Floquet states of kicked particle in a singular potential: Exponential and power-law profiles

TL;DR

This paper investigates how the decay profiles of Floquet states in a kicked particle system transition from exponential to power-law as the potential barrier height varies, revealing a dependence on energy band and spectral statistics.

Contribution

It introduces a detailed analysis of Floquet state profiles in a finite potential barrier system and links their nature to energy bands and spectral properties.

Findings

Floquet states transition from exponential to power-law profiles with barrier height.

Decay profile depends on the energy band relative to the potential height.

Spectral statistics vary, indicating non-uniform spectral correlations.

Abstract

It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.