# Resonance-assisted tunneling in 4D normal-form Hamiltonians

## TL;DR

This paper investigates how nonlinear resonances in four-dimensional Hamiltonian systems enhance quantum tunneling, revealing complex peak structures explained through normal-form Hamiltonians and perturbative analysis.

## Contribution

It introduces a universal normal-form Hamiltonian framework to explain resonance-assisted tunneling in 4D systems, providing quantitative insights and a minimal matrix model.

## Key findings

- Double resonances cause complex tunneling peak structures.
- Perturbative methods accurately explain tunneling enhancement and suppression.
- A minimal matrix model offers intuitive understanding.

## Abstract

Nonlinear resonances in the classical phase space lead to a significant enhancement of tunneling. We demonstrate that the double resonance gives rise to a complicated tunneling peak structure. Such double resonances occur in Hamiltonian systems with an at least four-dimensional phase space. To explain the tunneling peak structure, we use the universal description of single and double resonances by 4D normal-form Hamiltonians. By applying perturbative methods, we reveal the underlying mechanism of enhancement and suppression of tunneling and obtain excellent quantitative agreement. Using a minimal matrix, we obtain model an intuitive understanding.