Hallmarks of tunneling dynamics with broken reflective symmetry

TL;DR

This paper investigates tunneling phenomena in a supersymmetric quantum mechanics model with multi-well potentials and broken symmetry, highlighting the advantages of isospectral exactly-solvable Hamiltonians for studying localization and tunneling effects.

Contribution

It introduces the use of isospectral exactly-solvable Hamiltonians to analyze tunneling dynamics in multi-well potentials with broken symmetry, offering flexible modeling options.

Findings

Partial localization of under-barrier states observed.

Coherent tunneling destruction demonstrated.

Advantages of exactly-solvable models for potential design.

Abstract

We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type demonstrate the phenomenon of partial localization of under-barrier states, possibly resulting in the appearance of the so-called "resonant" tunneling, or the phenomenon of coherent tunneling destruction, referring to the complete localization. Taking the partial localization and the coherent tunneling destruction as basic examples, we indicate main advantages of using isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems with two- and three-well potentials. They, in particular, are: having enough freedom of changing the potential shape in a wide range, that allows one to choose an exactly-solvable model close to characteristics of the phenomenological one; ability of changing the number of local minima and symmetry characteristics of the potential (symmetric or deformed) without changing the main part of the spectrum; engaging a smart basis of states, that dramatically decreases the dimensionality of matrices used in the diagonalization procedure of the corresponding spectral problem.