Multidimensional tunneling between potential wells at non degenerate minima

TL;DR

This paper investigates quantum tunneling between potential wells in a 2-D semi-classical Schrödinger setting, focusing on energies near the potential minimum and analyzing both ground and excited states in symmetric wells.

Contribution

It provides a detailed analysis of tunneling phenomena for non-degenerate minima, extending understanding to excited states associated with Diophantine tori.

Findings

Tunneling behavior characterized for energies near the quadratic minimum.

Analysis includes both harmonic oscillator excitations and more general excited states.

Results contribute to understanding quantum dynamics in multi-well potentials.

Abstract

We consider tunneling between symmetric wells for a 2-D semi-classical Schr\"odinger operator for energies close to the quadratic minimum of the potential V in two cases: (1) excitations of the lowest frequency in the harmonic oscillator approximation of V; (2) more general excited states from Diophantine tori with comparable quantum numbers.