Topological origin of quantum mechanical vacuum transitions and tunneling

TL;DR

This paper explores how topological defect deformations induce quantum vacuum transitions and tunneling in double-well potentials, revealing a topological basis for quantum superposition and symmetry breaking phenomena.

Contribution

It introduces an analytical method linking topological defect deformation to quantum vacuum transitions in double-well potentials, highlighting a topological origin of tunneling dynamics.

Findings

Topological defect deformation induces quantum vacuum transitions.

Deformed defects support symmetry-breaking scenarios leading to tachyonic states.

Topological analysis explains the quantum superposition and tunneling coherence.

Abstract

The quantum transition between shifted zero-mode wave functions is shown to be induced by the systematic deformation of topological and non-topological defects that support the $1$-dim double-well (DW) potential tunneling dynamics. The topological profile of the zero-mode ground state, $\psi_{0}$, and the first excited state, $\psi_{1}$, of DW potentials is obtained through the analytical technique of topological defect deformation. Deformed defects create two inequivalent topological scenarios connected by a symmetry breaking that support the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state. Our theoretical findings reveal the topological origin of two-level models where a non-stationary quantum state of unitary evolution, $\psi_{0} + e^{\mbox{$-i E \,t$}}\psi_{1}$, that exhibits a stable tunneling dynamics, is converted into a quantum superposition involving a self-vanishing tachyonic mode, $e^{\mbox{$- E \,t$}}\psi_{0} + \psi_{1}$, that parameterizes a tunneling coherent destruction. The non-classical nature of the symmetry breaking dynamics is recreated in terms of the single particle quantum mechanics of $1$-dim DW potentials.