Related papers: The Open Quantum Brownian Motion and continual mea…
In this paper we investigate the Quantum Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless scalar field in (3 + 1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet, Neumann, mixed…
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…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
A new approach to the generalised Brownian motion introduced by M. Bozejko and R. Speicher is described, based on symmetry rather than deformation. The symmetrisation principle is provided by Joyal's notions of tensorial and combinatorial…
The analysis of local minima in time series data and random landscapes is essential across numerous scientific disciplines, offering critical insights into system dynamics. Recently, Kundu, Majumdar, and Schehr derived the exact…
Distribution functions defined in accord with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet…
We present a method for obtaining evolution operators for linear quantum trajectories. We apply this to a number of physical examples of varying mathematical complexity, in which the quantum trajectories describe the continuous projection…
The goal of this paper is twofold: we study metric measure spaces $(X,d,m)$ with variable lower bounds for the Ricci curvature and we study pathwise coupling of Brownian motions. Given any lower semicontinuous function $k:X\to \mathbb R$ we…
The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing…
We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.
A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions…
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and L\'evy processes which summarize and extend the literature on these subjects. The results surveyed include point…
This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
Brownian motion with darning (BMD in abbreviation) is introduced and studied in [4] and [5, Chapter 7]. Roughly speaking, BMD travels across the "darning area" at infinite speed, while it behaves like a regular BM outside of this area. In…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
We apply the restricted-path-integral (RPI) theory of non-minimally disturbing continuous measurements for correct description of frictional Brownian motion. The resulting master equation is automatically of the Lindblad form, so that the…
It is known that in a stationary Brownian queue with both arrival and service processes equal in law to Brownian motion, the departure process is a Brownian motion, that is, Burke's theorem in this context. In this short note we prove…