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The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the…
Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed…
The microscopic origin of dissipation of a driven quantum many body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation-dissipation theorem and we observe also…
We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in bcc-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a new self…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given `binding potential'. The…
This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known…
In this note, we recall the definition of the binary branching model with Moran type interactions (BBMMI) introduced in [8]. In this interacting particle system, particles evolve, reproduce and die independently and, with a probability that…
The time evolution of the Wigner distribution function for a single-particle excitation in a Fermi system was studied within the framework of the diffusion approximation of kinetic theory by numerically solving a nonlinear diffusion…
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes…
We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a…
Two-dimensional (2D) spectroscopy provides information about dissipative processes subsequent to electronic excitation, which play a functional role in energy harvesting materials and devices. This technique is particularly sensitive to…
Models of adhesion of extended particles on linear and planar substrates are of interest in interpreting surface deposition in colloid, polymer, and certain biological systems. An introduction is presented to recent theoretical advances in…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
An intriguing phenomenon in non-equilibrium quantum thermodynamics is the asymmetry of thermal processes. Relaxation to thermal equilibrium is the most important dissipative process, being a key concept for the design of heat engines and…
The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding…
Diffusion-based posterior samplers use pretrained diffusion priors to sample from measurement- or reward-conditioned posteriors, and are widely used for inverse problems. Yet their theoretical behavior remains poorly understood: even with…
This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a general L\'evy process and the switching part depends on the jump…