計算機。但是，科學家遇到的一大困難是，光子常常不能有效地穿過既定的傳送路徑而丟失，而且科學家無法有效檢測那些丟失光子的具體位置，這會產生信息傳輸洩密等一系列問題。

    格里菲斯大學的量子學家喬夫‧普雷德（Geoff Pryde）教授說：「這是現有光子量子超距作用驗證技術的缺陷。干預者很容易利用丟失光子的量子糾纏而破壞安全設置。」

    普雷德教授進一步解釋，他們的實驗可以解決這個難題，因為他們使用與眾不同的方法------量子隱形傳輸（quantum teleportation，也稱為量子遙傳等）來傳輸光子。之後，研究者使用量子操控（quantum steering）的方法驗證這些光子確實成功傳送到另一個量子通道，而不會丟失。

    而且，研究者表示，他們在與80公里通訊光纜相同的條件下，有效地檢測了光子的這些量子超距作用，這說明該方法在不良條件下也會起作用。

    量子超距作用等量子學理論遠遠超過認為時空不變的牛頓物理學，所以一直是人們關注的重大科學基本問題。

    量子超距作用不是我們三維空間的粒子所能比擬的另外時空存在形式。但是近年的研究顯示量子學理論正在變成現實的應用技術。

    2016年8月，美國馬里蘭大學的科學家展示了世界上由五個原子離子組成的量子計算機，在激光開關操控下，其中的量子位元（qubits，也稱量子比特）的計算精確率達到90%以上。

    澳洲科技網站ScienceAlert 2017年12月報導，澳大利亞新南威爾士大學（UNSW） 嘗試設計可以處理數以百萬計量子位元的糾錯編碼，利用常見的標準半導體元件製造量子計算機芯片。

浅谈量子贝叶斯

  • 科学网—拿什么拯救你量子力学-浅谈量子贝叶斯 - 张天蓉的博文

    • https://hyp.is/go?url=http%3A%2F%2Fblog.sciencenet.cn%2Fblog-677221-1054026.html

      著名理论物理学家Steven Weinberg今年1 月19日为纽约书评写了一篇文章^【^^1^^】^，表达了他对量子物理未来前景的困惑和担忧，其中对量子论概率解释的一段话发人深思。

      此段话的意思大致如下（是意解，不是直接翻译）：

      概率融入物理学使物理学家困扰，但是量子力学的真正困难并非概率，而是这概率从何而来？描述量子力学波函数演化的薛定谔方程是确定性的波动方程，本身并不涉及概率，甚至不会出现经典力学中对初始条件极为敏感的"混沌"现象（笔者译注：这是因为薛定谔方程是线性偏微分方程，混沌是非线性的特征）。那么，量子力学中反映不确定性的概率究竟是怎么来的呢?

      量子力学的困惑

      正如温伯格所述，物理学家们一直被量子力学中的种种诡异现象所困扰，并且在哲学理解的层面上互相难以达成共识。那么，是不是说量子力学就是错误的呢？当然不是，至少不能完全地绝对地如此下结论。相反地，量子力学被认为是自然科学史上被实验证明最精确的一个理论，它是我们理解原子、原子核、电磁性、半导体、超导，以及天文学中观测到的白矮星、中子星的结构等等微观理论的基础，以其为基础所发展的量子电动力学，对于某些原子性质的理论预测，被实验验证结果的准确性达到10^8^分之一。

      量子力学就是这么一个奇怪的理论，如今的高科技产品中随处可见其应用，可谓已经取得了巨大的成就，但却又争议不断，众说纷纭。物理学家们对量子理论的分歧不在计算结果，而是在于不同的诠释。从波尔和爱因斯坦的著名论战开始^【^^2^^】^，直到如今已经百年左右，在顶尖的物理学家之间仍然是争论不休。但是，只要我们遵循美国康奈尔大学物理学家DavidMermin所说的："闭上你的嘴，用心作计算吧！"那便万事大吉，无论哪派的物理学家，都能学会程式化地使用抽象而复杂的数学方法，对各种微观系统进行研究和计算，并给出准确度惊人的结果。

      温伯格的疑问表面看起来是从数学角度发出的问题：方程不涉及概率，为何最后的结果中就解释成了概率？事实上，从物理的角度看也是如此，概率的入侵搅浑了量子力学，搅浑了物理学家们的科学思维方式。

      概率是什么？概率可定义为对事物不确定性的描述。但在经典物理学框架中，不确定性是来自于我们知识的缺乏，是由于我们掌握的信息不够，或者是没有必要知道那么多。比如说，当人向上丢出一枚硬币，再用手接住时，硬币的朝向似乎是随机的，可能朝上，可能朝下。但按照经典力学的观点，这种随机性是因为硬币运动不易控制，从而使我们不了解（或者不想了解）硬币从手中飞出去时的详细信息。如果我们对硬币飞出时每个点的受力情况知道得一清二楚，然后求解宏观力学方程，就完全可以预知它掉下来时的方向了。换言之，经典物理认为，在不确定性的背后，隐藏着一些尚未发现的"隐变量"，一旦找出了它们，便能避免任何随机性。或者说，隐变量是经典物理中概率的来源。

      然而，量子论中的不确定性不一样，量子力学中的不确定性是否也来自于隐藏于更深层次的某些隐变量呢？这正是当年爱因斯坦说"上帝不会掷骰子！"的意思。爱因斯坦不是不懂概率，而是不接受当年以波尔为代表的"哥本哈根学派"对量子力学的概率解释以及测量时"波函数塌缩"到经典结果的"量子-经典"的边界图景。之后（1935年），爱因斯坦针对他最不能理解的量子纠缠现象，与两位同行共同提出著名的的EPR佯谬^【^^3^^】^，试图对哥本哈根诠释做出挑战，希望能找出量子系统中暗藏的"隐变量"。（在此，因为篇幅有限，我们无法对量子现象及诠释给予足够的介绍，更多有关量子及量子纠缠的内容，请参考笔者在科学网的系列文章，或中科院高能所微信casihep中笔者的"走近量子纠缠"）。

      爱因斯坦质疑量子力学主要有三个方面：确定性、实在性、局域性。这三者都与上面所说的"概率之来源"有关。如今，爱因斯坦的EPR文章已经发表了80余年，特别在约翰-贝尔提出贝尔定理后，爱因斯坦的EPR悖论有了明确的实验检测方法。然而，令人遗憾的是，许多次实验的结果并没有站在爱因斯坦一边，并不支持当年德布罗意-玻姆理论假设的"隐变量"观点。反之，实验的结论一次又一次地证实了量子力学计算结果的正确性。

      温伯格今年1月份的文章中提出的质疑，仍然是量子理论的诠释问题，不是计算问题。但他对现有理论的未来担忧，质疑量子力学中"测量的本质"。温伯格认为对量子力学有两类主要的诠释：与"多世界"对应的"现实主义"诠释，以及与哥本哈根表述一脉相承的"工具主义"诠释。两者都不能令人满意。或许有必要对量子力学的概念进行大修正。

      哥本哈根诠释及困扰

      简单解释一下量子力学主流学派的观点：以波尔和海森堡为代表的哥本哈根诠释。

      首先以电子双缝实验为例，回顾一下量子力学中的"诡异"现象---量子悖论。

      双缝实验中，让电子一个一个地发射到"双缝"附近（像发射子弹一样），从经典观点来看，一个电子不可分，并且电子之间不会互相干涉。但是，实验结果却表明，电子束在后面的屏幕上产生了干涉条纹。因此，这是一种量子效应，表明电子和光一样，既是粒子又是波，兼有粒子和波动的双重特性，这就是波粒二象性。

