This paper is a generalization of the models considered in [J. Stat. Phys. 128,1365 (2007)]. Using an analogy with free fermions, we compute exactly the large deviation function (ldf) of the energy injected up to time $t$ in a one-dimensional dissipative system of classical spins, where a drift is allowed. The dynamics are T=0 asymmetric Glauber dynamics driven out of rest by an injection mechanism, namely a Poissonian flipping of one spin. The drift induces anisotropy in the system, making the model more comparable to experimental systems with dissipative structures. We discuss the physical content of the results, specifically the influence of the rate of the Poisson injection process and the magnitude of the drift on the properties of the ldf. We also compare the results of this spin model to simple phenomenological models of energy injection (Poisson or Bernoulli processes of domain wall injection). We show that many qualitative results of the spin model can be understood within this simplified framework.
Using fermionic techniques, we compute exactly the large deviation function (ldf) of the time-integrated injected power in several one-dimensional dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics supplemented by an injection mechanism, which is taken as a Poissonian flipping of one particular spin. We discuss the physical content of the results, specifically the influence of the rate of the Poisson process on the properties of the ldf.
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a nontrivial stationary state. We discuss the results and in particular draw from our results some general features shared by these distributions in realistic dissipative systems.
We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where the energy is injected at the boundary and dissipated in the bulk. The large deviation functional for the particle currents flowing through the system is computed and some physical consequences are discussed: the mechanism for local current fluctuations, dynamical phase transitions, the fluctuation-relation.
In this paper, we consider the Langevin equation from an unusual point of view, that is as an archetype for a dissipative system driven out of equilibrium by an external excitation. Using path integral method, we compute exactly the probability density function of the power (averaged over a time interval of length $τ$) injected (and dissipated) by the random force into a Brownian particle driven by a Langevin equation. The resulting distribution, as well as the associated large deviation function, display strong asymmetry, whose origin is explained. Connections with the so-called ``Fluctuation…
We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme…
A granular gas may be modeled as a set of hard-spheres undergoing inelastic collisions; its microscopic dynamics is thus strongly irreversible. As pointed out in several experimental works bearing on turbulent flows or granular materials, the power injected in a dissipative system to sustain a steady-state over an asymptotically large time window is a central observable. We describe an analytic approach allowing us to determine the full distribution of the power injected in a granular gas within a steady-state resulting from subjecting each particle independently either to a random force (stoc…
We address, on the example of a simple solvable model, the issue of whether the stationary state of dissipative systems converges to an equilibrium state in the low dissipation limit. We study a driven dissipative Zero Range Process on a tree, in which particles are interpreted as finite amounts of energy exchanged between degrees of freedom. The tree structure mimicks the hierarchy of length scales; energy is injected at the top of the tree ('large scales'), transferred through the tree and dissipated mostly in the deepest branches of the tree ('small scales'). Varying a parameter characteriz…
We report the statistical properties of the fluctuations of the energy flux in an electronic RC circuit driven with a stochastic voltage. The fluctuations of the power injected in the circuit are measured as a function of the damping rate and the forcing parameters. We show that its distribution exhibits a cusp close to zero and two asymmetric exponential tails, the asymmetry being driven by the mean dissipation. This simple experiment allows to capture the qualitative features of the energy flux distribution observed in more complex dissipative systems. We also show that the large fluctuation…
Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary driving is increased, this minimal classical model recovers the main features of the "dissipative phase transition" seen experimentally. Between the transmitting and non-transmitting regimes on either side of this transition (which support ballistic and diffusive energy transport respectively), we observe additional dynamical regimes of interest. These include a r…
We define a characteristic energy density based on the measurement of the two first moments of the extrinsic injected power smoothed over time. Using the stationarity, we show that this definition characterizes an energy per degrees freedom of the intrinsic dissipation. Our framework can be applied to systems in contact with thermostats put out of equilibrium by an external driving but it holds also for intrinsically dissipative macroscopic systems that go at rest when the forcing is stopped. Moreover, we are not concerned about the fluctuations around zero of the smoothed injected power that …
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a dissipative process. We obtain our results in a random quantum circuit model that is constrained to have a conservation law. We find that a generic spreading operator consists of two parts: (i) a conserved part which comprises the wei…
Entanglement Hamiltonians in dissipative free fermions and the time-dependent GGE
SISSA（的里雅斯特高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Dipartimento di Fisica dell’Università di Pisa（比萨大学物理系）；INFN Sezione di Pisa（意大利国家核物理研究所比萨分部）
In this article we present an experimental study of the statistical properties for the injected power fluctuations of a dissipative system as a function of external environmental conditions. A Brownian motion analog is implemented using a series resistor and capacitor circuit with an Orstein-Ulhenbeck forcing. This system is tested in a controlled thermal bath at the laboratory, setting the bath temperature and different bath atmospheric pressures. The non-equilibrium system shows a higher correlation factor between the external forcing and the system response with increasing bath atmospheric …
Impact of thermal and dissipative effects in a periodically-kicked quantum battery
Instituto de Ciencia de Materiales de Madrid ICMM-CSIC（马德里材料科学研究所）；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物理理论系）
We prove an upper bound on the diffusivity of a general local and translation invariant quantum Markovian spin system: $D \leq D_0 + \left(α\, v_\text{LR} τ+ β\, ξ\right) v_\text{C}$. Here $v_\text{LR}$ is the Lieb-Robinson velocity, $v_\text{C}$ is a velocity defined by the current operator, $τ$ is the decoherence time, $ξ$ is the range of interactions, $D_0$ is a microscopically determined diffusivity and $α$ and $β$ are precisely defined dimensionless coefficients. The bound constrains quantum transport by quantities that can either be obtained from the microscopic interactions ($D_0, v_\te…
The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequlibrium statistical physics consisting of inertial Brownian particle diffusing in a tilted periodic potential by exploiting the state of t…
We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permit…
Scaling features in the Olami-Feder-Christensen model
Govt. College for Women, Prade Ground Jammu, Jammu and Kashmir 180001, India（政府女子学院）；Department of Physics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India（贝拿勒斯印度大学科学研究所）
We use the framework of sample space reducing processes (SSR) as an alternative to Boltzmann equation based approaches, to derive the energy and velocity distribution functions of an inelastic gas in a box as an example for a dissipative, driven system. SSR processes do not assume molecular chaos and are characterized by a specific type of eigenvalue equation whose solutions represent stationary distribution functions. The equations incorporate the geometry of inelastic collisions and a driving mechanism in a transparent way. Energy is injected by boosting particles that hit the walls of the c…
Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a non-vanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a superdiffusive ballistic current of order one, independent of s…
