Motion of heavy particles coupled to fermionic and bosonic environments in one dimension

TL;DR

This paper develops a method to analyze the motion of heavy particles in one-dimensional fermionic or bosonic environments by transforming the Hamiltonian, enabling calculation of damping constants based on interaction reflection and environmental occupation.

Contribution

It introduces a unitary transformation approach to simplify the Hamiltonian of a particle coupled to 1D quantum gases, facilitating the computation of damping effects.

Findings

Damping constant expressed via reflection coefficient and occupation number.

Application to delta repulsive potential demonstrates the method's effectiveness.

Provides a new analytical tool for particle-environment interaction in 1D systems.

Abstract

Making use of a simple unitary transformation we change the hamiltonian of a particle coupled to an one dimensional gas of bosons or fermions to a new form from which the many body degrees of freedom can be easily traced out. The effective dynamics of the particle allows us to compute its damping constant in terms of the reflection coefficient of the interaction potential and the occupation number of the environmental particles. We apply our results to a delta repulsive potential.