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.