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Vojkan Jaksic

Publications and source records attributed to Vojkan Jaksic.

23 records · Page 2Linked to original sources
arXiv2013

A note on reflectionless Jacobi matrices

The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the usual ones. We also show that the new characterization is equivalent to the notion of being dynamically reflectionless, thus providing a short proof of an important result of [Breuer-Ryckman-Simon]. The motivation for the new characterization comes from recent studies of the non-equilibrium statistical mechanics of the electronic black box model and we elaborate on this connection. To appear in Commun. Math. Phys.

math-ph↗
arXiv2013

Entropic fluctuations of quantum dynamical semigroups

We study a class of finite dimensional quantum dynamical semigroups exp(tL) whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroup arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator L. We show that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo's and Onsager's linear response relations.

math-ph↗
arXiv2012

Large deviations from a stationary measure for a class of dissipative PDE's with random kicks

We study a class of dissipative PDE's perturbed by a bounded random kick force. It is assumed that the random force is non-degenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviation principle for occupation measures of the Markov process in question. The proof is based on Kifer's large deviation criterion, a Lyapunov-Schmidt type reduction, and an abstract result on large-time asymptotic for generalised Markov semigroups.

math.AP↗
arXiv2012

Landauer-Büttiker formula and Schrödinger conjecture

We study the entropy flux in the stationary state of a finite one-dimensional sample S connected at its left and right ends to two infinitely extended reservoirs at distinct temperatures T1, T2 and chemical potentials mu1, mu2. The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator -Δ+ v. The Landauer-Büttiker formula expresses the steady state entropy flux in the coupled system in terms of scattering data. We study the behavior of this steady state entropy flux in the limit L->infinity and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrödinger operator h. A natural conjecture is that the set of energies at which transport persists in this limit is precisely the essential support of the absolutely continuous spectrum of h. We show that this conjecture is equivalent to the Schrödinger conjecture in spectral theory of one-dimensional Schrödinger operators, thus giving a physically appealing interpretation to the Schrödinger conjecture.

math-ph↗