Time-dependent approaches to open quantum systems

TL;DR

This paper reviews two time-dependent quantum approaches to modeling energy dissipation in open quantum systems, applying them to nuclear fusion and introducing a new solution method for complex coupled-channels equations.

Contribution

It introduces a new efficient method for solving large coupled-channels equations and compares two time-dependent approaches for open quantum system dissipation.

Findings

Effective Hamiltonian approach models dissipation in heavy-ion fusion.

New method simplifies solving large coupled-channels equations.

Dissipation influences Coulomb barrier penetrability.

Abstract

Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy dissipation. To this end, we discuss two different time-dependent methods. One is to introduce an effective time-dependent Hamiltonian, which leads to a classical equation of motion as a relationship among expectation values of quantum operators. We apply this method to a heavy-ion fusion reaction and discuss the role of dissipation on the penetrability of the Coulomb barrier. The other method is to start with a Hamiltonian with environmental degrees of freedom and derive an equation which the system degree of freedom obeys. For this, we present a new efficient method to solve coupled-channels equations, which can be easily applied even when the dimension of the coupled-channels equations is huge.