# Topological view of quantum tunneling coherent destruction

## TL;DR

This paper explores the topological aspects of quantum tunneling and coherent destruction in double-well potentials, analyzing how symmetry breaking influences quantum states and tunneling stability through Wigner function dynamics.

## Contribution

It introduces a novel analytical framework for understanding quantum tunneling and coherent destruction using topological scenarios in double-well potentials, including symmetry breaking effects.

## Key findings

- Symmetry breaking enables quantum conversion to tachyonic states.
- Topological scenarios differentiate stable tunneling from destruction.
- Wigner function analysis reveals dynamics of quantum states.

## Abstract

Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.