Topological origin of quantum mechanical vacuum transitions and tunneling

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, $ψ_{0}$, and the first excited state, $ψ_{1}$, 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, $ψ_{0} + e^{\mbox{$-i E \,t$}}ψ_{1}$, that exhibits a stable tunneling dynamics, is converted into a quantum superposition involving a self-vanishing tachyonic mode, $e^{\mbox{$- E \,t$}}ψ_{0} + ψ_{1}$, 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.