30 research outputs found
From the microscopic to the van Hove regime in the XY chain out of equilibrium
Using the framework of rigorous algebraic quantum statistical mechanics, we
construct the unique nonequilibrium steady state in the isotropic XY chain in
which a sample of arbitrary finite size is coupled by a bond coupling
perturbation of arbitrary strength to two infinitely extended thermal
reservoirs, and we prove that this state is thermodynamically nontrivial.
Moreover, extracting the leading second order contribution to its microscopic
entropy production and deriving its entropy production in the van Hove weak
coupling regime, we prove that, in the mathematically and physically important
XY chain, the van Hove regime reproduces the leading order contribution to the
microscopic regime.Comment: 44 pages, 2 figure
A remark on the subleading order in the asymptotics of the nonequilibrium emptiness formation probability
We study the asymptotic behavior of the emptiness formation probability for
large spin strings in a translation invariant quasifree nonequilibrium steady
state of the isotropic XY chain. Besides the overall exponential decay, we
prove that, out of equilibrium, the exponent of the subleading power law
contribution to the asymptotics is nonvanishing and strictly positive due to
the singularities in the density of the steady state.Comment: 20 pages, 2 figure
Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
We study the time dependent Hartree equation in the continuum, the
semidiscrete, and the fully discrete setting. We prove existence-uniqueness,
regularity, and approximation properties for the respective schemes, and set
the stage for a controlled numerical computation of delicate nonlinear and
nonlocal features of the Hartree dynamics in various physical applications.Comment: 25 pages, 1 figur
Heat flux in general quasifree fermionic right mover/left mover systems
With the help of time-dependent scattering theory on the observable algebra
of infinitely extended quasifree fermionic chains, we introduce a general class
of so-called right mover/left mover states which are inspired by the
nonequilibrium steady states for the prototypical nonequilibrium configuration
of a finite sample coupled to two thermal reservoirs at different temperatures.
Under the assumption of spatial translation invariance, we relate the 2-point
operator of such a right mover/left mover state to the asymptotic velocity of
the system and prove that the system is thermodynamically nontrivial in the
sense that its entropy production rate is strictly positive. Our study of these
not necessarily gauge-invariant systems covers and substantially generalizes
well-known quasifree fermionic chains and opens the way for a more systematic
analysis of the heat flux in such systems.Comment: 81 pages, 2 figure
Broken translation invariance in quasifree fermionic correlations out of equilibrium
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.Comment: 30 pages, 4 figure
On the instabilities of the static, spherically symmetric SU(2) Einstein-Yang-Mills-Dilaton solitons and black holes
We prove that the number of odd parity instabilities of the n-th SU(2)
Einstein-Yang-Mills-Dilaton soliton and black hole equals n.Comment: Added reference
Out of equilibrium correlations in the XY chain
We study the transversal XY spin-spin correlations in the non-equilibrium
steady state constructed in \cite{AP03} and prove their spatial exponential
decay close to equilibrium
Topics in nonequilibrium quantum statistical mechanics
These notes are an expanded and revised version of the lectures given by the second and fourth autor in the summer school "Open Quantum System" held in Grenoble, June 16-July 4, 2003. They provide an introduction to recent developments in non-equilibrium statistical mechanics of open quantum systems, including a completely worked out (simple) example. We discuss non-equilibrium steady states (NESS) and their structural properties, entropy production, linear response theory and weak coupling limit. The emphasis is on Ruelle's scattering approach to the construction of NESS