在強磁下超冷電子的奇特對稱（E8）
Exotic symmetry seen in ultracold electrons
By Pete Wilton, January 18, 2010
Spectrum of magnetic resonances observed by neutron scattering in cobalt niobate in zero magnetic field, data (left) and calculation (right).
(PhysOrg.com) -- An exotic type of symmetry - suggested by string theory and theories of high-energy particle physics, and also conjectured for electrons in solids under certain conditions - has been observed experimentally for the first time.
有種奇特的對稱類型 -- 由弦論與高能粒子物理學所提出，且據推測在某些狀態下的固體，其電子也會出現 -- 首度試驗性地被觀察到。
An international team, led by scientists from Oxford University, report in a recent article in Science how they spotted the symmetry, termed E8, in the patterns formed by the magnetic spins in crystals of the material cobalt niobate, cooled to near absolute zero and subject to a powerful applied magnetic field.
一個由牛津大學科學家所領導的國際性團隊，在 Science 最近一期的文章中報告，在冷卻至接近絕對零度、受強大磁場支配的鈮酸鈷（cobalt niobate）結晶體中，他們如何從它的磁自旋（magnetic spins）所形成的圖案裡發現這種被稱為 E8 的對稱。
The material contains cobalt atoms arranged in long chains and each atom acts like a tiny bar magnet that can point either ‘up’ or ‘down’.
這種材料包含以長鏈方式排列的鈷原子，而且每個原子作用如同微小的條狀磁鐵，那不是往「上」就是往「下」指。
When a magnetic field is applied at right angles to the aligned spin directions, the spins can ‘quantum tunnel’ between the ‘up’ and ‘down’ orientations. At a precise value of the applied field these fluctuations ‘melt’ the ferromagnetic order of the material resulting in a ‘quantum critical’ state.
當磁場以直角方式施加至排成直線的自旋方向上，這些自旋能在「上」與「下」的方向間進行量子穿隧（quantum tunnel）。所施加的磁場在一精確值下使這種材料的鐵磁序（ferromagnetic order）因這些波動而「消失（melt）」導致一種「量子臨界」態。
‘You might expect to see random fluctuations of the spins at this critical point but what we uncovered was a remarkable structure in the resonances of the magnetic spins indicating a perfectly harmonious state,’ said Radu Coldea from Oxford University’s Department of Physics who led the team.
"你也許預期在此臨界點上會看見這些自旋的隨機波動，但我們卻在磁自旋的共振中發現一種非凡的結構，那呈現出完美的調和態（harmonious state），" 來自牛津大學物理系的 Radu Coldea 表示，他領導此團隊。
As the critical state was approached the researchers observed that the chain of atoms behaved like a ‘magnetic guitar string’.當達到此臨界態時，研究者觀察到這條原子鏈表現如同「磁性吉他弦」。
Radu added: ‘The tension comes from the interaction between spins causing them to magnetically resonate. We found a series of resonant modes. Close to the critical field the two lowest resonant frequencies approached closely the golden ratio 1.618..., a characteristic signature of the predicted E8 symmetry.’
Radu 補充說："張力來自於自旋之間的交互作用，導致它們帶磁性地共振（magnetically resonate）。我們發現一系列共振模式。在臨界場附近，二個最低的共振頻率接近黃金比率 1.618... 這是預言中 E8 對稱特有的特徵。
"He is convinced that this is no coincidence and it reflects a subtle form of order present in the quantum system.
他確信這並非巧合，而且它反應出量子系統中所呈現出來的一種微妙有序形態。
A visual representation of E8 symmetry. The two smallest concentric rings of solid red dots have their radius in the golden ratio as seen experimentally for the two lowest resonance frequencies of the magnetic spins. Credit: Wikimedia/Claudio Rocchini.
The resonant states seen experimentally in cobalt niobate may be our first glimpse of complex symmetries that can occur in the quantum world. “The results suggest that similar ‘hidden’ symmetries may also govern the physics of other materials near quantum critical points where electrons organize themselves according to quantum rules for strong interactions,’ Radu told us.
這些在鈮酸鈷中被試驗性地看見的共振態，也許是我們第一次看見那些發生在量子世界中的複雜對稱。"這些結果指出，類似的「隱藏」對稱或許也統治了其他近量子臨界點材料的物理學，在那裡電子根據量子法則的「強交互作用（strong interactions）」組織它們自己，" Radu 表示。
The research was supported by EPSRC and Radu aims to use a new EPSRC grant to explore the physics of materials near quantum criticality.
這項研究由 EPSRC 支持，Radu 試圖利用新的 EPSRC 獎助金探索近量子臨界性材料的物理學。
The team included Dr Radu Coldea, Dr Elisa Wheeler and Dr D Prabhakaran from Oxford University’s Department of Physics, as well as researchers from Helmholtz Zentrum Berlin, ISIS Rutherford Laboratory, and Bristol University.
團隊成員包括牛津物理系的 Dr Radu Coldea、Dr Elisa Wheeler 與 Dr D Prabhakaran 以及來自 Helmholtz Zentrum Berlin、ISIS Rutherford Laboratory 與 Bristol 大學的研究者。
More information: http://www.sciencemag.org/cgi/content/abstract/327/5962/177
Provided by Oxford University (news : web)
※ 這與下面黃金比率那篇是同一份論文。
相關報導：
＊ Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry
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
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