Superballistic wavepacket spreading in double kicked rotors

Ping Fang,Jiao Wang

doi:10.1007/s11433-016-0076-y

Abstract

Abstract We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.

Highlights

In a quantum system, a wavepacket usually spreads following a power law of time, i.e., its variance increases in time as ∼ tγ, with γ being a constant and 0 γ 2
Investigations of the possible ways in which a quantum wavepacket spreads have led to some important findings
The model system in which the exponential spreading was found is a variant of the quantum kicked rotor (QKR) [7]

Summary

Introduction

A wavepacket usually spreads following a power law of time, i.e., its variance increases in time as ∼ tγ, with γ being a constant and 0 γ 2. Similar to the two cases [4,5] mentioned above, the time for which the exponential spreading lasts depends on the system’s parameters, which is finite but in principle can be infinite as the system’s parameters are tuned This finding unveils a new type of quantum motion. The model system in which the exponential spreading was found is a variant of the quantum kicked rotor (QKR) [7]. This result implies that the superballistic spreading exists in very general systems, restricted in the lattices with hybrid structures [4, 5] It suggests a new type of quantum motion in the QKR, evidencing again the dynamics wealth of this paradigmatic quantum chaos model.

Models

Quantum superballistic wavepacket spreading

Two characteristic time scales

Discussions and summary