      德布罗意引入"物质波"的概念，认为所有物质都有波粒二象性，但子弹（经典粒子）射到双缝上，观察不到干涉条纹，是因为子弹的质量太大，波长太小的缘故。而微观的电子便能观察到干涉现象。薛定谔导出的方程则更进一步，方程的解赋予了微观粒子（或量子系统）一个对应的"波函数"。

      电子双缝实验中出现的干涉条纹已经够奇怪，而更为诡异的行为是表现在对电子的行为进行"测量"之时！

      为了探索电子双缝实验中的干涉是如何发生的？物理学家在双缝实验的两个狭缝口放上两个粒子探测器，企图测量每个电子到底走了那条缝？如何形成了干涉条纹？然而，诡异的事情发生了：一旦想要用任何方法观察电子到底是通过了哪条狭缝，干涉条纹便立即消失了，波粒二象性似乎不见了，实验给出与经典子弹实验一样的结果！

      诸如此类的奇特量子现象已经被无数次的实验所证实。然而，如何从理论上来解释此类量子悖论呢？这便出现了各种诠释，我们仅仅看看哥本哈根派是怎么说的。

      哥本哈根派认为，微观世界的电子，通常处于一种不确定的、经典物理不能描述的叠加态：既是此，又是彼。比如说，被测量之前的电子到达狭缝时，处于某种（位置的）叠加态：既在狭缝位置A，又在狭缝位置B。之后，"每个电子同时穿过两条狭缝！"，产生了干涉现象。

      但是，一旦在中途对电子进行测量，量子系统便发生"波函数坍塌"，原来表示叠加态不确定性的波函数塌缩到一个固定的本征态。就是说：波函数坍塌改变了量子系统，使其不再是原来的量子系统。量子叠加态一经测量，就按照一定的概率规则，回到了经典世界。这儿所说的"概率规则"名为"玻恩法则"，量子系统坍塌到某本征值的概率与波函数的平方有关。

      以上诠释实质上的物理意义等同于公众皆知的"薛定谔的猫"：打开盖子前，猫是既死又活，只有揭开盖子后观测，猫之死活状态方能确定。

      这种解释带来很多问题（别的诠释又有别的问题），哥本哈根解释直接使人困惑的一点是：如何理解测量的本质？谁才能测量？只有"人"才能测量吗？测量和未测量的界限在哪里？

      按照惠勒引用波尔的话说："任何一种基本量子现象只在其被记录之后才是一种现象"，这个绕口令式的一段话导致人们如此质问哥本哈根诠释：难道月亮只有在我们回头望的时候才存在吗？

      此外，因为波函数塌缩是在同一时刻发生在所有地方，对量子纠缠中的两个粒子，导致了爱因斯坦的"幽灵般超距作用"之困惑。总而言之，看起来，对量子力学的诠释违反了确定性、实在性、和局域性。经典物理学从来认为物理学的研究对象是独立于"观测手段"存在的客观世界，而量子力学中的测量却将观测者的主观因素掺和到客观世界中，两者似乎无法分割。

      量子贝叶斯模型

      本世纪初，有三位学者（美国的凯夫斯、富克斯、及英国的沙克）发表了一篇题为《作为贝叶斯概率的量子概率》的短论文^【^^4^^】^，探索一种量子力学的新诠释。三人都是经验丰富的量子信息理论专家，他们将量子理论与贝叶斯派的概率观点结合起来，建立了"量子贝叶斯模型"(Quantum Bayesianism），或简称为"量贝模型"（QBism）。

      说来说去仍然回到了本文的起点：概率之本质及其来源的问题上，不过这次具体涉及到的是"贝叶斯派的概率观"。对于概率的"主观客观"性，通常有两种极端的解释：频率派和贝叶斯派。频率派强调概率的客观性，一般用随机事件发生的频率之极限来描述概率；贝叶斯派则将对不确定性的主观置信度作为概率的一种解释，并认为：根据新的信息，可以通过贝叶斯公式不断地导出或者更新现有的置信度。

      以下几个例子可以启发读者思考在各种情况下对不同概率类型的不同理解：

      1. 抛硬币或掷骰子实验中某一面出现的概率是由其物理属性决定的，具有明确的"客观"意义，可以通过多次试验的方法来逼近；

      2. 地震研究者预测某地区某月是否发生6级地震的概率，除了该地区的客观地层情况之外，还有与该研究者有关的许多"主观"因素，难以进行多次试验，但可以参考许多年的历史记录；

      3. 美军某月某日于某处抓到本拉登的概率，只是依靠主观臆测，不可能重复试验。

      贝叶斯派的主观概率思想与量子力学的哥本哈根诠释在某些方面有异曲同工之妙。更早期，美国物理学家埃德温-杰恩斯（EdwinJaynes，1922-- 1998）率先使用和推动用贝叶斯概率来研究统计物理和量子力学，由此而激发几个量子信息学家们之后构建了量贝模型。

      量贝模型与哥本哈根诠释有关联但又有所不同，哥本哈根诠释认为波函数是客观存在，人为的"测量"干扰破环了这个客观存在，使得原来的量子叠加态产生了"波函数塌缩"，从而造成悖论。量贝模型则认为波函数并非客观实在，只是观察者所使用的数学工具。波函数不存在，也就没有什么"量子叠加态"，如此便能避免诠释产生的悖论。

      根据量子贝叶斯模型，概率的发生不是物质内在结构决定的，而是与观察者对量子系统不确定性的置信度有关。实际上，当年的玻尔便曾经认为波函数是数学抽象而非真实存在，如今的量贝模型为玻尔的观点提供了数学支持。他们将与概率有关的波函数定义为某种主观信念，观察者得到新的信息之后，根据贝叶斯定理的数学法则得到后验概率，不断地修正观察者本人的主观信念。

      尽管认为波函数是主观的，但量贝模型并不是否认一切真实性的虚无主义理论。这个理论的支持者说，量子系统是独立于观察者而客观存在的。每个观察者使用不同测量技术，修正他们的主观概率，对量子世界作出判定。在观察者测量的过程中，真实的量子系统并不会发生奇怪的变化，变化的只是观察者选定的波函数。对同样的量子系统，不同观察者可能得出全然不同的结论。观察者彼此交流，修正各自的波函数来解释新获得的知识，于是，就逐步对该量子系统有了更全面的认识。

      根据量贝模型，盒子里的"薛定谔猫"并没有处于什么"既死又活"的恐怖状态。但盒子外的观察者对里面的"猫态"的知识不够，不足以准确确定它的"死活"，便主观想象它处于一种死活二者并存的叠加态，并使用波函数的数学工具来描述和更新观察者自己的这种主观信念。

      举一个通俗例子来说明此类主观臆想的"叠加态"。在2016年的美国总统大选中，特朗普和希拉里都有"胜败"的可能性，但结果难以预测。对某个特朗普的支持者而言，不知道特朗普最后到底是"胜"还是"败"之前，只能凭着他个人的主观臆测来估计特朗普"胜败"概率（比如52%：48%），就好象是类似于认为特朗普是处于某种"胜败"并存的叠加态中。这种叠加态的概率分配是这个人主观的，其他人可能会有不同概率分配的主观叠加态。

      量贝模型创建者之一的富克斯，为量贝模型数学基础作出了一个重大发现，他证明了计算概率的玻恩法则几乎可以用概率论彻底重写，而不需要引入波函数。因此，也许只用概率就可以预测量子力学的实验结果了？富克斯希望，玻恩法则的新表达能够成为重新解释量子力学的关键。由此想法开始，支持者们正在努力，企图用概率论来重新构建量子力学的标准理论。目前这个目标尚未达成，结论如何，还需拭目以待。但无论如何，量贝模型为量子力学的诠释提供了一种新的视角^【^^5^^】^。

      参考文献：

      【1】TheTrouble with Quantum Mechanics，Steven Weinberg，The NewYork Review of Books，January 19, 2017 Issue。

      http://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/

      【2】张天蓉. 走近量子纠缠系列之三：量子纠缠态[J].物理,2014, 43(09): 627-630.

      http://www.wuli.ac.cn/CN/abstract/abstract61515.shtml

      【3】Einstein,A.; Podolsky, B.; Rosen, N. (1935). "Can Quantum-Mechanical Description ofPhysical Reality Be Considered Complete?". Physical Review. 47 (10):777--780.

