Statistical approach to quantum chaotic ratchets

Interaction-induced directed transport in quantum chaotic subsystems

Quantum directed transport can be realized in noninteracting, deterministic, chaotic systems by appropriately breaking the spatiotemporal symmetries in the potential. In this work, the focus is on the class of interacting two-body quantum systems whose classical limit is chaotic. It is shown that one subsystem effectively acts as a source of "noise" to the other leading to intrinsic temporal symmetry breaking. Then, the quantum directed currents, even if prohibited by symmetries in the composite system, can be realized in the subsystems. This current is of quantum origin and does not arise from semiclassical effects. This protocol provides a minimal framework-broken spatial symmetry in the potential and presence of interactions-for realizing directed transport in interacting chaotic systems. It is also shown that the magnitude of directed current undergoes multiple current reversals upon varying the interaction strength and this allows for controlling the currents. It is explicitly demonstrated in the two-body interacting kicked rotor model. The interaction-induced mechanism for subsystem directed currents would be applicable to other interacting quantum systems as well.

Quantum properties of double kicked systems with classical translational invariance in momentum

Double kicked rotors (DKRs) appear to be the simplest nonintegrable Hamiltonian systems featuring classical translational symmetry in phase space (i.e., in angular momentum) for an infinite set of values (the rational ones) of a parameter η. The experimental realization of quantum DKRs by atom-optics methods motivates the study of the double kicked particle (DKP). The latter reduces, at any fixed value of the conserved quasimomentum βℏ, to a generalized DKR, the "β-DKR." We determine general quantum properties of β-DKRs and DKPs for arbitrary rational η. The quasienergy problem of β-DKRs is shown to be equivalent to the energy eigenvalue problem of a finite strip of coupled lattice chains. Exact connections are then obtained between quasienergy spectra of β-DKRs for all β in a generically infinite set. The general conditions of quantum resonance for β-DKRs are shown to be the simultaneous rationality of η,β, and a scaled Planck constant ℏ(S). For rational ℏ(S) and generic values of β, the quasienergy spectrum is found to have a staggered-ladder structure. Other spectral structures, resembling Hofstadter butterflies, are also found. Finally, we show the existence of particular DKP wave-packets whose quantum dynamics is free, i.e., the evolution frequencies of expectation values in these wave-packets are independent of the nonintegrability. All the results for rational ℏ(S) exhibit unique number-theoretical features involving η,ℏ(S), and β.

Classical and quantum transport in one-dimensional periodically kicked systems

This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems will be considered: those satisfying the classical Kolmogorov−Arnol’d−Moser scenario and those that do not. The experimental realization of some of these systems using atom-optics methods will be mentioned.

Weak-chaos ratchet accelerator

Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.