Macroscopic quantum tunneling of two coupled particles in the presence of a transverse magnetic field

TL;DR

This paper investigates the quantum tunneling behavior of two coupled particles with opposite charges in a magnetic field, revealing that the problem remains inherently two-dimensional and analyzing the effects of dissipation and external potentials.

Contribution

It demonstrates that the two-particle coupled system cannot be simplified to a one-dimensional model and derives the effective action considering magnetic field and dissipation effects.

Findings

The problem remains two-dimensional and cannot be reduced to a one-dimensional model.

Effective action reduces to a two-dimensional Caldeira-Leggett form under strong dissipation.

Analyzed the impact of Ohmic dissipation on the tunneling process.

Abstract

Two coupled particles of identical masses but opposite charges, with a constant transverse external magnetic field and an external potential, interacting with a bath of harmonic oscillators are studied. We show that the problem cannot be mapped to a one-dimensional problem like the one in Ref. \cite{pa}, it strictly remains two-dimensional. We calculate the effective action both for the case of linear coupling to the bath and without a linear coupling using imaginary time path integral at finite temperature. At zero temperature we use Leggett's prescription to derive the effective action. In the limit of zero magnetic field we recover a two dimensional version of the result derived in Ref. \cite{em1} for the case of two identical particles. We find that in the limit of strong dissipation, the effective action reduces to a two dimensional version of the Caldeira-Leggett form in terms of the reduced mass and the magnetic field. The case of Ohmic dissipation with the motion of the two particles damped by the Ohmic frictional constant $\eta$ is studied in detail.