Related papers: Efficient circular Dyson Brownian motion algorithm
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein-Uhlenbeck process for active speed generation. Using a…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds…
Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian…
The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability... The usual procedure is to use discretiza-tion schemes…
In this paper we investigate the class of grey Brownian motions $B_{\alpha,\beta}$ ($0<\alpha<2$, $0<\beta\leq1$). We show that grey Brownian motion admits different representations in terms of certain known processes, such as fractional…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
During training, weight matrices in machine learning architectures are updated using stochastic gradient descent or variations thereof. In this contribution we employ concepts of random matrix theory to analyse the resulting stochastic…
This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g.…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
In colloidal systems, Brownian motion emerges from the massive separation of time and length scales associated to characteristic dynamics of the solute and solvent constituents. This separation of scales produces several temporal regimes in…
We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their properties, and we show how they arise from particle systems with…
Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes. Here, we report the…
In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in…
We present a method to design driving protocols that achieve fast thermal equilibration of a system of interest using techniques inspired by machine learning training algorithms. For example, consider a Brownian particle manipulated by…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
Recently, dispersionless (coherent) motion of (noninteracting) massive Brownian particles, at intermediate time scales, was reported in a sinusoidal potential with a constant tilt. The coherent motion persists for a finite length of time…