Gamma-burst emission from neutron-star accretion

A model for emission of the hard photons of gamma bursts is presented. The model assumes accretion at nearly the Eddington limited rate onto a neutron star without a magnetic field. Initially soft photons are heated as they are compressed between the accreting matter and the star. A large electric field due to relatively small charge separation is required to drag electrons into the star with the nuclei against the flux of photons leaking out through the accreting matter. The photon number is not increased substantially by Bremsstrahlung or any other process. It is suggested that instability in an accretion disc might provide the infalling matter required

Diffusion and subdiffusion of interacting particles on comb-like structures

We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only, and, in the limit of high density of particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior $\sim t^{3/4}$. At longer times, a second regime is observed, where standard diffusion is recovered, with a surprising non analytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like Continuous Time Random Walk description, we unveil a rich and complex scenario, with several successive subdiffusive regimes, resulting from the coupling between the inhomogeneous comb geometry and particle interactions. Remarkably, the presence of hard-core interactions speeds up the TP motion along the backbone of the structure in all regimes.Comment: 5 pages, 3 figures + supplemental materia

Scaling properties of field-induced superdiffusion in Continous Time Random Walks

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.Comment: 17 pages, 8 figures, Proceedings of the Conference "Small system nonequilibrium fluctuations, dynamics and stochastics, and anomalous behavior", KITPC, Beijing, Chin

Rare events and scaling properties in field-induced anomalous dynamics

We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long spatial tails and strong anomalous superdiffusion.Comment: 11 pages, 3 figure

Non-equilibrium fluctuations in a driven stochastic Lorentz gas

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production \Delta s_tot. One is the entropy production of the medium \Delta s_m, which is equal to the energy exchanged with the scatterers, divided by a parameter \theta, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by \theta. At small E, a good collapse of the two distributions is found: in this case the two quantities also verify the Fluctuation Relation (FR), indicating that both are good approximations of \Delta s_tot. Differently, for large values of E, the fluctuations of W violate the FR, while \Delta s_m still verifies it.Comment: 6 pages, 4 figure

Microscopic theory for negative differential mobility in crowded environments

We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.Comment: 5 pages, 2 figures + supplemental materia

On anomalous diffusion and the out of equilibrium response function in one-dimensional models

We study how the Einstein relation between spontaneous fluctuations and the response to an external perturbation holds in the absence of currents, for the comb model and the elastic single-file, which are examples of systems with subdiffusive transport properties. The relevance of non-equilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down, as is known to happen in systems with standard diffusion. In the case of the comb model, a general relation, which has appeared in the recent literature, between the response function and an unperturbed suitable correlation function, allows us to explain the observed results. This suggests that a relevant ingredient in breaking the Einstein formula, for stationary regimes, is not the anomalous diffusion but the presence of currents driving the system out of equilibrium.Comment: 10 pages, 4 figure

Entropy production for velocity-dependent macroscopic forces: the problem of dissipation without fluctuations

In macroscopic systems, velocity-dependent phenomenological forces $F(v)$ are used to model friction, feedback devices or self-propulsion. Such forces usually include a dissipative component which conceals the fast energy exchanges with a thermostat at the environment temperature $T$, ruled by a microscopic Hamiltonian $H$. The mapping $(H,T) \to F(v)$ - even if effective for many purposes - may lead to applications of stochastic thermodynamics where an $incomplete$ fluctuating entropy production (FEP) is derived. An enlightening example is offered by recent macroscopic experiments where dissipation is dominated by solid-on-solid friction, typically modelled through a deterministic Coulomb force $F(v)$. Through an adaptation of the microscopic Prandtl-Tomlinson model for friction, we show how the FEP is dominated by the heat released to the $T$-thermostat, ignored by the macroscopic Coulomb model. This problem, which haunts several studies in the literature, cannot be cured by weighing the time-reversed trajectories with a different auxiliary dynamics: it is only solved by a more accurate stochastic modelling of the thermostat underlying dissipation.Comment: 6 pages, 3 figure