An Exact Solution for Quantum Tunneling in a Dissipative System

TL;DR

This paper provides an exact analytical solution for quantum tunneling in an Ohmic dissipative system with an inverted harmonic potential, revealing how dissipation and Brownian motion influence tunneling probabilities.

Contribution

It introduces a novel exact solution for quantum tunneling in dissipative systems, accounting for initial conditions and parameter dependencies.

Findings

Dissipation suppresses quantum tunneling.

Brownian motion enhances tunneling.

Tunneling rate depends on initial conditions.

Abstract

Applying a technique developed recently [1,2] for an harmonic oscillator coupled to a bath of harmonic oscillators, we present an exact solution for the tunneling problem in an Ohmic dissipative system with inverted harmonic potential. The result shows that while the dissipation tends to suppress the tunneling, the Brownian motion tends to enhance the tunneling. Whether the tunneling rate increases or not would then depend on the initial conditions. We give a specific formula to calculate the tunneling probability determined by various parameters and the initial conditions.