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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Random matrix approach to quantum dissipation

Aurel Bulgac, G. Do Dang, Dimitri Kusnezov

Published Oct 1, 1996• 43 citations
Publisher

Abstract

The microscopic origin of dissipation in collective motion of a quantum many-body system is addressed in the framework of a parametric random matrix approach to the intrinsic dynamics. There are noticeable violations of the fluctuation-dissipation theorem and the energy diffusion has a markedly non-Gaussian character. Such features do not support the usual Fokker-Planck approach to dissipation in large amplitude motion of many fermion systems. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.54.3468

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The microscopic origin of dissipation in collective motion of a quantum many-body system is addressed in the framework of a parametric random matrix approach to the intrinsic dynamics. There are noticeable violations of the fluctuation-dissipation theorem and the energy diffusion has a markedly non-Gaussian character. Such features do not support the usual Fokker-Planck approach to dissipation in large amplitude motion of many fermion systems. \textcopyright{} 1996 The American Physical Society.
The microscopic origin of dissipation of a driven quantum many-body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation-dissipation theorem and we observe also that the energy diffusion has a markedly non-Gaussian character. Within the Feynman-Vernon path integral formalism and in the Markovian limit, we further consider the time evolution of a slow subsystem coupled to such a ‘bath’ of intrinsic degrees of freedom. We show that dissipation leads to qualitative modifications of the time evolution of the density matrix of the slow subsystem. In either the spatial, momentum or energy representation the density distribution acquires very long tails and tunneling is greatly enhanced.
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived in the limit of weak coupling of the collective and intrinsic subsystems. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.
We address the problem of the dissipative character of collective motion in finite Fermi systems. We study this problem from the point of view of chaotic features of the fermionic degrees of freedom of the many-body Fermi systems. Our main aim is of two kinds: first, we investigate how quantum chaos sets in in many-body systems and then, we try to relate quantum many-body chaos of the intrinsic fermionic degrees of freedom to the corresponding dissipative properties of the macroscopic collective motion. The main focus is on the role of two-body interaction between fermions in onset of the quantum many-body chaos and collective dissipation.
The Schrodinger equation with Gaussian dynamic fluctuating potentials is considered. This model gives a convenient example of an open quantum system coupled to a given external environment. The evolution equations for averaged correlators are derived and it is shown that a system coupled to a thermoequilibrium environment tends asymptotically with time to a thermodynamic density matrix. At high temperatures the quantum evolution equation for the density matrix can be approximated by the quasiclassical Fokker-Planck equation. The generalisation for multiparticle systems is also given. The results are illustrated by the particular examples of coupling with phonons and of two-level systems. Finally, it is shown how the problem can be reformulated in terms of continuous stochastic evolution in the space of psi functions and a corresponding functional formalism based on the continuous Fokker-Planck equation in the space of psi functions.
Standard methods used for computing the dynamics of a quantum many-body system are the mean-field (MF) approximations such as the time-dependent Hartree-Fock (TDHF) approach. Even though MF approaches are quite successful, they suffer some well-known shortcomings, one of which is insufficient dissipation of collective motion. The stochastic mean-field approach (SMF), where a set of MF trajectories with random initial conditions are considered, is a good candidate to include dissipative effects beyond mean field. In this approach, the one-body density matrix elements are treated initially as a set of stochastic Gaussian c numbers that are adjusted to reproduce first and second moments of collective one-body observables. It is shown that the predictive power of the SMF approach can be further improved by relaxing the Gaussian assumption for the initial probabilities. More precisely, using Gaussian or uniform distributions for the matrix elements generally leads to overdamping for long times, whereas distributions with smaller kurtosis lead to much better reproduction of the long time evolution.