Effective time-independent analysis for quantum kicked systems

TL;DR

This paper introduces a method to convert chaotic quantum kicked systems into equivalent integrable time-independent models, enabling better analysis of their spectra and dynamics, especially in non-chaotic regimes.

Contribution

The authors develop a mapping technique that produces an effective time-independent Hamiltonian for quantum kicked systems, avoiding divergences and accurately capturing spectral and dynamical properties.

Findings

Effective Hamiltonian matches quasienergy spectrum with high accuracy.

Density of states shows sharp peaks indicating quantum criticality.

Classical dynamics of the effective system aligns with the original in non-chaotic regimes.

Abstract

We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent effective time-independent scenario, whereby the system is rendered integrable. The time-evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained, does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peak-like features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the non-integrable map corresponding to the actual time-dependent system in the non-chaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the non-chaotic regime at both the quantum and classical level.