Kicked Rotor Model: A Prototypical System for Studying Classical and Quantum Chaos

The kicked rotor model is a prototypical model used to study classical and quantum chaos /cite{Casati1977, shepelyanskii1981dynamical, chirikov1988quantum, izrailev1990simple, chirikov1997linear, korsch2008kicked, frahm2009diffusion, joos2013decoherence}. The model perturbs a circular free-moving rotor with a periodic δ function potential. In classical theory, the phase space trajectory changes from regular to chaotic when the driving strength exceeds the critical point Kc ≈ 0.971635, resulting in a linear increase in kinetic energy with dynamical evolution /cite{Casati1977, shepelyanskii1981dynamical, frahm2009diffusion, amin2015nonperturbative}. In quantum theory, if the kick strength is an irrational multiple of 2π, the wave function in the momentum space exhibits a localized state similar to Anderson Localization, due to the phase coherent superposition /cite{anderson1958absence, casati1990scaling}. Even if the corresponding classical system is chaotic, the system's energy tends to a specific saturate value /cite{shepelyanskii1981dynamical, chirikov1988quantum, izrailev1990simple, korsch2008kicked, joos2013decoherence}. However, introducing a noisy external reservoir into the model results in a loss of phase coherence, or decoherence, shifting the system kinetic energy from a quantum saturating value to classical linear diffusion /cite{klappauf1998observation, korsch2008kicked, cohen1991localization, schomerus2008controlled}.