The arrow of time in open quantum systems and dynamical breaking of the resonance-anti-resonance symmetry
The arrow of time in open quantum systems and dynamical breaking of the resonance-anti-resonance symmetry
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DOI：
10.1088/1751-8121/aa85ae
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发表时间：
2017-10-06
影响因子：
2.1
通讯作者：
Hatano, Naomichi
中科院分区：
文献类型：
--
作者：
Ordonez, Gonzalo;Hatano, Naomichi
开放量子系统通常由具有与共振相关联的复本征值的非厄米有效哈密顿算子表示。在以前的工作中，我们表明，紧束缚开放系统的演化可以表示为一个明确的时间反演对称扩展，涉及所有的离散本征态的有效哈密顿量。这些本征态包括共振态和反共振态的复共轭对。一个初始的时间反演对称态包含来自共振态和反共振态的相等贡献。在这里，我们表明，随着状态随时间的演变，共振和反共振状态之间的对称性自动打破，共振状态成为占主导地位的t > 0和反共振状态成为占主导地位的t < 0。此外，我们表明，有一个时间尺度为这一突破，我们与“芝诺时间”。我们还比较了时间反演对称膨胀与以前使用的几个研究人员的非对称膨胀。我们展示了目前的时间反演对称膨胀如何绕过共振和反共振态的非希尔伯特性质，该性质先前将指数发散引入到非对称膨胀中。
Open quantum systems are often represented by non-Hermitian effective Hamiltonians that have complex eigenvalues associated with resonances. In previous work we showed that the evolution of tight-binding open systems can be represented by an explicitly time-reversal symmetric expansion involving all the discrete eigenstates of the effective Hamiltonian. These eigenstates include complex-conjugate pairs of resonant and anti-resonant states. An initially time-reversal-symmetric state contains equal contributions from the resonant and anti-resonant states. Here we show that as the state evolves in time, the symmetry between the resonant and anti-resonant states is automatically broken, with resonant states becoming dominant for t > 0 and anti-resonant states becoming dominant for t < 0. Further, we show that there is a time-scale for this symmetry-breaking, which we associate with the 'Zeno time'. We also compare the time-reversal symmetric expansion with an asymmetric expansion used previously by several researchers. We show how the present time-reversal symmetric expansion bypasses the non-Hilbert nature of the resonant and anti-resonant states, which previously introduced exponential divergences into the asymmetric expansion.