Tracing out a Galilean-invariant Caldeira-Leggett bath breaks Galilean boost covariance in the reduced dynamics, localized in the dissipative anticommutator term and incompatible with the fluctuation-dissipation theorem for non-trivial baths.
Zanardi, Phys
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Galilean boost invariance does not survive the trace: symmetry breaking in open quantum systems
Tracing out a Galilean-invariant Caldeira-Leggett bath breaks Galilean boost covariance in the reduced dynamics, localized in the dissipative anticommutator term and incompatible with the fluctuation-dissipation theorem for non-trivial baths.