Related papers: Power Law Blinking Quantum Dots: Stochastic and Ph…
In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field {where the sojourn time in one of the two states are distributed according to a given…
We study a particle immersed in a heat bath, in the presence of an external force which decays at least as rapidly as $1/x$, for example a particle interacting with a surface through a Lennard-Jones or a logarithmic potential. As time…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
We study generalised anomalous diffusion processes whose diffusion coefficient $D(x,t)\sim D_0|x|^{\alpha}t^{\beta}$ depends on both the position $x$ of the test particle and the process time $t$. This process thus combines the features of…
It is a common assumption that quantum systems with time reversal invariance and classically chaotic dynamics have energy spectra distributed according to GOE-type of statistics. Here we present a class of systems which fail to follow this…
Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity $D(x)$. We investigate the ergodic and non-ergodic behavior of these processes in an arbitrary potential well $U(x)$…
Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a…
We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the…
Small (but still containing many atoms) quantum systems (traditionally termed nano-systems) are dramatically different from their macroscopic or genuine microscopic (atomic) cousins. Microscopic molecular systems (with a few atoms) obey a…
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…
We study a Schr{\"o}dinger equation modeling the dynamics of an electron in a crystal in the asymptotic regime of small wavelength comparable to the characteristic scale of the crystal. Using Floquet Bloch decomposition, we obtain a…
It is shown that in systems with time-dependent and/or spatially nonuniform temperature $T(t,x)$, (i) most of the transport processes is weakly non-ergodic, and (ii) the diffusion (Brownian motion, BM) is anomalous. A few examples of simple…
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without…
Recent advances in electron microscopy trigger the question whether attosecond electron diffraction can resolve atomic-scale electron dynamics in crystalline materials in space and time. Here we explore the physics of the relevant…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…
Despite its intrinsic non-equilibrium origin, thermoelectricity in nanoscale systems is usually described within a static scattering approach which disregards the dynamical interaction with the thermal baths that maintain energy flow. Using…
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy…
Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of a broken ergodicity in long-range interacting systems. For the widely studied Hamiltonian Mean-Field model, the lifetime of some QSSs has been shown to diverge…
We investigate both analytically and by computer simulations the ensemble averaged, time averaged, non-ergodic, and ageing properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic…