Related papers: Dynamical Lee-Yang zeros for continuous-time and d…
We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…
We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but…
The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity $e^{h\Delta\tau}$, and the Euclidean-time lattice spacing $\Delta\tau$ can…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Spatiotemporal evolution in the real Ginzburg-Landau equation is studied with space-time noise and a slowly increasing critical parameter. Analytical estimates for the characteristic size of the domains formed in a slow sweep through the…
We report on an experiment achieving the dynamical generation of non-Gaussian states of motion of a levitated optomechanical system. We access intrinsic Duffing-like nonlinearities by thermal squeezing of an oscillator's state of motion by…
We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic…
We discuss the stochastic process of creation and annihilation of particles, i.e., the $A^{n} \rightleftarrows B$ process in which $n$ particles $A$s and one particle $B$ are transformed to each other. Considering the case that the…
We present a prototype of behavior of glassy systems driven by quantum dynamics in a quenching protocol by analyzing the random energy model in a transverse field. We calculate several types of dynamical quantum amplitude and find a…
For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especially its characteristic time, for zero-range processes. The…
We investigate the life time distribution in one and two dimensional coarsening processes modelled by Ising - Glauber dynamics at zero temperature. We find that the life time distribution obeys a scaling ansatz, asymptotically. An…
The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
We study the driven dynamics of quantum coarsening. We analyze models of M-component rotors coupled to two electronic reservoirs at different chemical potentials that generate a current threading through the system. In the large M limit we…
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…