Shigeru Ajisaka

Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

(Dated: April 6, 2012)We propose a model of nonequilibrium quantum transport of particles and energy in a system con-nected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs are in turn thermalizedto prescribed temperatures and chemical potentials by a simple dissipative mechanism described bythe Lindblad equation. As an example, we study transport in monoatomic and diatomic chains ofnon-interacting spinless fermions. We show numerically the breakdown of the Onsager reciprocityrelation due to the dissipative terms of the model.

Nonequilibrium Peierls Transition

Nonequlibrium phase transition of an open Takayama-Lin Liu-Maki chain coupled with two reservoirs is investigated by combining a mean-field approximation and a formula characterizing nonequlibrium steady states, which is obtained from the algebraic field approach to nonequlibrium statistical mechanics. When the bias voltage is chosen to be a control parameter, the phase transition between ordered and normal phases is found to be first or second order. Then, the voltage-current characteristics is S-shaped in some parameter region. In contrast, when the current is chosen to be a control parameter, all the non-trivial solutions of the self-consistent equation are found to become stable. In this case, the phase transition between the ordered and normal phases is always second order and negative differential conductivity appears at low temperature.

Nonequilibrium mesoscopic Fermi-reservoir distribution and particle current through a coherent quantum system

We study particle current and occupation distribution in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (mesoreservoir) is driven out of equilibrium by the action of superreservoirs with prescribed temperatures and chemical potentials described by a simple dissipative mechanism with the Lindblad equation. We compare exact (numerical) results for the non-equilibrium steady state particle current with theoretical expectations based on the Landauer formula and show that the model reproduce the behavior of coherent quantum systems in the expected parameter region. We also obtain the occupation distribution on the mesoreservoir in the non-equilibrium steady state and compare them with the occupation distribution on the leads in usual description of coherent quantum transport.

Current in coherent quantum systems connected to mesoscopic Fermi reservoirs

We study particle current in a recently proposed model for coherent quantum transport. In this model, a system connected to mesoscopic Fermi reservoirs (meso-reservoir) is driven out of equilibrium by the action of super-reservoirs thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. We compare exact (numerical) results with theoretical expectations based on the Landauer formula.

Particle and energy transport in quantum disordered and quasi-periodic chains connected to mesoscopic Fermi reservoirs

We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.

Polaron formation as a genuine nonequilibrium phenomenon

Solitons and polarons at nonequilibrium steady states are investigated for the spinless Takayama Lin-Liu Maki model. Polarons are found to be possible {\it only out of equilibrium}. This polaron formation is a genuine nonequilibrium phenomenon, as there is a lower threshold current below which they cannot exist. It is considered to be an example of microscopic dissipative structure.

Analytical study for reconnection of stable/unstabl manifolds of the Harper map

The Harper map is one of the simplest chaotic systems exhibiting reconnection of invariant manifolds. The method of asymptotics beyond all orders (ABAO) is used to construct unstable/stable manifolds of the Harper map. When the parameter changes to the reconnection threshold, the unstable/stable manifolds are analytically shown to acquire new oscillatory portion corresponding to the heteroclinic tangle after the reconnection.

Reconnection of Unstable/Stable Manifolds of the Harper Map — Asymptotics-Beyond-All-Orders Approach —

The Harper map is one of the simplest chaotic systems exhibiting reconnection of invariant manifolds. The method of asymptotics beyond all orders (ABAO) is used to construct unstable/stable manifolds of the Harper map. By enlarging the neighborhood of a singularity, the perturbative solution of the unstable manifold is expressed as a Borel summable asymptotic expansion in a sector including t = -∞ and is analytically continued to the other sectors, where the solution acquires new terms describing heteroclinic tangles. It is shown that when the parameter is changed, upon reaching the reconnection threshold, the unstable/stable manifolds acquire new oscillatory parts corresponding to the heteroclinic tangle after the reconnection.