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Physics Reports

Stochastic aspects of large amplitude collective motion

Aurel Bulgac, G. Do Dang, Dimitri Kusnezov

Published Jan 1, 1996• 8 citations
Publisher

Abstract

We consider externally driven many-body systems with complex spectra of intrinsic states. The effects of the coupling to the external world are analyzed by assuming time-dependent random matrix properties for the intrinsic system. We derive and solve evolution equations for intrinsic state population probabilities, average excitation energy and its fluctuations. The diffusive process is likely to be dominated by memory effects and an unexpected type of fluctuations.

DOI
10.1016/0370-1573(95)00028-3

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We consider externally driven many-body systems with complex spectra of intrinsic states. The effects of the coupling to the external world are analyzed by assuming time-dependent random matrix properties for the intrinsic system. We derive and solve evolution equations for intrinsic state population probabilities, average excitation energy and its fluctuations. The diffusive process is likely to be dominated by memory effects and an unexpected type of fluctuations.
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 present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system (environment). By modeling the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models that emerge from random matrix theory. Using the Feynman-Vernon path integral formalism, we derive the influence functional and obtain either analytical or numerical solutions for the time evolution of the entire quantum system. We discuss thoroughly the structure of the solutions for some representative cases and make connections to well known limiting results, particularly to Brownian motion, Kramers classical limit, and the Caldeira-Leggett approach.
We study the perturbative response of a complex quantum system on time changes of an external parameter XXX. The driven dynamics is treated in adiabatic basis of the system's Hamiltonian H^[X]\hat{H}[X]H^[X]. Within a random matrix approach we obtained non--Markovian Fokker--Planck equation for the occupancy of given adiabatic state. We observed normal diffusion regime of the driven quantum dynamics at quite small values of the memory time defined by the time scales of the XXX--correlations and energy--distribution of the coupling matrix elements (∂H^/∂X)nm(\partial \hat{H}/\partial X)_{nm}(∂H^/∂X)nm​. Here the normal energy diffusion was found to drop out with the width of the matrix elements' energy--distribution and the diffusion may be significantly suppressed with the decrease of the correlations between the matrix elements. In the opposite limit of relatively large memory times we obtained ballistic regime of the dynamics.
We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ``state-dependent" rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-)local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models.
Abstract We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ‘state-dependent’ rates. The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-) local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models.