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Physical review. B, Condensed matter

Coupled spin-boson systems far from equilibrium

M. I. Salkola, A. R. Bishop, V. M. Kenkre, S. Raghavan

Published Nov 1, 1996• 10 citations
Publisher

Abstract

Nonequilibrium quantum dynamics of a system comprising a (pseudo) spin-\textonehalf{} object coupled to a boson degree of freedom is studied. It is shown that the time evolution of the system is described by a set of elementary scattering processes. Through these processes the system approaches an equilibrium in which the spin is in a mixed state that on average maximizes its entropy. However, the irregular behavior of the system is unrelated to "quantum chaos" as the Hamiltonian is integrable.

DOI
10.1103/physrevb.54.r12645

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Nonequilibrium quantum dynamics of a system comprising a (pseudo) spin-\textonehalf{} object coupled to a boson degree of freedom is studied. It is shown that the time evolution of the system is described by a set of elementary scattering processes. Through these processes the system approaches an equilibrium in which the spin is in a mixed state that on average maximizes its entropy. However, the irregular behavior of the system is unrelated to "quantum chaos" as the Hamiltonian is integrable.
We study the nonequilibrium dynamics of two-component bosonic atoms in a one-dimensional optical lattice in the presence of spin-orbit coupling. In the Mott-insulating regime, the two-component bosonic system at unity filling can be described by the quantum spin XXZXXZXXZ model. The atoms are initially prepared in their lower spin states. The system becomes out of equilibrium by suddenly introducing spin-orbit coupling to the atoms. The system shows the relaxation and nonstationary dynamics, respectively, in the different interaction regimes. We find that the time average of magnetization is useful to characterize the many-body dynamics. The effects of even and odd numbers of sites are discussed. Our result sheds light on nonequilibrium dynamics due to the interplay between spin-orbit coupling and atomic interactions.
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The primary goals of this dissertaion are to describe and elucidate a new formalism to study the out of equilibrium dynamics of integrable models, and to apply this formalism to some specific problems. In particular, I describe the “quench dynamics” of a gas of interacting bosons in one dimension, and provide details of some preliminary work on the isotropic Heisenberg chain. The formalism, based on earlier work by Yudson, provides a way of getting around some of the difficulties involved in calculating the time evolution of arbitrary initial states evolved with integrable Hamiltonians. In addition to this, I aim to discuss some of the general aspects of quench dynamics in quantum systems. The description of the nonequilibrium dynamics of a given system depends significantly on initial states, and the time scales at which the system is probed compared with the various inherent time scales in the system. I present the experimental context and motivation for these studies, and survey the existing techniques and efforts at understanding the relaxation of systems that are far from their equilibrium states or ground states.
A stringent analysis of nonequilibrium dynamics and thermalization in a complex interacting spin system, which transits from integrability to chaos, is performed. The applicability of both standard thermodynamical ensembles—canonical and microcanonical—and the generalized Gibbs ensemble is tested. The role of constants of motion is studied, and a critical analysis of the usual definition of quantum integrability is performed. Different possible thermalization mechanisms are also analyzed. We find significant discrepancies between the time averages of some observables and the prediction from the thermodynamical ensembles within the ergodic region, so we conclude that quantum chaos does not guarantee thermalization. We also find that quantum integrable dynamics keeps more memory concerning the initial state, which is in part stored in a set of constants of motion that can be explicitly obtained.