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arXiv 2201.08287gr-qcquant-ph
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(2+1)维均匀加速布朗振子:耗散和频移随温度的变化

Uniformly accelerated Brownian oscillator in (2+1)D: temperature-dependent dissipation and frequency shift

Dimitris Moustos

摘要:

我们考虑在(2+1)维闵可夫斯基时空中将Unruh-DeWitt探测器模型化为一个谐振子,它与一个无质量的量子标量场耦合.我们把探测器作为一个开放量子系统,并采用量子朗之万方程来描述其时间演化,与场,这是由一个频率无关的谱密度,作为一个随机力的特点。我们研究了一个点状探测器通过闵可夫斯基真空和一个惯性浸没在热储在Unruh温度的恒定加速度移动,探讨了这两种情况下,他们的动力学之间的众所周知的非等价性的影响。我们发现,加速探测器的耗散率和耦合到场浴引起的频率偏移依赖于加速温度。有趣的是,这不仅与热浴中的惯性运动的情况相反,而且与开放系统中的任何类似的量子布朗运动模型相反,在开放系统中,耗散和频移不具有温度依赖性。尽管如此,我们表明,波动耗散定理仍然成立的检测器场系统和在弱耦合限制的加速检测器被驱动在晚些时候的热平衡状态在Unruh温度。

英文摘要:

We consider an Unruh-DeWitt detector modeled as a harmonic oscillator that is coupled to a massless quantum scalar field in the (2+1)-dimensional Minkowski spacetime. We treat the detector as an open quantum system and employ a quantum Langevin equation to describe its time evolution, with the field, which is characterized by a frequency-independent spectral density, acting as a stochastic force. We investigate a point-like detector moving with constant acceleration through the Minkowski vacuum and an inertial one immersed in a thermal reservoir at the Unruh temperature, exploring the implications of the well-known non-equivalence between the two cases on their dynamics. We find that both the accelerated detector's dissipation rate and the shift of its frequency caused by the coupling to the field bath depend on the acceleration temperature. Interestingly enough this is not only in contrast to the case of inertial motion in a heat bath but also to any analogous quantum Brownian motion model in open systems, where dissipation and frequency shifts are not known to exhibit temperature dependencies. Nonetheless, we show that the fluctuating-dissipation theorem still holds for the detector-field system and in the weak-coupling limit an accelerated detector is driven at late times to a thermal equilibrium state at the Unruh temperature.

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