TY - JOUR

T1 - Necessary condition for the thermalization of a quantum system coupled to a quantum bath

AU - Lychkovskiy, Oleg

PY - 2010/7/16

Y1 - 2010/7/16

N2 - A system put in contact with a large heat bath normally thermalizes. This means that the state of the system ρS (t) approaches an equilibrium state ρ eq S, the latter depending only on macroscopic characteristics of the bath (e.g., temperature) but not on the initial state of the system. The above statement is the cornerstone of the equilibrium statistical mechanics; its validity and its domain of applicability are central questions in the studies of the foundations of statistical mechanics. In the present paper we concentrate on one aspect of thermalization, namely, on the system initial state independence (ISI) of ρ eq S. A necessary condition for the system ISI is derived in the quantum framework. We use the derived condition to prove the absence of the system ISI in a specific class of models. Namely, we consider a single spin coupled to a large bath, the interaction term commuting with the bath self-Hamiltonian (but not with the system self-Hamiltonian). Although the model under consideration is nontrivial enough to exhibit the decoherence and the approach to equilibrium, the derived necessary condition is not fulfilled and thus ρ eq S depends on the initial state of the spin.

AB - A system put in contact with a large heat bath normally thermalizes. This means that the state of the system ρS (t) approaches an equilibrium state ρ eq S, the latter depending only on macroscopic characteristics of the bath (e.g., temperature) but not on the initial state of the system. The above statement is the cornerstone of the equilibrium statistical mechanics; its validity and its domain of applicability are central questions in the studies of the foundations of statistical mechanics. In the present paper we concentrate on one aspect of thermalization, namely, on the system initial state independence (ISI) of ρ eq S. A necessary condition for the system ISI is derived in the quantum framework. We use the derived condition to prove the absence of the system ISI in a specific class of models. Namely, we consider a single spin coupled to a large bath, the interaction term commuting with the bath self-Hamiltonian (but not with the system self-Hamiltonian). Although the model under consideration is nontrivial enough to exhibit the decoherence and the approach to equilibrium, the derived necessary condition is not fulfilled and thus ρ eq S depends on the initial state of the spin.

UR - http://www.scopus.com/inward/record.url?scp=77954824758&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.82.011123

DO - 10.1103/PhysRevE.82.011123

M3 - Article

AN - SCOPUS:77954824758

VL - 82

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

M1 - 011123

ER -