Related papers: Universal first-passage time statistics for quantu…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…
The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U(1) coset element. Analysis in terms of quantum…
We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…
Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…
The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact…
The distribution of the first-passage time (FPT)$T_a$ for a Brownian particle with drift $\mu$ subject to hitting an absorber at a level $a>0$ is well-known and given by its density $\gamma(t) = \frac{a}{\sqrt{2 \pi t^3} } e^{-\frac{(a-\mu…
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a…
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating…
How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…
In this paper we are interested to model quantum signal by statistical signal processing methods. The Gaussian distribution has been considered for the input quantum signal as Gaussian state have been proven to a type of important robust…
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…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
We study the transport of many partially distinguishable and possibly interacting particles under the action of repeated projective measurements on a target space and investigate how the particles' interference affects the mean first…
Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in…
A quantum mechanical theory is developed for the statistics of momentum transferred to the lattice by conduction electrons. Results for the electromechanical noise power in the semiclassical diffusive transport regime agree with a recent…