      【4】C. M.Caves, C. A. Fuchs and R. Schack, "Quantum Probabilities as BayesianProbabilities," Phys. Rev. A65, 022305 (2002).

      【5】Hans ChristianVon Baeyer，QBism: The Future of Quantum Physics，HarvardUniversity Press，10/3/2016。

Quantum effects lead to more powerful battery charging

  • Quantum effects lead to more powerful battery charging

    researchers showed that quantum entanglement can allow more work to be extracted from a nanoscale energy-storage device, or "quantum battery," than would be possible without entanglement.

    They also found that the process does not necessarily require entanglement, although it does require operations that have the potential to generate entangled states.

    "Our work shows how entangling operations—that is, interactions between two or more bodies—are necessary to obtain a quantum advantage for the charging power of many-body batteries, whereas entanglement itself does not constitute a resource,"

    They show that for locally coupled batteries the quantum advantage grows with the number of interacting batteries. These bounds for the quantum advantage are based on quantum speed limits, which are used, for example, to estimate the maximum speed of quantum processes, such as calculations on a quantum computer.

Four-dimensional physics in two dimensions

  • Four-dimensional physics in two dimensions

    physicists have built a two-dimensional experimental system that allows them to study the physical properties of materials that were theorized to exist only in four-dimensional space.

    the behavior of particles of light can be made to match predictions about the four-dimensional version of the "quantum Hall effect"—a phenomenon that has been at the root of three Nobel Prizes in physics—in a two-dimensional array of "waveguides."

    "When it was theorized that the quantum Hall effect could be observed in four-dimensional space," said Mikael Rechtsman, assistant professor of physics and an author of the paper, "it was considered to be of purely theoretical interest because the real world consists of only three spatial dimensions;

    we have now shown that four-dimensional quantum Hall physics can be emulated using photons—particles of light—flowing through an intricately structured piece of glass—a waveguide array."

    When electric charge is sandwiched between two surfaces, the charge behaves effectively like a two-dimensional material. When that material is cooled down to near absolute-zero temperature and subjected to a strong magnetic field, the amount that it can conduct becomes "quantized"—fixed to a fundamental constant of nature and cannot change.

    "This robustness of electron flow—the quantum Hall effect—is universal and can be observed in many different materials under very different conditions."

    To model this four-dimensional space, the researchers built waveguide arrays. Each waveguide is essentially a tube, which behaves like a wire for light.

    The researchers used a recently-developed technique to encode "synthetic dimensions" into the positions of the waveguides. In other words, the complex patterns of the waveguide positions act as a manifestation of the higher-dimensional coordinates.

    For example, 'quasicrystals'—metallic alloys that are crystalline but have no repeating units and are used to coat some non-stick pans—have been shown to have 'hidden dimensions:' their structures can be understood as projections from higher-dimensional space into the real, three-dimensional world.

Small entropy changes allow quantum measurements to be nearly reversed

  • Small entropy changes allow quantum measurements to be nearly reversed

    Swedish physicist Göran Lindblad developed a theorem that describes the change in entropy that occurs during a quantum measurement. Today, this theorem is a foundational component of quantum information theory

    the quantum relative entropy cannot increase after a measurement.

    quantum relative entropy is interpreted as a measure of how well one can distinguish between two quantum states, so it's this distinguishability that can never increase.

    if the quantum relative entropy decreases by only a little, then the quantum measurement (or any other type of so-called "quantum physical evolution") can be approximately reversed.

    What my work did was to prove this result as a theorem: if the quantum relative entropy goes down only by a little under a quantum physical evolution, then we can approximately reverse its action."

    "If the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small," he said, "then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other.

    So the smaller the relative entropy decrease, the better the reversal process.

    Lindblad's original theorem can also be used to prove the uncertainty principle of quantum mechanics in terms of entropies, as well as the second law of thermodynamics for quantum systems, so the new results have implications in these areas, as well.

    We could go as far as to say that the above entropy inequality constitutes a fundamental law of quantum information theory, which is a direct mathematical consequence of the postulates of quantum mechanics."

    They explain that the uncertainty principle involves quantum measurements, which are a type of quantum physical evolution and therefore subject to Lindblad's theorem.

    "The uncertainty principle is the statement that you cannot generally make the uncertainties of both experiments arbitrarily small, i.e., there is generally a limitation,"

    "It is now known that a statement of the uncertainty principle in terms of entropies can be proved by using the 'decrease of quantum relative entropy inequality.' So what the new theorem allows for doing is relating the uncertainties of the measurement outcomes to how well we could try to reverse the action of one of the measurements.

    "The new theorem allows for quantifying how well we can approximately reverse a thermodynamic transition from one state to another without using any energy at all," he said.

    a thermodynamic transition from one quantum state to another is allowed only if the free energy decreases from the original state to the final state.

    This law can be rewritten as a statement involving relative entropies and can be proved as a consequence of the decrease of quantum relative entropy.

    "We can say that if the free energy does not go down by very much under a thermodynamic transition (i.e., if there is not too much work gained in the process), then it is possible to go back approximately to the original state from the final state, without investing any work at all.

Hardy's Paradox

  • Classical Physics and Quantum Physics Can't Come to Terms on Hardy's Paradox

    This experiment was first known as Hardy’s paradox. Some argue that it’s not a paradox per se, like say the Einstein-Podolsky-Rosen paradox. In many ways, it’s more of a theorem.

    In the Universe, when matter and antimatter meet, particles and antiparticles annihilate one another through a flow of energy in the form of gamma radiation.

    Hardy, however, showed that it’s theoretically possible that sometimes (in 6 to 9 percent of cases) when there’s no observer, matter and antimatter can interact and survive the encounter – classical physics cannot allow this.

Quantum 'Maxwell's demon'

  • Researchers find quantum 'Maxwell's demon' may give up information to extract work

    To get information, even using the weak observation method, the researchers still had to take a peek at the particle, which meant they needed light. So they sent some photons in, and observed the photons that came back.

    "But the demon misses some photons," Murch said. "It only gets about half. The other half are lost." But—and this is the key—even though the researchers didn't see the other half of the photons, those photons still interacted with the system, which means they still had an effect on it. The researchers had no way of knowing what that effect was.

    They took a weak measurement and got some information, but because of quantum backaction, they might end up knowing less than they did before the measurement. On the balance, that's negative information.

    Read more at: https://phys.org/news/2018-07-quantum-maxwell-demon.html#jCp

Researchers blur the line between classical and quantum physics by connecting chaos and entanglement

  • Researchers blur the line between classical and quantum physics by connecting chaos and entanglement

    "It's kind of surprising because chaos is this totally classical concept—there's no idea of chaos in a quantum system," Charles Neill, a researcher in the UCSB Department of Physics and lead author of a paper that appears in Nature Physics. "Similarly, there's no concept of entanglement within classical systems. And yet it turns out that chaos and entanglement are really very strongly and clearly related."

    the means of describing in a quantum sense the chaotic behavior of, say, air molecules in an evacuated room, remains limited.

    the molecules will more likely take off in a variety of velocities and directions, bouncing off walls and interacting with each other, resting after the room is sufficiently saturated with them.

    But in the infinitesimal world of quantum physics, there is still little to describe that behavior. The mathematics of quantum mechanics, Roushan said, do not allow for the chaos described by Newtonian laws of motion.

