Abstract
We prove that a recently derived correlation equality between conserved charges and their associated conserved currents for quantum systems far from equilibrium [O.A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X 6, 041065 (2016)], is valid under more general conditions than assumed so far. Similar correlation identities, which in generalized Gibbs ensembles give rise to a current symmetry somewhat reminiscent of the Onsager relations, turn out to hold also in the absence of translation invariance, for lattice models, and in any space dimension, and to imply a symmetry of the non-equilibrium linear response functions.
Highlights
Of particular interest in the general context of transport far from thermal equilibrium are the correlations between the conserved charges Qα and their associated currents Jiα in space direction i
Charge-current correlations in one-dimensional quantum integrable systems have been shown to play an important role in work on the Drude weight [2, 3] and for generalized hydrodynamics [4, 5]
〈 QαJβ 〉c = 〈 JαQβ 〉c for the connected correlation functions has been derived in [4] under quite general circumstances, viz., assuming only translation invariance of the stationary density matrix and the quantum Hamiltonian, a generic assumption on the decay of correlations, and, more significantly, commutativity of the stationary density matrix with the charges Qα. This result was subsequently generalized to a stronger local version 〈 qα(x, t) jβ (0, 0) 〉c = 〈 jα(x, t)qβ (0, 0) 〉c [6] which does not require the assumption of commutativity of the charges and which is valid for any decay of correlations with distance
Summary
Of particular interest in the general context of transport far from thermal equilibrium are the correlations between the conserved charges Qα and their associated currents Jiα in space direction i. For the connected correlation functions has been derived in [4] under quite general circumstances, viz., assuming only translation invariance of the stationary density matrix and the quantum Hamiltonian, a generic assumption on the decay of correlations, and, more significantly, commutativity of the stationary density matrix with the charges Qα. This result was subsequently generalized to a stronger local version 〈 qα(x, t) jβ (0, 0) 〉c = 〈 jα(x, t)qβ (0, 0) 〉c [6] which does not require the assumption of commutativity of the charges and which is valid for any decay of correlations with distance. The main aim of the present work is to derive related global and local charge-current correlation equalities and to clarify the necessary and sufficient conditions under which such correlation equalities, including (1) and its local version, are valid
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