The Kick Rotor Model: A Paradigm for Studying Classical and Quantum Chaos

The kick rotor model serves as a widely employed paradigm for the exploration of both classical and quantum chaos, as attested by a substantial body of research [Casati1977, shepelyanskii1981dynamical, chirikov1988quantum, izrailev1990simple, chirikov1997linear, korsch2008kicked, frahm2009diffusion, joos2013decoherence, shivamoggi2014nonlinear, santhanam2022quantum]. This model depicts a freely moving rotor traversing a circular trajectory subjected to a periodic delta function potential. Within the framework of classical mechanics, the trajectory in phase space undergoes a transition from a regular to a chaotic regime when the driving strength surpasses a critical value, approximated as Kc ≈ 0.971635, resulting in a linear augmentation of kinetic energy as the dynamical evolution progresses [de1990hamiltonian, amin2015nonperturbative, jalabert2001environment]. In the quantum mechanical realm, when the kick strength assumes an irrational multiple of 2π, the wave function in momentum space exhibits a localized state analogous to Anderson Localization, attributable to phase-coherent superposition [anderson1958absence, casati1990scaling, kanem2007observation]. However, as the corresponding classical system exhibits chaotic behavior, the kinetic energy of the quantum system tends towards a specific, saturating value. The introduction of an external noise reservoir into the model leads to the loss of phase coherence and consequently shifts the system's kinetic energy from the quantum saturating value to classical linear diffusion [cohen1991localization, schomerus2008controlled, fishman1989scaling].