Quantum chaos and H\'enon-Heiles model: Dirac's variational approach with Jackiw-Kerman function

TL;DR

This paper develops a semiclassical model of the Hénon-Heiles system using Dirac's variational principle and Jackiw-Kerman functions, revealing quantum-induced chaos in classically regular regions.

Contribution

It introduces a novel semiclassical approach employing a Hartree-type wavefunction with Jackiw-Kerman form to analyze quantum effects on chaos.

Findings

Quantum effects induce chaos in non-chaotic classical regions

Effective semiclassical Hamiltonian derived from variational principle

Numerical simulations demonstrate quantum chaos emergence

Abstract

A simple semiclassical H\'enon-Heiles model is constructed based on Dirac's time-dependent variational principle. We obtain an effective semiclassical Hamiltonian using a Hatree-type two-body trial wavefunction in the Jackiw-Kerman form. Numerical results show that quantum effects can in fact induce chaos in the non-chaotic regions of the classical H\'enon-Heiles model.