Quantum and Classical Superballistic Transport in a Relativistic Kicked-Rotor System

TL;DR

This paper demonstrates that both quantum and classical superballistic transport can occur in a simple relativistic kicked-rotor system with a mass term, revealing new insights into anomalous transport and quantum-classical correspondence.

Contribution

It shows that superballistic transport arises in a relativistic kicked-rotor system with a mass term, a novel finding linking classical and quantum anomalous transport phenomena.

Findings

Quantum and classical superballistic transport occur in the same system.

Different system parameters are needed for quantum versus classical superballistic transport.

The mass term creates a junction-like scenario affecting transport properties.

Abstract

As an unusual type of anomalous diffusion behavior, superballistic transport is not well known but has been experimentally simulated recently. Quantum superballistic transport models to date are mainly based on connected sublattices which are constructed to have different properties. In this work, we show that both quantum and classical superballistic transport in the momentum space can occur in a simple periodically driven Hamiltonian system, namely, a relativistic kicked-rotor system with a nonzero mass term. The nonzero mass term essentially realizes a junction-like scenario: regimes with low or high momentum values have different dispersion relations and hence different transport properties. It is further shown that the quantum and classical superballistic transport should occur under much different choices of the system parameters. The results are of interest to studies of anomalous transport, quantum and classical chaos, and the issue of quantum-classical correspondence.