A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath

Abstract

To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is computationally much less expensive in a sense that a reduced density matrix is obtained by calculating the time evolution of vectors, instead of matrices, which enables one to deal with large dimensional systems. As a benchmark test, we consider a quantum damped harmonic oscillator, and show that the exact results can be well reproduced. In addition to the reduced density matrix, our approach also provides a link to the total wave function by introducing new boson operators.

Quantum Surface Friction Model for Fusion Reactions around the Coulomb Barrier

“…In that approach, a fluctuation force is automatically incorporated into the formalism, while the present approach neglects it. A work towards this direction is now in progress [12].…”

Time-Dependent Approaches to Open Quantum Systems

“…One can also introduce the influence functional [28]. Here we discuss the coupled-channels approach [29].…”

“…In that situation, it is almost hopeless to solve the coupled-channels equations directly. In order to overcome this problem, we introduce a more efficient basis to expand the total wave function [29]. To this end, we first expand the function e −iωt with a finite basis set as,…”

“…Ref. [29] also provides an alternative derivation of the coupled-channels equations, which uses the influence functional of the path integral method. This allows one to extend the present formalism to finite temperatures.…”

“…This allows one to extend the present formalism to finite temperatures. Figures 2 and 3 show results of a time evolution for a damped harmonic oscillator [29], for which we take the Hamiltonian for the system, H S in Eq. (10), as…”