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

Aschbacher, Walter H.

doi:10.1142/s1793744210000193

Cited by 1 publication

(6 citation statements)

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“…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].…”

Section: Remark 24supporting

confidence: 65%

“…Remark 27 Note that Theorem 26 holds for any coupling strength. In the small coupling limit, we recover the exact decay rate from Aschbacher [9], and the bound derived for general quasifree systems in Aschbacher [7].…”

Section: Remark 24mentioning

confidence: 74%

“…There, 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 ground states and the equilibrium states at positive temperature treated in Abanov and Franchini [1,18] and Shiroishi et al [23] but also for the translation invariant NESS in the isotropic XY chain analyzed in Aschbacher [9].…”

Section: Introductionmentioning

confidence: 71%

“…In the limit κ → 0, we recover the symbol derived in Aschbacher [7,9] for the translation invariant case.…”

Section: Remark 24mentioning

confidence: 89%

“…It follows from (9) in Definition 3 that, w.r.t. this decomposition, the decoupled Hamiltonian h 0 does not couple the different subsystems to each other, indeed, i.e.…”

Section: Definition 8 (Initial State)mentioning

confidence: 99%

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Broken translation invariance in quasifree fermionic correlations out of equilibrium

Aschbacher¹

2011

Journal of Functional Analysis

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Using the C * algebraic scattering approach to study quasifree fermionic systems out of equilibrium in quantum statistical mechanics, we construct the nonequilibrium steady state in the isotropic XY chain whose translation invariance has been broken by a local magnetization and analyze the asymptotic behavior of the expectation value for a class of spatial correlation observables in this state. The effect of the breaking of translation invariance is twofold. Mathematically, the finite rank perturbation not only regularizes the scalar symbol of the invertible Toeplitz operator generating the leading order exponential decay but also gives rise to an additional trace class Hankel operator in the correlation determinant. Physically, in its decay rate, the nonequilibrium steady state exhibits a left mover-right mover structure affected by the scattering at the impurity.

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Section: Remark 24supporting

confidence: 65%

Section: Remark 24mentioning

confidence: 74%

Section: Introductionmentioning

confidence: 71%

“…In the limit κ → 0, we recover the symbol derived in Aschbacher [7,9] for the translation invariant case.…”

Section: Remark 24mentioning

confidence: 89%

“…It follows from (9) in Definition 3 that, w.r.t. this decomposition, the decoupled Hamiltonian h 0 does not couple the different subsystems to each other, indeed, i.e.…”

Section: Definition 8 (Initial State)mentioning

confidence: 99%

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