Quantum and classical behavior in interacting bosonic systems
Quantum and classical behavior in interacting bosonic systems
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相互作用的玻色子系统中的量子和经典行为
DOI：
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发表时间：
2016
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通讯作者：
M. Hertzberg
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作者：
M. Hertzberg
据了解，在自由玻色子理论中，当系统的占有数非常大时，经典场论可以准确地描述完整的量子理论。然而，在相互作用理论中，人们对这种情况了解较少，特别是在比动态弛豫时间更长的时间尺度上。最近有人声称量子理论在这个时间尺度上与经典理论有很大的偏差，即使占用数非常大。此外，据称量子理论会快速热化，而经典理论却不会。这些主张的证据来自于注意到量子算子期望值的时间演化与经典微观状态演化相比的巨大差异。如果属实，这将对许多重要现象产生巨大的影响，包括相互作用的 BEC、暗物质轴子、膨胀后预热等的实验室研究。在这项工作中，我们批判性地检验了这些说法。我们证明，事实上，即使相互作用很大，经典理论也可以描述高占用率下的量子行为。联系在于，单个量子微观状态中量子算子的期望值由许多经典微观状态上相应的经典系综平均值来近似。此外，根据遍历定理，具有统计平移不变性的局部场的经典系综平均值是单个微观状态的空间平均值。因此，即使在相互作用的系统中，单个微观状态的量子场论和经典场论的相关函数在高占有率下也大致一致。此外，当引入适当的粗粒化时，量子场论和经典场论都可以热化，经典情况需要截止低占用紫外模式。我们讨论我们的结果的应用。
It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.