# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1705.04156