Giu Do Dang

DYNAMICS OF A SIMPLE QUANTUM SYSTEM IN A COMPLEX ENVIRONMENT

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models which 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.

Self-consistent theory of large-amplitude collective motion: Applications to approximate quantization of nonseparable systems and to nuclear physics

Abstract The goal of the present account is to review our efforts to obtain and apply a “collective” Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large-amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other topics included are a nuclear Born–Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and noncollective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included.

Turbulent-like diffusion in complex quantum systems

Abstract We study a quantum particle propagating through a “quantum mechanically chaotic” background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion under very general situations, without the a priori introduction of power law noise or scaling in the background properties.

Dynamics of complex quantum systems: dissipation and kinetic equations ☆

Abstract We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is modeled by means of parametric banded random matrices coupled to the subsystem of interest. We do not assume the weak coupling limit and allow for an independent dynamics of the “reservoir”. We discuss the reasons for having a new theoretical approach and the new elements introduced by us. The present approach incorporates known limits and previous results, but at the same time includes new cases, previously never derived on a microscopic level. We briefly discuss the kinetic equation and its solution for a particle in the absence of an external field.

Local harmonic approaches with approximate cranking operators

Methods of large amplitude collective motion in the adiabatic limit are examined with a special emphasis on conservation laws. We show that the restriction to point transformations, which is a usual assumption of the adiabatic time-dependent mean-field theory, needs to be lifted. In order to facilitate the application of large-amplitude collective motion techniques, we examine the possibility of representing the random-phase-approximation normal-mode coordinates by linear combinations of a limited number of one-body operators. We study the pairing-plus-quadrupole model of Baranger and Kumar as an example, and find that such representations exist in terms of operators that are state dependent in a characteristic manner.

Quantum diffusion and tunneling with parametric banded random matrix hamiltonians

Abstract 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.

A basis of cranking operators for the pairing-plus-quadrupole model

We investigate the RPA normal-mode coordinates in the pairing-plus-quadrupole model, with an eye on simplifying the application of large amplitude collective motion techniques. At the Hartree-Bogoliubov minimum, the RPA modes are exactly the cranking operators of the collective coordinate approach. We examine the possibility of representing the self-consistent cranking operator by linear combinations of a limited number of one-body operators. We study the Sm nuclei as an example, and find that such representations exist in terms of operators that are state-dependent in a characteristic manner.

GENERATION OF COLLECTIVE SUBSPACES AND SELF-CONSISTENT CRANKING OPERATORS

Abstract Within the framework of the theory of large amplitude collective motion and with special emphasis of the fission process, we examine the question of the question of the difinition of the collective space and the possibility of the representation of cranking operators by linear combinations of elementary one-body operators. For a numerical example related to our previous work on 28 Si, it is found that cranking operators may have a strong radial and spin dependence.