Journal
PHYSICAL REVIEW B
Volume 92, Issue 13, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.92.134307
Keywords
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Funding
- START [Y 581-N16]
- European Research Council through Synergy Grant UQUAM
- German Research Foundation [ZUK 64]
- Austrian Science Fund (FWF) [Y 581] Funding Source: researchfish
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Extended quantum systems can be theoretically described in terms of the Schwinger-Keldysh functional integral formalism, whose action conveniently describes both dynamical and static properties. We show here that in thermal equilibrium, defined by the validity of fluctuation-dissipation relations, the action of a quantum system is invariant under a certain symmetry transformation, and thus it is distinguished from generic systems. In turn, the fluctuation-dissipation relations can be derived as the Ward-Takahashi identities associated with this symmetry. Accordingly, the latter provides an efficient test for the onset of thermodynamic equilibrium and it makes checking the validity of fluctuation-dissipation relations unnecessary. In the classical limit, this symmetry reduces to the well-known one that characterizes equilibrium in the stochastic dynamics of classical systems coupled to thermal baths, described by Langevin equations.
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