We demonstrate that directed transport of particles in a two dimensional driven lattice can be dynamically reversed multiple times by superimposing additional spatially localized lattices on top of a background lattice. The timescales of such current reversals can be flexibly controlled by adjusting the spatial locations of the superimposed lattices. The key principle behind the current reversals is the conversion of the particle dynamics from chaotic to ballistic, which allow the particles to explore regions of the underlying phase space which are inaccessible otherwise. Our results can be experimentally realized using cold atoms in driven optical lattices and allow for the control of transport of atomic ensembles in such setups.
In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally decaying superimposed field up to a prescribed threshold. The general system analyzed here describes the sub-threshold signal integration of integrate-and-fire neuron models, of any kind, supplemented by an adaptation-like current, whereas the first-passage-time corresponds to the declaration of a spike…
We show that the direction of directed particle transport in a two dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is …
Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators un…
In this paper, we address an important question of the relationship between fluctuation theorems for the dissipated work $W_{d} = W-ΔF$ with general finite-time (like Jarzynski equality and Crooks relation) and infinite-time (like Gallavotti-Cohen theorem) drive protocols and their time-reversal symmetric versions. The relations between these kinds of fluctuation relations are uncovered based on the examples of a classical Markovian $N$-level system. Further consequences of these relations are discussed with respect to the possible experimental verifications.
At molecular scales, fluctuations play a significant role and prevent biomolecular processes from always proceeding in a preferred direction, raising the question of how limited amounts of free energy can be dissipated to obtain directed progress. We examine the system and process characteristics that efficiently break time-reversal symmetry at fixed energy loss; in particular for a simple model of a molecular machine, an intermediate energy barrier produces unusually high asymmetry for a given dissipation. We relate the symmetry-breaking factors found in this model to recent observations of b…
The two dimensional Spin-1 Blume-Capel ferromagnet is studied by Monte Carlo simulation with Metropolis algorithm. Starting from initial ordered spin configuration the reversal of magnetisation is investigated in presence of a magnetic field ($h$) applied in the opposite direction. The variations of the reversal time with the strength of single site anisotropy are investigated in details. The exponential dependence was observed. The systematic variations of the mean reversal time with positive and negative anisotropy was found. The mean macroscopic reversal time was observed to be linearly dep…
Directed transport in ratchets is determined by symmetry-breaking in a system out of equilibrium. A hallmark of rocking ratchets is current reversals: an increase in the rocking force changes the direction of the current. In this work for a bi-harmonically driven spatially symmetric rocking ratchet we show that a class of current reversal is precisely determined by symmetry-breaking, thus creating a link between dynamical and symmetry-breaking mechanisms.
Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics more general than those of bosons or fermions. Such anyons emerge as quasiparticles in fractional quantum Hall states and certain frustrated quantum magnets. Quantum liquids of anyons exhibit degenerate ground states where the degeneracy depends on the topology of the underlying surface. Here we present a novel type of continuous quantum phase transition in such anyonic quantum liquids that is driven by quantum fluctuations of topology. The critical state connecting two anyonic liquids on surfaces …
The thermodynamic uncertainty relation gives a lower bound on the amount of dissipation in a mesoscopic system. By considering the fluctuations in the hysteresis of the current -- the sum of the currents in the time-forward and time-reversed processes -- we extend this relation to systems with broken time-reversal symmetry, either due to the presence of odd state variables, odd driving field or due to explicit time-dependent driving that is time-reversal asymmetric. We illustrate our predictions on a dilute, weakly-interacting gas driven out of equilibrium by the slow compression of a piston a…
In this work, the ratchet dynamics of Brownian particles driven by an external sinusoidal (harmonic) force is investigated. The gating ratchet effect is observed when another harmonic is used to modulate the spatially symmetric potential in which the particles move. For small amplitudes of the harmonics, it is shown that the current (average velocity) of particles exhibits a sinusoidal shape as a function of a precise combination of the phases of both harmonics. By increasing the amplitudes of the harmonics beyond the small-limit regime, departures from the sinusoidal behavior are observed and…
We consider motion of a particle in a one-dimensional tilted ratchet potential subject to two-sided tempered stable Lévy noise characterised by strength $Ω$, fractional index $α$, skew $θ$ and tempering $λ$. We derive analytic solutions to the corresponding Fokker-Planck Lévy equations for the probability density. Due to the periodicity of the potential, we carry out reduction to a compact domain and solve for the analogue there of steady-state solutions which we represent as wrapped probability density functions. By solving for the expected value of the current associated with the particle mo…
We consider a deterministic chaotic ratchet model for which the driving force is designed to allow the rectification of current as well as the control of chaos of the system. Besides the amplitude of the symmetric driving force which is often used in this framework as control parameter, a phase has been newly included here. Exploring this phase, responsible of the asymmetry of the driven force, a number of interesting departures have been revealed. Remarkably, it becomes possible to drive the system into one of the following regime: the state of zero transport, the state of directed transport …
For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator or pump, is imposed in both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio of fluctuations between the output and the input current is obtained.…
An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of equilibrium by time-dependent forces or by coupling to large reservoirs of particles and energy. The symmetry relations are established for the exchange of energy and particles between the subsystem and its environment. These results have important consequences. In particular, generalizations of the Kubo formula and the Casimir-Onsager reciprocity relations …
Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Though there is no convergence on the origin of time's preferential direction, many researchers believe that the direction of time is towards increasing entropy. In this paper, we provide an alternate point of view. In driven-dissipative nonequilibrium systems forced at large scale, the energy flows from large scales to dissipative scales. This generic and multiscale process breaks time reversal symmetry and principle of detailed balance, thus can yield an…