    By manipulating these qubits with electronic pulses, Neill caused them to interact, rotate and evolve in the quantum analog of a highly sensitive classical system.

    a map of entanglement entropy of a qubit that, over time, comes to strongly resemble that of classical dynamics—the regions of entanglement in the quantum map resemble the regions of chaos on the classical map. The islands of low entanglement in the quantum map are located in the places of low chaos on the classical map.

    "And, it turns out that thermalization is the thing that connects chaos and entanglement. It turns out that they are actually the driving forces behind thermalization.

    in almost any quantum system, including on quantum computers, if you just let it evolve and you start to study what happens as a function of time, it's going to thermalize,"

    ties together the intuition between classical thermalization and chaos and how it occurs in quantum systems that entangle."

Doubling down on Schrödinger's cat

  • Doubling down on Schrödinger's cat

    This cat lives or dies in two boxes at once, which is a marriage of the idea of Schrödinger's cat and another central concept of quantum physics: entanglement.

    "This cat is big and smart. It doesn't stay in one box because the quantum state is shared between the two cavities and cannot be described separately,"

    "One can also take an alternative view, where we have two small and simple Schrodinger's cats, one in each box, that are entangled."

    Yet one of the main problems in developing a reliable quantum computer is how to correct for errors without disturbing the information.

Physicists create quantum state detector

  • Physicists create quantum state detector

    The detector consists of two superconducting aluminum loops coupled by Josephson junctions.

    the critical current in the device to change from zero to maximum and back to zero in a steplike manner with the change of the quantum numbers in each of the loops.

    A Josephson junction is a device made of two superconductors separated by a 1-2 nanometer layer of dielectric material.

    In a variable magnetic field, the physicists observed periodic voltage jumps corresponding to the changes in the quantum states of the superconducting loops of the detector.

    A flux quantum is the minimum amount by which a magnetic flux threading a superconducting contour can change.

    the researchers showed (see the appendix) that the superconducting current through the two Josephson junctions in the new interferometer is equal to the sum of the individual currents through each of the junctions with some phase corrections

    detector response is determined by the quantum numbers. The new device is therefore a perfect quantum state detector.

    The double-contour interferometer with one of the loops replaced with a qubit may be used to direct the detection of qubit quantum states.

    The change in the phase of the wave function on each of the junctions, which is determined by the geometry of the new interferometer and is the same for both junctions, is denoted by ϕa.

    Because the parity of the quantum number sum nu + nd changes when one of the two numbers changes by 1, the second term in the equation changes its sign in a steplike manner.

    It either amounts to Ia + Ib or—when the two terms are opposite—equals zero.

    If the quantum number sum is even, the voltage across the interferometer is zero. In the case of an uneven sum, a known and easily measurable voltage will be detected.

quantum thermodynamics

What is quantum in quantum thermodynamics?

  • What is quantum in quantum thermodynamics?

    thermal engines and refrigerators—quantum and classical systems so far appear to be nearly identical.

    in part of the quantum regime, the three main engine types (two-stroke, four-stroke, and continuous) are thermodynamically equivalent. This means that, despite operating in different ways, all three types of engines exhibit all of the same thermodynamic properties, including generating the same amounts of power and heat, and doing so at the same efficiency.

    in this quantum regime where all engines are thermodynamically equivalent, it's possible to extract a quantum-thermodynamic signature that further confirms the presence of quantum effects.

    any engine that surpasses this bound must be using a quantum effect—namely, quantum coherence—to generate the additional work.

    While the current work deals with single-particle engines, the researchers expect that quantum effects may also emerge in multi-particle engines, where quantum entanglement between particles may play a role similar to that of coherence.

Physicists design zero-friction quantum engine

  • Physicists design zero-friction quantum engine

    physicists have designed an engine that operates with zero friction while still generating power by taking advantage of some quantum shortcuts.

    one intriguing question is whether it may be possible to build a reversible quantum engine—one in which the engine's operation can be reversed without energy dissipation (an "adiabatic" process).

    the engine uses quantum shortcuts to achieve a state that is usually achieved only by slow adiabatic processes. This engine can achieve a state that is fully frictionless; in other words, the engine reaches its maximum efficiency, while still generating some power.

    by using a shortcut to adiabaticity, friction-like effects would get quenched, the cycle performance being the same as that of a quasistatic motor."

    As the scientists note, this pursuit is complicated by the existence of a trade-off between the running time of the super-adiabatic process and the corresponding amount of work dissipated.

Maxwell's demon can use quantum information to generate work

  • Maxwell's demon can use quantum information to generate work

    But as physicist Leó Szilárd pointed out in 1929, entropy does not decrease in such a situation because the demon's measurement process requires information, which is a form of entropy.

    the Szilárd engine (SZE), demonstrates how work can be generated by using information.

    "It is known that classical information can be used to extract work, which is important because this saves the second law of thermodynamics!"

    "The mathematical expression of such work is given as the mutual information between the system and the measurement device multiplied by kT.

    the demon consists of not one but two memories, which the scientists physically demonstrate using a molecule containing two atoms. Each atom has two internal states that are physically equivalent to each atom's two spin states.

    Before measurements are performed, the two atoms are prepared in a maximally entangled quantum state, and are also classically correlated. But as measurements are performed to separate the molecules, the quantum entanglement between the two atoms decreases while the classical correlation does not.

    The physicists also note that the quantum heat engine is not cyclic, so the memory does not return to its initial maximally entangled state. In other words, the quantum information is not free, and work must be done to recover the initial state.

Quantum Gravity

Petr Horava's quantum Gravity ( without strings!)

多世界理論

Grasshopper Theory

  • From Edgy Labs: “Grasshopper Theory Might Map the Multiverse” | sciencesprings

    From Edgy Labs: "Grasshopper Theory Might Map the Multiverse"

    Edgy Labs

    January 10, 2018\ William McKinney

    1\ Genty | Pixabay.com

    New research suggests quantum theory doesn't follow the rules of "reality". Let's see how hypothetical grasshoppers might lead us to the multiverse.

    Who knew that grasshoppers could help us understand quantum theory?

    Apparently, they can. At least, theoretically speaking they can. Recently, two physicists, Olga Goulko and Adrian Kent, have released a paper [Proceedings of The Royal Society A] that wrestles with something called the grasshopper problem.

    The grasshopper problem is a relatively new puzzle for the field of geometry. The problem is simple to state, but very hard to solve. However, solving it may help us understand the Bell inequalities and so mathematicians and physicists worldwide have attempted to posit an answer.

    It works like this:

    Let's say that a grasshopper lands on a random point in a lawn, then jumps at a fixed distance in a random direction. What shape does the lawn have to be so that the grasshopper stays on the lawn after it jumps?

    Seems simple, right? In truth, it's anything but. It sounds like something that Euclid (the Greek father of modern geometry) would have dreamed up. It's not, though; the grasshopper problem is, surprisingly, pretty new.

    Because the problem is rather new, researchers have been looking at it through a modern lens. Instead of merely trying to solve the problem, they are getting deep into the variables. Those variables are pretty important, too, because they may help us resolve Bell's inequalities.

    Let's start with Goulko and Kent's work.

    Today Grasshoppers, Tomorrow the Multiverse

    Conventional theories state that a disc-shaped lawn is optimal to solve the grasshopper problem, but Goulko and Kent know better.

    According to them, the optimal lawn shape changes depending on the distance of the jump. For distances smaller than 1/π1/2 (the radius of a circle of area 1, or approximately 0.56), for example, a cogwheel shape is best. For larger distances, other shapes such as a 'three bladed fan' or a row of stripes is best.

    2

    Oh, and it makes a difference if the surface of the lawn is flat or spherical, but I'll get back to that.

    Sometimes the pieces of the lawn are connected, sometimes they are not. It all depends on variables, which is where Bell's inequalities come in.

    One of the open problems regarding the Bell inequalities is determining what the optimal bounds are. These bounds are violated by quantum theory when quantum correlations get measured on a sphere at any angle between 0 and 90 degrees.

