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Condensed Matter Physics

NONEQUILIBRIUM QUANTUM EVOLUTION OF OPEN SYSTEMS

Kim

Published Jan 1, 2000• 5 citations
Publisher

Abstract

We apply the Liouville-von Neumann (LvN) approach to open systems to describe the nonequilibrium quantum evolution.The Liouville-von Neumann approach is a unified method that can be applied to both time-independent (closed) and time-dependent (open) systems and to both equilibrium and nonequilibrium systems.We study the nonequilibrium quantum evolution of oscillator models for open boson and fermion systems

DOI
10.5488/cmp.3.1.23

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The effective theory of an open boson or fermion system is studied, which evolves out of equilibrium with time-dependent Hamiltonian H^(t)\hat{H}(t)H^(t). A measure of nonequilibrium temperature for the open system evolving from an equilibrium is proposed as the time-averaged energy expectation value T(t)=Ti(<H^(t)>Ψˉ/<I^(t)>Ψˉ)T(t) = T_i(\bar{< \hat{H} (t) >_Ψ}/ \bar{< \hat{I} (t) >_Ψ})T(t)=Ti​(<H^(t)>Ψ​ˉ​/<I^(t)>Ψ​ˉ​), where I^(t)\hat{I} (t)I^(t), the action operator, satisfies the quantum Liouville-von Neumann equation and determines the true density operator. It recovers the result for the adiabatic (quasi-equilibrium) and nonadiabatic (out of equilibrium) evolution from one static Hamiltonian to another and takes into account the particle production due to the intermediate processes.
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We present a nonperturbative field theoretic method based on the Liouville-Neumann (LN) equation. The LN approach provides a unified formulation of nonperturbative quantum fields and also nonequilibrium quantum fields, which makes use of mean-field type equations and whose results at the lowest level are identically the same as those of the Gaussian effective potential approach and the mean-field approach. The great advantageous point of this formulation is its readiness of applicability to time-dependent quantum systems and to finite temperature field theory, and its possibility to go beyond the Gaussian approximation.