# Quantum tunneling with friction

## TL;DR

This paper investigates how quantum friction models affect tunneling probabilities in a one-dimensional system, showing that energy dissipation reduces tunneling and that different models yield similar results with varying computational efficiency.

## Contribution

It compares three phenomenological quantum friction models in the context of quantum tunneling, highlighting their similarities and differences in calculating tunneling probabilities.

## Key findings

- Friction reduces quantum tunneling probability.
- The three models produce similar tunneling penetrabilities.
- Caldirola-Kanai model is computationally most efficient.

## Abstract

Using the phenomenological quantum friction models introduced by Caldirola-Kanai, Kostin, and Albrecht, we study quantum tunneling of a one-dimensional potential in the presence of energy dissipation. To this end, we calculate the tunneling probability using a time-dependent wave packet method. The friction reduces the tunneling probability. We show that the three models provide similar penetrabilities to each other, among which the Caldirola-Kanai model requires the least numerical effort. We also discuss the effect of energy dissipation on quantum tunneling in terms of barrier distributions.