相关论文: Local Time Statistics and Permeable Barrier Crossi…

We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…

Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…

Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If…

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected recently for a SQUID ratchet dynamics (Spiechowicz J. & Luczka J. Phys. Rev. E 91, 062104 (2015)), the…

One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical…

While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different. Here we study the dynamics of polymers in a viscous medium containing…

We revisit the problem of Brownian diffusion with drift in order to study finite-size effects in the geometric Galton-Watson branching process. This is possible because of an exact mapping between one-dimensional random walks and geometric…

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses…

Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or…

We review and study a one-parameter family of functional transformations, denoted by $(S^{(\beta)})_{\beta\in \R}$, which, in the case $\beta<0$, provides a path realization of bridges associated to the family of diffusion processes…

Recent progress in experimental techniques such as single particle tracking allows to analyze both nonequilibrium properties and approach to equilibrium. There are examples showing that processes occurring at finite timescales are…

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…

We introduce a class of Markov coalescent processes on the continuous $d$-dimensional torus, in the most general setting of simultaneous multiple mergers, called the Brownian spatial coalescent. It is axiomatically defined through a…

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity…

Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…

We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the…

Relaxation to equilibrium of a drifted Brownian motion is quantified by a probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kernel of the Schr\"{o}dinger semigroup operator. Although seemingly devoid…

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective…