We consider heat conduction in a 1D dynamical channel. The channel consists of an ensemble of noninteracting particles, which move between two heat baths according to some dynamical process. We show that the essential thermodynamic properties of the heat channel can be obtained from the diffusion properties of the underlying particles. Emphasis is put on the conduction under anomalous diffusion conditions.

We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.

We investigate experimentally the route to quasiperiodicity in a driven ratchet for cold atoms and examine the relationship between symmetries and transport while approaching the quasiperiodic limit. Depending on the specific form of driving, quasiperiodicity results in the complete suppression of transport, or in the restoration of the symmetries which hold for a periodic driving. DOI: 10.1103/PhysRevLett.96.240604 PACS numbers: 05.40.Fb, 05.60.Cd, 32.80.Pj The ratchet effect [1-3], i.e., the possibility of obtaining directed transport of particles in the absence of a net bias force, has recently been attracting considerable interest [4 -8]. Initially introduced to point out the strict limitations on directed transport at equilibrium imposed by the second principle of thermodynamics [9], the ratchet effect has subsequently received much attention as it was identified as a model elucidating the working principle of molecular motors [7]. More recently, considerable activity on ratchets by the condensed matter community was stimulated by the possibility of using the ratchet phenomenon to realize new types of electron pumps [10].In order to obtain directed transport in the absence of a net bias, the ensemble of particles has to be driven out of equilibrium, so to overcome the restrictions imposed by the second principle of thermodynamics. Additionally, relevant symmetries of the system have to be broken to allow directed transport. Theoretical work [5,6] precisely identified the relationship between symmetries and transport in the case of periodically driven ratchets, and experiments with cold atoms in optical lattices validated the theoretical predictions [11,12]. The theoretical analysis was then extended to explore the relationship between symmetries and transport for quasiperiodically driven ratchets, and the general symmetries which forbid directed transport were identified [13,14].In the present work we investigate experimentally the route to quasiperiodicity in a driven ratchet for cold atoms, and we examine the relationship between symmetries and transport while approaching the quasiperiodic limit. It will be shown that, depending on the specific form of driving, quasiperiodicity may result in the complete suppression of transport, or in the restoration of the symmetries which hold for a periodic driving.Our experiments are based on caesium atoms cooled and trapped in a near-resonant driven optical lattice [15]. The lattice beam geometry is the same as the one used in our previous experiments [12]: one beam (beam 1) propagates in the z direction; the three other beams (beams 2 -4) propagate in the opposite direction, arranged along the edges of a triangular pyramid having the z direction as axis. We refer to Ref. [12] for further details of the setup, and we summarize here only the essential features. The interference between the lattice fields creates a periodic and spatially symmetric potential for the atoms. The interaction with the light also leads to damping of the atomic motion, and the level of d...

Strong anomalous diffusion, where ⟨|x(t)|(q)⟩ ∼ tqν(q) with a nonlinear spectrum ν(q) ≠ const, is wide spread and has been found in various nonlinear dynamical systems and experiments on active transport in living cells. Using a stochastic approach we show how this phenomenon is related to infinite covariant densities; i.e., the asymptotic states of these systems are described by non-normalizable distribution functions. Our work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multifractal anomalous diffusion, as it is complementary to the central limit theorem.

To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties of these operators, including the shape of the spectrum in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate universality of the spectral features. The notion of ensemble of random generators of Markovian qauntum evolution constitutes a step towards categorization of dissipative quantum chaos.

When a periodically modulated many-body quantum system is weakly coupled to an environment, the combined action of these temporal modulations and dissipation steers the system towards a state characterized by a time-periodic density operator. To resolve this asymptotic non-equilibrium state at stroboscopic instants of time, we use the dissipative propagator over one period of modulations, 'Floquet map', and evaluate the stroboscopic density operator as its invariant. Particle interactions control properties of the map and thus the features of its invariant. In addition, the spectrum of the map provides insight into the system relaxation towards the asymptotic state and may help to understand whether it is possible (or not) to construct a stroboscopic time-independent Lindblad generator which mimics the action of the original time-dependent one. We illustrate the idea with a scalable many-body model, a periodically modulated Bose-Hubbard dimer. We contrast the relations between the interaction-induced bifurcations in a mean-field description with the numerically exact stroboscopic evolution and discuss the characteristics of the genuine quantum many-body state vs the characteristics of its mean-field counterpart.

Recent symmetry considerations [Flach et al., Phys. Rev. Lett. 84, 2358 (2000)] have shown that dc currents may be generated in the stochastic layer of a system describing the motion of a particle in a one-dimensional potential in the presence of an ac time-periodic drive. In this paper we explain the dynamical origin of this current. We show that the dc current is induced by the presence and desymmetrization of ballistic channels inside the stochastic layer. The existence of these channels is due to resonance islands with nonzero winding numbers. The characterization of the flight dynamics inside ballistic channels is described by distribution functions. We obtain these distribution functions numerically and find very good agreement with simulation data.

Thermalization and prethermalization in isolated quantum systems: a theoretical overview Takashi Mori, Tatsuhiko N Ikeda, Eriko Kaminishi et al.Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory Gerardo A Paz-Silva, Seung-Woo Lee, Todd J Green et al. Abstract A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather nontrivial task. It was recently shown that in the limit of an infinitesimal coupling, using the so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.