Canonical Quantization Approach of a Class of a Dissipative System: Applications to Quantum Tunnelling with Dissipative Coupling

TL;DR

This paper develops a canonical quantization formalism for dissipative systems with monotonic trajectories, deriving their Lagrangian and Hamiltonian, and applies it to analyze quantum tunneling affected by dissipation.

Contribution

It introduces a variational principle-based formalism for dissipative systems and extends canonical quantization to such systems, including applications to quantum tunneling with dissipation.

Findings

Dissipation affects quantum tunneling probability significantly.

The formalism reproduces results similar to Caldeira and Leggett.

Quantization of dissipative systems is feasible within this framework.

Abstract

We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the Hamiltonian, we quantize canonically the classical particle in a viscous media. We study the free quantum particle in a viscous media and the dissipative quantum tunnelling. It is found that the dissipation influences tunnelling probability by a factor that closely resembles the result of Caldeira and Leggett.