Topological origin of quantum mechanical vacuum transitions and tunneling
arXiv:1409.1505 · doi:10.1142/S0217732315501187
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 -dim double-well (DW) potential tunneling dynamics. The topological profile of the zero-mode ground state, , and the first excited state, , 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 -dim DW potentials.
arXiv comment13 pages and 07 figures
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