Non-zero Entropy Density in the XY Chain Out of Equilibrium

Abstract

The von Neumann entropy density of a block of n spins is proved to be non-zero for large n in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right which act as thermal reservoirs at different temperatures. Moreover, the non-equilibrium density is shown to be strictly greater than the density in thermal equilibrium. Mathematics Subject Classifications (2000). 46L60, 47B35, 82C10, 82C23.

A Remark on the Subleading Order in the Asymptotics of the Nonequilibrium Emptiness Formation Probability

“…It turned out that suitable basic spectral information on the density of the state is sufficient to derive a bound on the rate of the exponential decay of the EFP in general translation invariant fermionic quasifree states. This bound proved to be exact not only for the decay rates of the EFP in the ground states and the equilibrium states at positive temperature treated in Abanov and Franchini [1,13] and Shiroishi et al [16], but it will also do so for the nonequilibrium situation treated here exhibiting the socalled left mover-right mover structure already found in Aschbacher [7] and Aschbacher and Barbaroux [8] for nonequilibrium expectations of different correlation observables. 6 Hence, given this exponential decay in leading order which parallels qualitatively the behavior in thermal equilibrium at positive temperature, one may wonder whether there is some characteristic signature of the nonequilibrium left at some lower order of the EFP asymptotics.…”

“…10 The concept of a selfdual CAR algebra has been introduced and developed by Araki [2,3]. Here, it is just a convenient way of working with the linear combination (7). 11 I write L 0 (H) for the finite rank operators on the Hilbert space H. Moreover, δ x ∈ h for x ∈ Z denotes the Kronecker function.…”

“…10 The concept of a selfdual CAR algebra has been introduced and developed by Araki [2,3]. Here, it is just a convenient way of working with the linear combination (7).…”

“…This may be interpreted as the manifestation, in subleading order, of the long-range nature of the underlying formal effective Hamiltonian of the NESS. 7 This connection is not made precise here, though, but it is left to be studied in greater detail elsewhere. Section 2 contains the setting and Section 3 the main assertion.…”

Broken translation invariance in quasifree fermionic correlations out of equilibrium

“…It is composed of a left mover carrying temperature β R and coming from +∞, a left mover carrying temperature β R having been reflected at the perturbation at the origin, and a right mover carrying temperature β L having been transmitted through the origin. This left mover -right mover structure has already been observed in translation invariant systems for several types of correlation functions, see Aschbacher [8,9] and Aschbacher and Barbaroux [10].…”