从等效拉格朗日量到不等价的开放量子系统动力学
From equivalent Lagrangians to inequivalent open quantum system dynamics
AI总结：
研究发现，开放量子系统中相差全导数的拉格朗日量可能导致不等价的动力学，通过QED推导出第二阶的Bremsstrahlung主方程，解释了退相干现象并解决文献中的不一致问题。
摘要：
拉格朗日量可以通过全导数的不同而改变，而不会改变运动方程，因此编码相同的物理。这在经典力学和量子力学中都是成立的。然而，我们证明在开放量子系统的情况下，两个相差全导数的拉格朗日量可能导致不等价的缩减动力学。虽然这些拉格朗日量在系统加环境的全局描述层面通过幺正变换相连，但在追踪环境后等价性会破裂。我们主张只有那些系统机械动量和规范动量相等的拉格朗日量才能导致操作上有意义的动力学。将这一见解应用于量子电动力学（QED），我们推导出由于非相对论性加速电子相互作用的第二阶的Bremsstrahlung主方程。所得到的缩减动力学预测位置基的退相干，并且与Caldeira-Leggett形式非常接近，从而解决了文献中的先前不一致之处。我们的发现对QED和引力退相干都有影响，其中出现类似的模糊性。
英文摘要：
Lagrangians can differ by a total derivative without altering the equations of motion, thus encoding the same physics. This is true both classically and quantum mechanically. We show, however, that in the context of open quantum systems, two Lagrangians that differ by a total derivative can lead to inequivalent reduced dynamics. While these Lagrangians are connected via unitary transformations at the level of the global system-plus-environment description, the equivalence breaks down after tracing out the environment. We argue that only those Lagrangians for which the canonical and mechanical momenta of the system coincide lead to operationally meaningful dynamics. Applying this insight to quantum electrodynamics (QED), we derive the master equation for bremsstrahlung due to an accelerated non-relativistic electron upto second order in the interaction. The resulting reduced dynamics predicts decoherence in the position basis and closely matches the Caldeira-Leggett form, thus resolving previous discrepancies in the literature. Our findings have implications for both QED and gravitational decoherence, where similar ambiguities arise.
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