Dynamics of localized states in extended supersymmetric quantum mechanics with multi-well potentials

TL;DR

This paper introduces a self-consistent method to analyze the time evolution of localized states in multi-well supersymmetric quantum systems, highlighting limitations of the two-state approximation in complex tunneling scenarios.

Contribution

It presents an exactly solvable quantum model framework for studying localized state dynamics and tunneling, considering multi-state effects beyond simple approximations.

Findings

Two-state approximation is limited for systems with multiple under-barrier states.

The approach accounts for all Hamiltonian states, improving tunneling analysis.

Application to superconducting devices and cold atom traps demonstrates practical relevance.

Abstract

In this paper we propose a self--consistent approach to the description of temporal dynamics of localized states. This approach is based on exactly solvable quantum mechanical models with multi-well potentials and their propagators. States of Hamiltonians with multi-well potentials form a suitable basis for the expansion of wave packets with different shapes and localization degrees. We also consider properties of the tunneling wave packets, taking into account all states of Hamiltonians with symmetric and asymmetric potentials, as well as their dependence on the degree of localization and deformations of potentials. The study of the dynamics of initially localized states shows that application of the two-state approximation for the description of tunneling is considerably limited, especially for systems, which have several states in the under-barrier region, as for example in modern superconducting quantum interference devices and traps for cold atoms.