Kick Rotor Model: A Prototypical Model for Studying Classical and Quantum Chaos

The kick rotor model has been widely used as a prototypical model for studying classical and quantum chaos [Casati1977, shepelyanskii1981dynamical, chirikov1988quantum, izrailev1990simple, chirikov1997linear, korsch2008kicked, frahm2009diffusion, joos2013decoherence]. This model describes a circular free-moving rotor that is perturbed by a periodic 'delta' 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 the kinetic energy increasing linearly with the dynamical evolution[Casati1977, shepelyanskii1981dynamical, frahm2009diffusion, amin2015nonperturbative]. In quantum theory, when the kick strength is an irrational multiple of 2π, the wave function in momentum space exhibits a localized state similar to Anderson Localization due to phase coherent superposition [anderson1958absence, casati1990scaling]. Even if the corresponding classical system is chaotic, the system's energy tends to a specific saturate value [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 the quantum saturating value to classical linear diffusion[ klappauf1998observation, korsch2008kicked, cohen1991localization, schomerus2008controlled].