    As it turns out, that problem is pretty much equal to the problem of determining the shape of the lawn when it is spherical rather than flat. Goulko and Kent only analyzed the flat version in their paper, though they don't think it's a stretch to apply their method to the spherical case.

    The interesting part is that, when accounting for additional constraints, it might be possible to finally resolve the problem of optimal bounds for the Bell inequalities.

    Why is that so interesting? Well, if we can understand the optimal bounds for the Bell inequalities, we may be able to map out universes that we can't see. How's that for a final frontier?

    Exploring the Possibilities of the Multiverse

    Adding to that, we have theories about pocket universes, alternate dimensions, and the Upside Down. Okay, that last one was from Stranger Things, but just try and prove to me that the Upside Down isn't there.

    One thing you always run into with multiverse theory, though, is quantum entanglement. See, many would believe that other universes and other dimensions are the same thing, but they aren't. They are entirely different realities, but they could be linked through the quantum fabric of reality-at-large.

    For now, though, we can only speculate. Studying one universe is like an ant studying a deity. Studying the multiverse is going to be a much harder nut to crack. That said, we currently don't have any better leads on it than quantum theory.

    And the latest leap in quantum theory is coming from a hypothetical grasshopper. Don't you just love quantum physics?

    See the full article here .

    Please help promote STEM in your local schools.

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> A grasshopper lands at a random point on a lawn of area 1, then jumps once, a fixed distance, in a random direction. What shape should the lawn be in order to maximize the chance that the grasshopper stays on the lawn after jumping?
> 
> the optimal lawn shape takes on a variety of complex shapes for different jumping distances, such as a cogwheel shape for distances smaller than 1/π1/2 (the radius of a circle of area 1, or approximately 0.56), while for larger distances, the optimal lawn consists of disconnected pieces.
> 
> the grasshopper problem is connected to the Bell inequalities, which famously show that, unlike classical physics models, quantum theory does not obey local realism.
> 
> One example that the researchers point out is nuclear chain reactions.
> 
> By modeling this situation with the grasshopper problem, the optimal lawn area corresponds to the maximum initial reaction rate, which maximizes the number of nuclei that participate in the chain reaction.
> 
> Another potential application of the grasshopper problem lies in modeling quantum communication protocols, which the researchers explain can be thought of as a grasshopper model in which one party must choose which algorithm (lawn shape) to use to communicate with a second party.

  • How to cut your lawn for grasshoppers

    To find the best lawn, Goulko and Kent had to convert the grasshopper problem from a mathematical problem to a physics one, by mapping it to a system of atoms on a grid. They used a technique called simulated annealing, which is inspired by a process of heating and slowly cooling metal to make it less brittle. "The process of annealing essentially forces the metal into a low-energy state, and that's what makes it less brittle," said Kent. "The analogue in a theoretical model is you start in a random high-energy state and let the atoms move around until they settle into a low-energy state. We designed a model so that the lower its energy, the greater the chance the grasshopper stays on the lawn.

    When measuring the spin - the intrinsic angular momentum - of two particles on two random axes for particular states, quantum theory predicts you will get opposite answers more often than any classical model allows,

    "To understand precisely what classical models do allow, and see how much stronger quantum theory is, you need to solve another version of the grasshopper problem, for lawns on a sphere,"

nano insulator

光學

Training of photonic neural networks through in situ backpropagation

> ![Researchers move closer to completely optical artificial neural network](https://3c1703fe8d.site.internapcdn.net/newman/csz/news/800/2018/27-researchersm.jpg)
>

重力

Surfaces away from horizons are not thermodynamic

  • Surfaces away from horizons are not thermodynamic | Nature Communications

  • Study finds flaw in emergent gravity

    In the new paper, the scientists tested whether different kinds of surfaces obey an analogue of the first law of thermodynamics, which is a special form of energy conservation. Their results reveal that, while surfaces near black holes (called stretched horizons) do obey the first law, ordinary surfaces—including holographic screens—generally do not. The only exception is that ordinary surfaces that are spherically symmetric do obey the first law.

凝態/晶格/質數/超齊構體

Uncovering Multiscale Order in the Prime Numbers via Scattering

  • [1802.10498] Uncovering Multiscale Order in the Prime Numbers via Scattering

  • Surprising hidden order unites prime numbers and crystal-like materials

    Compared to typical crystals, quasicrystals yield a distinct and more complex arrangement of Bragg peaks. The peaks in a typical crystal form at regular intervals with empty gaps between them. In quasicrystals, between any two selected Bragg peaks is another Bragg peak.

    Surprising hidden order unites prime numbers and crystal-like materials "esearchers at Princeton have discovered a similarity between the patterns of atoms in certain crystal-like materials and prime numbers. Here, red dots denote non-prime numbers and black dots denote prime numbers, which are treated as "atoms.". Credit: Image courtesy of the researchers"

    esearchers at Princeton have discovered a similarity between the patterns of atoms in certain crystal-like materials and prime numbers. Here, red dots denote non-prime numbers and black dots denote prime numbers, which are treated as "atoms.". Credit: Image courtesy of the researchers

    The pattern that Torquato and his colleagues discovered in the primes is similar to that of quasicrystals and another system called limit-periodic order, but it differs enough that the researchers call it "effectively limit-periodic" order. The prime numbers appear in "self-similar" groupings, meaning that between peaks of certain heights, there are groupings of smaller peaks, and so on.

鸟类眼睛中隐藏着不为人知的自然秩序 “超齐构体”（hyperuniformity）

  • 鸟类眼睛中隐藏着不为人知的自然秩序_《环球科学》（“科学美国人”中文版）【唯一官方网站】

    科学家们从鸟类的眼睛、盒装的玻璃弹珠和其他匪夷所思的地方发现了一种神秘的排列模式。

    七年前，当圣路易斯华盛顿大学的乔・科尔博（Joe Corbo）教授透过显微镜观察鸡的眼睛装片时，一些非常奇妙的东西映入了他的视野：分布在鸡视网膜上的、用来感知色彩的视锥细胞竟以斑点状的形态呈现出5种不同大小和颜色。更令科尔博教授感到吃惊的是，鸡的视锥细胞排布呈现出一种他从未见过的模式：已知人类的视锥细胞是随机分布的，许多鱼类的视锥细胞则是整齐地一列列排布的，而鸡类的视锥细胞居然是一种同时兼具偶然性和高度均匀性的分布模式（见下图）。这些视锥细胞的斑点并没有什么特定的分散规律，但是不同的斑点之间的距离总是不远不近。无论是单独考察5种不同视锥细胞的任意一种，还是同时考察所有的视锥细胞，它们都呈现出一种迷人的随机与秩序的统一。科尔博被这种现象深深地迷住了。

    图片1.png

    【图注】鸟类视网膜经400倍显微镜放大后的照片

    "仅仅是看着这些图案，就能感受到它们的美丽，"科尔博说道，"被这种美丽深深吸引的同时，就算是单纯出于好奇心，我们也想更深入去了解它。"科尔博和他的合作者希望能弄清楚这种视锥细胞呈现的图案的形成过程，以及它的功能。不过，此时的他并不知道这些类似问题在此之前是否已经被许多人在不同的情境下问过，还是他通过这些生物学现象首次发现了一条在数学和物理学领域也时常出现的隐藏规律。

