Galilean boost invariance does not survive the trace: symmetry breaking in open quantum systems

• URL: http://arxiv.org/abs/2604.27459v1
• Date: Thu, 30 Apr 2026 06:00:44 GMT
• Title: Galilean boost invariance does not survive the trace: symmetry breaking in open quantum systems
• Abstract summary: A Galilean-in Caldeira-Leggett environment breaks Galilean boost covariance of reduced dynamics.<n>An operator-level analysis of the exact Hu-Paz-Zhang master equation localizes the violation entirely in the dissipative anticommutator term.<n>The fluctuation-dissipation theorem ties this coefficient to the absorptive bath response that drives equilibrium momentum diffusion.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Tracing out a Galilean-invariant Caldeira-Leggett environment breaks Galilean boost covariance of the reduced dynamics, while spatial translations and rotations survive intact. An operator-level analysis of the exact Hu-Paz-Zhang master equation localizes the violation entirely in the dissipative anticommutator term, scaling with the damping coefficient $Γ(t)f(t)$. The fluctuation-dissipation theorem ties this coefficient to the absorptive bath response that drives equilibrium momentum diffusion, so for any non-trivial bath spectral density bilinear-coupled Galilean invariance, the fluctuation-dissipation theorem, and reduced boost covariance cannot hold simultaneously. The stochastic decomposition of the influence functional extends the mechanism beyond the quadratic regime. The dimensionless ratio $\hbarγ/k_\mathrm{B} T$ delineates the crossover: cold atoms in dissipative optical lattices and ultracold molecules sit at its edge. Parametric driving offers a one-directional escape: the squeezing rate that protects nonequilibrium entanglement above the standard quantum limit also suppresses boost-breaking over a driving cycle.

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