科學家在量子世界中發現「黃金比率」
Golden ratio discovered in a quantum world
January 7, 2010
The magnetic field is used to tune the chains of spins to a quantum critical state. The resonant modes (“notes”) are detected by scattering neutrons. These scatter with the characteristic frequencies of the spin chains. Credit: Tennant/HZB
Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB, Germany), in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture.
來自 Helmholtz-Zentrum Berlin fur Materialien und Energie（HZB，德國）的研究者，與來自牛津、Bristol 大學還有英國 Rutherford Appleton實驗室的同僚合作，率先看見隱藏在固態物質中的奈米級對稱性。他們在測量這種對稱性的特徵之後，證明該屬性與因藝術與建築而聞名的黃金比率（golden ratio，黃金比例）一樣。
The research team is publishing these findings in Science on the 8 January.
研究團隊將這些發現發表在 1/8 的 Science 期刊中。
On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge which are the result of an effect known as the Heisenberg's Uncertainty Principle. In order to study these nanoscale quantum effects the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.
粒子在原子尺度下的表現與我們在巨原子（macro-atomic）世界中所知並不相同。新特性因某種效應而浮現，稱為 Heisenberg（海森堡）的測不準原理（Uncertainty Principle，不確定性原理）。為了研究這些奈米級的量子效應，研究者聚焦在磁性材料鈮酸鈷（cobalt niobate）上。那由磁性原子串接而成，形成鏈狀，如同一條非常薄的條狀磁鐵，但只有一個原子寬，且在奈米級固態材料中是一種描述鐵磁性（ferromagnetism）的實用模型。
When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains "The system reaches a quantum uncertain - or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."
若在正確角度上排成直線的自旋施加一磁場，這條磁鏈將變成新狀態，稱為量子臨界態（quantum critical），可以想成量子版本的碎形圖案。Alan Tennant 教授，這個柏林小組的領導者，解釋："該系統達到一種量子不確定性 -- 即「Schrodinger（薛丁格）貓」狀態。那正是我們在我們實驗中以鈮酸鈷達成的事。我們精確調整該系統，使其轉變成量子臨界態。"
By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: "Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture." Radu Coldea is convinced that this is no coincidence. "It reflects a beautiful property of the quantum system - a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material", he explains.
在調整系統並人為引入更多量子不確定性之後，研究者觀察到這條原子鏈表現如同奈米級的吉他弦。牛津大學的 Radu Coldea 博士（該論文的首席作者，而且打從十年前這個國際計畫開始就推動它到現在）表示："在這裡，張力來自自旋間的交互作用，導致它們帶磁性地共振。在這些交互作用中，我們發現一系列的共振音符（音階）：頭二個音符彼此顯現一種完美的關係。它們的頻率（音高）呈現出 1.618... 的比率，那是因藝術與建築而聞名的黃金比率。" Radu Coldea 確信這不是巧合。"那反映出量子體系的美妙特性 -- 一種隱藏的對稱性。那真的是很特別的一個，被數學家稱為 E8，而且這是它在某種材料中的首度觀察，" 他解釋。
The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology. Prof. Tennant remarks on the perfect harmony found in quantum uncertainty instead of disorder. "Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order. Similar surprises may await researchers in other materials in the quantum critical state."
「在鈮酸鈷中所觀察到的共振態」是一種戲劇性的實驗室實例，在這當中，為粒子物理學所開發的數學理論也許能在奈米科學中還有最終地未來技術裡找到應用。Tennant 教授表示在量子不確定性中發現了完美的協調性（harmony）而非失序（disorder）。"這發現正導致物理學家思索，量子、原子尺度的世界也許自有其內含的秩序。類似的驚奇也許在其他處於量子臨界態的材料中等待研究者。"
The researchers achieved these results by using a special probe - neutron scattering. It allows physicists to see the actual atomic scale vibrations of a system. Dr. Elisa Wheeler, who has worked at both Oxford University and Berlin on the project, explains "using neutron scattering gives us unrivalled insight into how different the quantum world can be from the every day". However, "the conflicting difficulties of a highly complex neutron experiment integrated with low temperature equipment and precision high field apparatus make this a very challenging undertaking indeed." In order to achieve success "in such challenging experiments under extreme conditions" the HZB in Berlin has brought together world leaders in this field. By combining the special expertise in Berlin whilst taking advantage of the pulsed neutrons at ISIS, near Oxford, permitted a perfect combination of measurements to be made.
這些研究者利用一種特殊探針實現這些結果 -- 中子散射（neutron scattering）。那讓物理學家觀察某系統真正的原子級振動。Elisa Wheeler 博士，她在牛津大學與柏林都參與此計畫，解釋 "利用中子散射賦予我們無敵的洞察力：量子世界與日常生活能有多麼不同。" 然而，"極複雜的中子實驗與低溫設備以及精密的高場（high field）裝置整合的衝突性難題，真的使它成為一項非常具有挑戰性的工作。" 為了在 "極端狀態中" 成功達成 "這麼有挑戰性的實驗" 柏林的 HZB 使該領域的世界級領導者聚首。藉由結合位於柏林的特殊專門知識，同時獲得牛津附近 ISIS 的脈衝中子源優勢，使得該測量方法得以達到完美的結合。
More information: Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Article in Science, DOI:RE1180085/JEC/PHYSICS
Provided by Helmholtz Association of German Research Centres (news : web)
※ 相關報導：
＊ Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry
http://www.sciencemag.org/cgi/content/abstract/327/5962/177
R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska,
D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl,
K. Kiefer
Science 8 January 2010: Vol. 327. no. 5962, pp. 177 - 180
DOI: 10.1126/science.1180085
Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi–one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.
留言列表