Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator

TL;DR

This paper analyzes the quantum-resonant dynamics of the delta-kicked accelerator, revealing that even-order momentum moments grow following a power law, with growth exponents depending on initial temperature conditions.

Contribution

It provides analytic expressions for the evolution of momentum moments and demonstrates power law growth in quantum-resonant dynamics for the first time.

Findings

Even-order momentum moments grow as a power law.

Exponent depends on initial temperature: full exponent at zero temperature, reduced by one at finite temperature.

Explicit demonstration for Gaussian initial momentum distribution.

Abstract

We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. To demonstrate the power law behavior explicitly we consider the evolutions of the second- and fourth-order momentum moments, and cumulants, for an initially Gaussian momentum distribution corresponding to the Maxwell-Boltzmann distribution of an ideal gas at thermal equilibrium.