    科尔博觉得，这个问题的答案应该从鸟类视网膜本身的功能去寻找。鸟类的视觉一直非常出色，比如鹰就可以从一千米以外的高空锁定一只小小的老鼠。科尔博的实验室研究的课题，就是鸟类如何从进化性适应中得到如此出色的视力。鸟类的许多特性都被认为是从一种生活在3亿年前的生物那里继承来的，这种生物类似蜥蜴，是所有恐龙和哺乳动物原型的共同祖先。当鸟类的祖先------也就是恐龙------称霸整个地球的时候，我们哺乳动物的祖先只能在黑夜中出门行动------这使它们渐渐丧失了对色彩的分辨能力。哺乳动物视锥细胞在那时仅剩下了两种，达到了进化史上的最低谷。幸运的是，3000万年前，我们灵长类的一支祖先的视锥细胞分裂成了两种------感受红色光的红敏视锥细胞和感受绿色的绿敏视锥细胞；这两种视锥细胞，再加上我们本来就有的蓝色感受视锥细胞，让我们有了三色视觉。但是人类的视锥细胞，尤其是较年轻的红敏和绿敏视锥细胞，分布得杂乱无章，而且感光能力也不均匀。

    与哺乳动物不同，鸟类的眼睛有足够长的时间在演化中优化，它们视锥细胞的数量更多，分布也更为均匀。科尔博教授和他的同行感到困惑的是，为什么鸟类的视锥细胞没有演化出更为完美的秩序规则------比如网格或晶格状排列呢？似乎看起来最有可能的解释是，这种在鸟类视网膜中发现的奇怪的、无法分类的分布是在某种未知约束条件下的最优态。这些约束条件是什么？这种视锥细胞的分布是什么？鸟类的视觉系统是如何变成这样子的？这些问题都还没有答案。生物学家们已经竭尽全力去寻找视网膜上细胞的分布规律，但这属于他们不熟悉的领域，他们需要帮助。

    2012年，科尔博教授联系了普林斯顿大学的理论化学教授萨尔瓦托雷-托尔夸托（Salvatore Torquato），他是研究堆积（packing）问题的著名学者。所谓堆积问题，就是研究如何在有限维度中最密集地堆积物体的问题，而在这里，就是研究在鸟类视网膜的二维空间中如何排下最多的五种不同的视锥细胞。"我想知道，我观察到的这种分布系统是不是最优化的堆叠方式。"科尔博说道。托尔夸托对这个问题产生了浓厚的兴趣，他对这些视网膜图案的数码照片运行了一些算法，结果让他完全惊呆了。科尔博教授说："他发现，他在这些视网膜图案中观察到的现象，同样发生于许多无机化学和物理的系统之中。"

    托尔夸托从21世纪初就开始研究这种他称之为"超齐构体"（hyperuniformity）的全新分布模式（同一时期，罗格斯大学的Joel Lebowitz也发现了这种模式，并给它起了另一个名字叫 "superhomogeneity"）。从那之后，这种现象在不同系统中层出不穷：不仅仅是鸟类的眼睛，准晶体、随机数阵、宇宙的大尺度结构、量子系综，甚至乳浊液和胶质等软物质系统中都发现了"超齐构体"的身影。

    当某些事情发生在一些从未想过的新领域时，科学家们往往为这种意外所着迷------这种惊喜和期待的感觉就像在和宇宙玩"打地鼠"一样。科学家们喜欢寻找这种现象背后所隐藏的普遍真理。而在对"超齐构体"现象研究的这一过程中，他们发现了这种"超齐构体"材料有许多实用的新特性。

    从数学的角度来看，它也很有研究价值。"我越深入地研究它，就越能发现它的原理是多么优雅，它的概念是多么令人叹服。"当亨利-科恩（Henry Cohn）提起"超齐构体"时，他是这么形容的，"而且不单是它的理论，更让我惊讶的是它广泛的应用前景。"

    隐藏的规律

    托尔夸托和他的一位同事研究"超齐构体"现象已有13年，为了从理论上阐释这一现象，他们举了一个简单却出人意料的例子："想象你有许多玻璃弹珠，你把它们都放进一个瓶子里，使劲摇晃直到所有可移空间都被填满，珠子不再移动，"托尔夸托今年春天在他普林斯顿的办公室里说道，"类似这样的系统，就是'超齐构体'。"

    上述情况中玻璃珠子的排布模式在学术上有着专业的名称------最大随机堵塞堆积（maximally random jammed packing），这种排布仅填满所有区域的64%，剩下的区域留空。这种排布并不是已知球体最密集的堆积方式，已知的球体最密集堆积方式是晶格堆积（想象集装箱里堆橘子的方式），这种排布能填满总体积的74%。但是晶格排布并不是在所有情况下都能达到的，你不可能轻松地将一盒玻璃弹珠"摇"成无比规则的晶体状分布，更不用说还要使五种不同大小的物体形成规则的晶格，托尔夸托解释道，而这，正是鸡类视锥细胞所遇到的困境。

    让我们用放在水平桌面上的硬币来代替视锥细胞。"如果你想在桌面上平铺若干枚1美分硬币，让它们占的总面积最小，你肯定会选择把它们排成最小单位为三角形的一种排布方式。"托尔夸托这么说道，"但如果又加入了若干枚五美分硬币呢？新加入的不同种硬币将会阻碍整个体系形成规则的晶格。而鸟的视网膜中有5种不同的成分------想象桌面上又新添了10美分、25美分，还有其他别的硬币------这必将使得体系的晶格化变得越来越困难。"同理，鸟类的几种视锥细胞大小也各不相同，几何学原理迫使它们无序化，但是在演化过程中无比激烈的竞争又希望视网膜能够尽可能均匀地感光，即希望同种颜色感受细胞相距尽可能远的距离。权衡利弊，"系统最后呈现出来的就是这样一种无序超齐构体。"托尔夸托这样解释。

    图片2.png

    超齐构体让鸟类在视觉方面同时最大限度地拥有了两个优势因素：既有多达5种的视锥细胞，又让每种视锥细胞近乎均匀地镶嵌在视网膜上，这带给了鸟类惊人的色彩分辨能力，只不过这种隐藏的规律我们还无法用自己的眼睛感知到。

    判断一个系统是否属于超齐构体所用的算法其实和游乐园里的套圈游戏非常类似。首先，想象一个完全均匀的点阵，然后再想象自己不断地向那个点阵抛掷塑料圈，每当塑料圈落地的时候，清点圈内套到的点数。你会发现，尽管每次套到的点数有些许波动，但总是相差不远。这是因为圈内部覆盖的点阵的单元数量是固定的，唯一可能造成差异的只有塑料圈边界覆盖的点数。所以不难想象，如果让塑料圈变大，造成差异的周长也就越长，你套到的点数（晶格的密度）的浮动范围也随之等比例扩大。在更高的维度，晶格的密度波动范围和（维度数-1）成比例。

    现在再想象一个随机分布的点阵------在有的地方点阵可能密集成堆，而有的地方却可能只是一片空白。同样向这个点阵抛掷塑料圈，这次你会发现，当你增加塑料圈的大小时，你套到的点数的浮动范围是与塑料圈的面积（而不是周长）成比例的。这个结果告诉我们，在数据规模较大的时候，随机分布的密度浮动范围比有序分布的密度浮动范围要极端得多。

    当我们把这个套圈游戏的理论应用在超齐构体分布上之后，一些有趣的现象发生了。从局部来看，超齐构体点数的分布是混乱的；所以对较小的塑料圈来说，超齐构体的密度波动类似于随机分布的密度波动，大于晶格分布；可是当塑料圈增大后，我们发现超齐构体的密度波动竟开始和塑料圈的周长（而不是面积）成正比了。这个现象告诉我们，当取样规模较大时，超齐构体分布和晶格分布同样均匀。普林斯顿大学的物理学家保罗-施泰因哈特（Paul Steinhardt）称，研究者已从超齐构体系统中发现了进一步的"结构生态规律"：在超齐构体系统中，密度的波动与圆圈周长的n次幂成比例，这个n在1到2之间逐渐变化，比例系数也有所不同。

    图片3.png

    "这到底意味着什么？"托尔夸托教授问道，"可惜的是，现在我们并不知道答案，相关研究仍在进展当中，许多论文还有待发表。"

