How to calculate a decoherence matrix numerically and the microscopic mechanism for decoherence in the Caldeira-Leggett model

TL;DR

This paper develops a numerical algorithm to efficiently compute the dominant elements of the decoherence matrix in quantum systems, demonstrated on the Caldeira-Leggett model, addressing computational challenges in high-dimensional matrices.

Contribution

It introduces a novel algorithm that combines numerical calculation with estimation to identify and compute only the dominant decoherence matrix elements.

Findings

Algorithm successfully identifies dominant matrix elements.

Application to Caldeira-Leggett model demonstrates efficiency.

Provides a practical method for high-dimensional decoherence calculations.

Abstract

A central object in the interpretation of quantum mechanics of closed systems with decoherent histories is the decoherence matrix. But only for a very small number of models one is able to give explicit expressions for its elements. So numerical methods are required. Unfortunately the dimensions of this matrices are usually very high, which makes also a direct numerical calculation impossible. A solution of this problem would be given by a method which only calculates the dominant matrix elements. This includes to make a decision about the dominance of an element before it will be calculated. In this paper I will develop an algorithm that combines the numerical calculation of the elements of the decoherence matrix with a permanent estimation, so that finally the dominant elements will be calculated only. As an example I apply this procedure to the Caldeira- Leggett-modell.