Exact Dynamics of Quantum Dissipative System in Constant External Field

TL;DR

This paper provides an exact quantum mechanical analysis of a dissipative particle in a constant external field, deriving explicit solutions and an effective Hamiltonian, revealing how dissipation influences wave packet dynamics.

Contribution

It introduces a method to obtain exact solutions and an effective Hamiltonian for a dissipative quantum system with a constant external field, extending previous work.

Findings

Exact solutions for coordinate operator and wavefunction are obtained.

Dissipation suppresses wave packet spreading.

Effective Hamiltonian derived for arbitrary potentials when Brownian motion is negligible.

Abstract

The quantum dynamics of a simplest dissipative system, a particle moving in a constant external field , is exactly studied by taking into account its interaction with a bath of Ohmic spectral density. We apply the main idea and methods developed in our recent work [1] to quantum dissipative system with constant external field. Quantizing the dissipative system we obtain the simple and exact solutions for the coordinate operator of the system in Heisenberg picture and the wave function of the composite system of system and bath in Schroedinger picture. An effective Hamiltonian for the dissipative system is explicitly derived from these solutions with Heisenberg picture method and thereby the meaning of the wavefunction governed by it is clarified by analyzing the effect of the Brownian motion. Especially, the general effective Hamiltonian for the case with arbitrary potential is directly derived with this method for the case when the Brownian motion can be ignored. Using this effective Hamiltonian, we show an interesting fact that the dissipation suppresses the wave packet spreading.