    群"材"荟萃

    超齐构体无疑是许多不同系统都共有的一种状态，但到底如何去解释这种统一性还有待继续研究。"我认为，超齐构体从根本上来说，一定是某种深层次优化过程的标志性特征，"科恩这么说道，"只是对于不同问题而言，这种优化的外在过程可能相差很大。"

    超齐构体系统主要分为两类。第一类是在系统达到平衡状态（equilibrium）时呈现出的超齐构体分布，准晶体------一类内部原子不遵守重复规律排布，却能完全镶嵌满空间的神奇固体------就是其中之一。在第一类超齐构体系统（平衡系统）之中，同一系统中微粒间的相互斥力使不同成分间保持距离，从而维系超齐构体状态。类似的数学原理同样可以解释鸟类眼中的超齐构体分布，甚至还能解释任意矩阵的本征值分布，以及黎曼ζ函数（就是那个可以推出素数有无限多个的函数）的零点分布等数学问题。

    人们对另一类超齐构体系统的理解还远不及第一类。第二类超齐构体属于非平衡系统，组成系统的微粒之间相互碰撞，但彼此之间不存在相互斥力，必须要有外力施加于这些系统才能使系统维持超齐构体的状态。玻璃弹珠、乳浊液、胶质及冷原子系综都属于上述类型。而在非平衡超齐构体这一大类中，其实还存在着更深入、更棘手的分类。去年秋天，由法国里昂高等师范学校的德尼-巴尔托洛（Denis Bartolo）为首的物理学家们在《物理评论快报》（Physical Review Letters）上发表了他们的研究成果，他们发现乳浊液的超齐构体是可以被特定振幅的晃动所诱发的，这一振幅标志了材料从可逆到不可逆性的临界转变：当体系以低于临界振幅的幅度晃动时，分散在乳浊液体系中的微粒在每次晃动停止之后还可以回到它们之前的相对位置；而当体系以高于临界振幅的幅度晃动时，微粒的运动就是不可逆的了。巴尔托洛的工作暗示，非平衡系统中可逆性开关和超齐构体现象可能存在本质上的联系。然而，与此同时，解释最大随机堵塞排布（摇晃玻璃弹珠的排列方式）的原理，却又是一套完全不同的理论。"我们能将这两种差异巨大的物理现象联系起来吗？"巴尔托洛问自己，"不行啊！根本不行！我们完全不明白超齐构体现象是如何同时出现在这两种如此不同的物理系统当中的。"

    当科学家们苦思冥想、试图把所有线索都串在一起的时候，超齐构体材料的一些惊人特性也随之浮出了水面：它们其实具备着一些晶体所特有的性质，而且还不那么易受结构差异的影响------在这点上，它们的性质更接近玻璃，或是其他一些没有相干性的非晶体。在Optica杂志新发表的一篇论文中，以雷米-卡尔米纳蒂（ Rémi Carminati）为首的法国科学家们报道致密的超齐构体材料可以被制作成透明材料，而同样密度的无序布局材料却达不到这一点，这是因为隐藏在微粒相对位置间的神秘规律干扰、抵消了散射光。"这些干扰因素破坏了光的散射，"卡尔米纳蒂解释道，"由于材料是匀质的，光线就直接透了过去。"这种致密、透明的非晶体的材料到底有什么用？回答这个问题可能还为时尚早，"但是它们肯定有应用前景------尤其在光子学这一方面。"

    而巴尔托洛近期关于乳浊液超齐构体体系的研究成果已经应用到了实践当中，成为混合水泥、美容面霜、玻璃，甚至食物的简易秘方。"无论何时，如果你想将小分子颗粒混入一团浆糊之中，你永远得面对恼人的搅拌问题，"他说道，"而研究超齐构体时找出的规律可能就能给我们带来一种均匀分散固体小分子的新方法。你只要先找到该材料的特征振幅，然后用该振幅震荡若干次，就能得到一个均匀混合的超齐构体分散体系了。"他还开玩笑说："我不该免费告诉你这个方法的，我应该以此来大发一笔。"

    事实上，托尔夸托、施泰因哈特和他们的合作者已经这么做了。他们组建了一家名为Etaphase的创业公司，生产超齐构体光子回路------一种以光而不是电子为介质来传输信息的设备。几年前，普林斯顿的科学家发现超齐构体材料存在"带隙"，可以在传播过程中屏蔽特定的频率。带隙使得数据的控制传输成为可能，因为被屏蔽的频率可以用波导管来容纳并引导。带隙曾经一度被认为是晶体材料所特有的性质，传输方向取决于晶体材料的对称轴，这意味着光子波导只能沿着特定的方向传播，制约了该材料作为电路的应用前景。不过，由于超齐构体材料没有传输方向的限制，带隙在这里可能更为实用，帮助我们造出能满足任何需求的强力波导。

    图片4.png

    【图注】萨尔瓦托雷-托尔夸托，普林斯顿大学化学家，从21世纪初就开始研究超齐构体现象。

    至于鸟类眼睛中，被科学家们称为"多视锥超齐构体"（Multihyperuniform）的五色分布模式，至少迄今为止，是大自然独一无二的存在。科尔博教授仍然不能明确指出这种图案是如何形成的。它是像第一类平衡系统那样，是由于不同视锥细胞的分子互斥而出现的，还是像一盒被摇出来的玻璃弹珠？科尔博认为事情的真相可能更偏向前者，细胞可以在不影响其它异种细胞的情况下分泌一种排斥同种细胞的小分子，很有可能在胚胎发育阶段，每种视锥细胞的分化信号在促使特定细胞分化的同时，也会抑制周围细胞发生一样的变化。"但这只是一个有待完善的简单模型，"他说，"每个细胞的局部活动都会事关整体。"

    除了鸡之外（鸡是实验室最容易获得的禽类动物），科尔博在其他三种鸟类身上也发现了同样的"多视锥超齐构体"现象。这种现象表明，"超齐构体"方向的适应性进化是普遍存在的，并不仅仅只是某种特定环境下的产物。不过，科尔博还想知道对于夜行动物而言，演化会不会以另一种不同于超齐构体的方式去优化视力。"如果这是真的，那就太有意思了。"他这么说，"不过对我们来说，拿到猫头鹰的眼睛难度还比较大。"

    撰文 Natalie Wolchover

    翻译 叶宣伽

    原文链接：https://www.quantamagazine.org/20160712-hyperuniformity-found-in-birds-math-and-physics/

超導

Pseudogap theory puts physicists closer to high temperature superconductors

  • Pseudogap theory puts physicists closer to high temperature superconductors

    The theory explains the transition phase to superconductivity, or "pseudogap" phase, which is one of the last obstacles to developing the next generation of superconductors and one of the major unsolved problems of theoretical condensed matter physics.

    To understand why room-temperature superconductivity has remained so elusive, physicists have turned their sights to the phase that occurs just before superconductivity takes over: the mysterious "pseudogap" phase.

    "Understanding the pseudogap is as important as understanding superconductivity itself," said Melko.

    This new study found that YBa2Cu3O6+x oscillates between two quantum states during the pseudogap, one of which involves charge-density wave fluctuations. These periodic fluctuations in the distribution of the electrical charges are what destabilize the superconducting state above the critical temperature.

Physicists explain the unusual behavior of strongly disordered superconductors

  • Physicists explain the unusual behavior of strongly disordered superconductors

    A distinction is made between superconductors with a "conventional" gap and special superconductors, which, even in their normal state, demonstrate something similar to a gap – it is called a "pseudogap."

    In BCS theory, a key role is played by Cooper pairs – two electrons bound together with opposite spins.

    they do not interact with the crystal lattice and therefore move freely within a substance and do not lose energy in collisions.

    The formation of Cooper pairs alters not only the electrical properties of a substance as a whole, but also electron energy distribution—the energy spectrum.

