Quantum and classical dissipation of charged particles

TL;DR

This paper develops a Hamiltonian framework to analyze the dissipative dynamics of charged particles in electromagnetic fields, providing solutions for classical and quantum cases, and examining wave packet evolution.

Contribution

It introduces a Hamiltonian approach with canonical transformations to study dissipative charged particles quantum mechanically and classically, including Green's function construction.

Findings

Derived solutions for classical and quantum dissipative charged particle motion.

Constructed Green's functions for the system.

Analyzed Gaussian wave packet dynamics in the dissipative environment.

Abstract

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail.