Dynamics Of Complex Quantum Systems Research Articles

Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology

An efficient method, the self-consistent hybrid method, is proposed for accurately simulating time-dependent quantum dynamics in complex systems. The method is based on an iterative convergence procedure for a dynamical hybrid approach. In this approach, the overall system is first partitioned into a “core” and a “reservoir” (an initial guess). The former is treated via an accurate quantum mechanical method, namely, the time-dependent multiconfiguration self-consistent field or multiconfiguration time-dependent Hartree approach, and the latter is treated via a more approximate method, e.g., classical mechanics, semiclassical initial value representations, quantum perturbation theories, etc. Next, the number of “core” degrees of freedom, as well as other variational parameters, is systematically increased to achieve numerical convergence for the overall quantum dynamics. The method is applied to two examples of quantum dissipative dynamics in the condensed phase: the spin-boson problem and the electronic resonance decay in the presence of a vibrational bath. It is demonstrated that the method provides a practical way of obtaining accurate quantum dynamical results for complex systems.

Dynamics of complex quantum systems: dissipation and kinetic equations

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.