    If the substance is a superconductor, and after cooling to critical temperature superconductivity was reached at the same time as the formation of the Cooper pairs, it is called a gap.

    if this occurs in the electron spectrum diagram after cooling, but superconductivity has not yet been reached, the term "pseudogap" is used (meaning it is not a "true" gap, and its formation is not linked to the onset of superconductivity). If this substance is cooled further, it will become a superconductor and the gap in its spectrum will increase – its value will include both the pseudogap and the superconducting gap itself.

    According to this theory, superconducting current density is directly proportional to the magnitude of the superconducting gap: ρs ~ Δ, the more Cooper pairs formed per unit volume, the larger the gap in the energy spectrum, i.e. the size of the gap.

    Physicists explain the unusual behavior of strongly disordered superconductors

    The difference between conventional superconductors and pseudogapped superconductors. In normal superconductors, when the temperature rises above critical level superconductivity disappears due to the breakdown of the Cooper pairs, but in ...more

    Studying the structure of pseudogapped superconductors at microscopic level showed that these materials are strongly disordered.

    Disorder plays a key role because the transition to a superconducting state does not happen at the same time as the formation of Cooper pairs.

    It should be emphasized that Cooper pairs in a pseudogapped superconductor cannot be described as motionless.

    they do not freeze motionless in one place, but "spread out" over a rather large (dozens of interatomic distances), but finite region.

    The researchers note that using indium oxide, a typical pseudogapped superconductor, it is already possible to create a superconducting quantum device that can be used as a prototype component for a quantum computer.

    the scientists deduced the theoretical dependence of the density of Cooper pairs ρs in the substance on pseudogap width.

    it is inversely proportional to the inductance of the film (the materials described are obtained in film form) in the superconducting state. Films such as this, with high inductance and zero resistance, are needed to produce qubits, the fundamental units of quantum computing devices.

    In conventional superconductors, the dependence of the density of Cooper pairs on pseudogap width is linear (ρs ~ Δ). However, in the test substances the dependence is squared (ρs ~ Δ2).

Physicists find clues to the origins of high-temperature superconductivity

  • Physicists find clues to the origins of high-temperature superconductivity

    researchers have discovered the existence of a positive feedback loop that gratly enhances the superconductivity of cuprates

    the positive feedback mechanism arises from the fact that the electrons in the non-superconducting cuprate state are correlated differently than in most other systems,

    cuprates in their non-superconducting state have strongly incoherent "strange-metal" correlations, which are at least partly removed or weakened when the cuprates become superconducting.

    some research has suggested that cuprate superconductors have such unusual electronic properties that even attempting to describe them with the notion of particles of any kind becomes useless.

    what role, if any, do the strange-metal correlations play in high-temperature cuprate superconductivity?

    these correlations don't simply disappear in the cuprate superconducting state, but instead get converted into coherent correlations that lead to an enhancement of the superconductive electron pairing. This process results in a positive feedback loop, in which the conversion of the incoherent strange-metal correlations into a coherent state increases the number of superconductive electron pairs, which in turn leads to more conversion, and so on.

    due to this positive feedback mechanism, the strength of the coherent electron correlations in the superconducting state is unprecedented, greatly exceeding what is possible for conventional superconductors. Such a strong electron interaction also opens up the possibility that cuprate superconductivity might occur due to a completely unconventional pairing mechanism—a purely electronic pairing mechanism that could arise solely due to quantum fluctuations.

    the incoherent electron correlations in the strange metal 'normal state' are converted to coherent correlations in the superconducting state that help strengthen the superconductivity, with an ensuing positive feedback loop,"

    "Such a strong positive feedback loop should strengthen most conventional pairing mechanisms but could also allow for a truly unconventional (purely electronic) pairing mechanism."

    whether this positive feedback mechanism can be integrated into other materials, perhaps leading to new kinds of high-temperature superconductors.

Physics in Deep learning

  • The Extraordinary Link Between Deep Neural Networks and the Nature of the Universe - MIT Technology Review

    Now Lin and Tegmark say they've worked out why. The answer is that the universe is governed by a tiny subset of all possible functions. In other words, when the laws of physics are written down mathematically, they can all be described by functions that have a remarkable set of simple properties.

    So deep neural networks don't have to approximate any possible mathematical function, only a tiny subset of them.

    To put this in perspective, consider the order of a polynomial function, which is the size of its highest exponent. So a quadratic equation like y=x^2^ has order 2, the equation y=x^24^ has order 24, and so on.

    Obviously, the number of orders is infinite and yet only a tiny subset of polynomials appear in the laws of physics. "For reasons that are still not fully understood, our universe can be accurately described by polynomial Hamiltonians of low order," say Lin and Tegmark. Typically, the polynomials that describe laws of physics have orders ranging from 2 to 4.

[1410.3831] An exact mapping between the Variational Renormalization Group and Deep Learning

Machine Learning in Physics

Resources

Papers | 〈 physics | machine learning 〉

AI in Quantum

Researchers use artificial neural network to simulate a quantum many-body system

  • Researchers use artificial neural network to simulate a quantum many-body system

    how they coaxed a neural network to simulate some aspects of a quantum many-body system.

    One of the difficult challenges facing physicists today is coming up with a way to simulate quantum many-body systems, i.e., showing all the states that exist in a given system, such as a chunk of matter.

    instead of attempting to calculate every possible state, they used a neural network to generalize the entire system.

    The pair began by noting that the system used to defeat a Go world champion last year might be modified in a way that could simulate a many-body system.

    They then followed up by getting the neural network to figure out the ground state of a system. To see how well their system worked, they ran comparisons with problems that have already been solved and report that their system was better than those that rely on a brute-force approach.

Neural networks take on quantum entanglement

  • Neural networks take on quantum entanglement

    certain neural networks—abstract webs that pass information from node to node like neurons in the brain—can succinctly describe wide swathes of quantum systems .

    In particular, the team studied neural networks that use two distinct groups of neurons. The first group, called the visible neurons, represents real quantum particles, like atoms in an optical lattice or ions in a chain. To account for interactions between particles, the researchers employed a second group of neurons—the hidden neurons—which link up with visible neurons.

    Specifying a number for each connection and mathematically forgetting the hidden neurons can produce a compact representation of many interesting quantum states, including states with topological characteristics and some with surprising amounts of entanglement.

    For instance, neural networks with only short-range interactions—those in which each hidden neuron is only connected to a small cluster of visible neurons—have a strict limit on their total entanglement.

    the collection of states that they do represent efficiently, and the overlap of that collection with other representation methods, is an open problem that Deng says is ripe for further exploration.

Solving the quantum many-body problem with artificial neural networks

AI in 天文

Studying the stars with machine learning | symmetry magazine

Exploring galaxy evolution with generative models

  • Exploring galaxy evolution with generative models | Astronomy & Astrophysics (A&A)

    Abstract

    Context. Generative models open up the possibility to interrogate scientific data in a more data-driven way.

    Aims. We propose a method that uses generative models to explore hypotheses in astrophysics and other areas. We use a neural network to show how we can independently manipulate physical attributes by encoding objects in latent space.

    Methods. By learning a latent space representation of the data, we can use this network to forward model and explore hypotheses in a data-driven way. We train a neural network to generate artificial data to test hypotheses for the underlying physical processes.

    Results. We demonstrate this process using a well-studied process in astrophysics, the quenching of star formation in galaxies as they move from low-to high-density environments. This approach can help explore astrophysical and other phenomena in a way that is different from current methods based on simulations and observations.

Fast automated analysis of strong gravitational lenses with convolutional neural networks | Nature

AI in 材料

硼酸鋇鈉，一種因機器學習而誕生的LED熒光粉

Ai in Nonlinear/Chaos

Phys. Rev. Lett. 120, 024102 (2018) - Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

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