Particle and energy transport in strongly driven one-dimensional quantum systems

Abstract

This Dissertation concerns the transport properties of a strongly–correlated one–dimensional system of spinless fermions, driven by an external electric field which induces the flow of charges and energy through the system. Since the system does not exchange information with the environment, the evolution can be accurately followed to arbitrarily long times by solving numerically the time–dependent Schrödinger equation, going beyond Kubo’s linear response theory. The thermoelectric response of the system is here characterized, using the ratio of the induced energy and particle currents, in the nonequilibrium state under the steady applied electric field. Even though the equilibrium response can be reached for vanishingly small driving, strong fields produce quantum–mechanical Bloch oscillations in the currents, which disrupt the proportionality of the currents. The effects of the driving on the local state of the ring are analyzed via the reduced density matrix of small subsystems. The local entropy density can be defined and shown to be consistent with the laws of thermodynamics for quasistationary evolution. Even integrable systems are shown to thermalize under driving, with heat being produced via the Joule effect by the flow of currents. The spectrum of the reduced density matrix is shown to be distributed according the Gaussian unitary ensemble predicted by random–matrix theory, both during driving and a subsequent relaxation. The first fully–quantum model of a thermoelectric couple is realized by connecting two correlated quantum wires. The field is shown to produce heating and cooling at the junctions according to the Peltier effect, by mapping the changes in the local entropy density. In the quasiequilibrium regime, a local temperature can be defined, at the same time verifying that the subsystems are in a Gibbs thermal state. The gradient of temperatures, established by the external field, is shown to counterbalance the flow of energy in the system, terminating the operation of the thermocouple. Strong applied fields lead to new nonequilibrium phenomena. At the junctions, observable Bloch oscillations of the density of charge and energy develop at the junctions. Moreover, in a thermocouple built out of Mott insulators, a sufficiently strong field leads to a dynamical transition reversing the sign of the charge carriers and the Peltier effect.