Related papers: Brownian motion and thermal capacity
The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from…
In a recent work, Fleischmann and Mueller (2004) showed the existence of a super-Brownian motion in R^d, d=2,3, with extra birth at the origin. Their construction made use of an analytical approach based on the fundamental solution of the…
A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length $\Lambda$ in the electric field $\mathscr{E}$ that pushes the particle to the surface is presented both in the canonical and…
Quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we…
Consider a large system of $N$ Brownian motions in $\R ^d$ fixed on a time interval $[0,\beta]$ with symmetrized initial and terminal conditions, under the influence of a trap potential. Such systems describe systems of bosons at positive…
Based on the Unruh effect, we calculate the critical acceleration for the Bose-Einstein condensation in a free complex scalar field at finite density in the Rindler space. Our model corresponds to an ideal gas performing constantly…
Starting from an analogy between the Planck-Einstein scale and the dual length scales in Ginzburg-Landau theory of superconductivity, and assuming that space-time is a condensate of neutral fermionic particles with Planck mass, we derive…
We first consider the additive Brownian motion process $(X(s_1,s_2),\ (s_1,s_2) \in \mathbb{R}^2)$ defined by $X(s_1,s_2) = Z_1(s_1) - Z_2 (s_2)$, where $Z_1$ and $Z_2 $ are two independent (two-sided) Brownian motions. We show that with…
In this study, we investigate the behavior of free inertial Active Brownian Particles (ABP) in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using…
A theory of Brownian motion is presented for an assembly of vortices. The attempt is motivated by a realization of Dyson' Coulomb gas in the context of quantum condensates. By starting with the time-dependent Landau-Ginzburg (LG) theory,…
We show that with probability 1, the trace B[0,1] of Brownian motion in space, has positive capacity with respect to exactly the same kernels as the unit square. More precisely, the energy of occupation measure on B[0,1] in the kernel…
We demonstrate that the energy density of an accelerated fermion gas evaluated within quantum statistical approach in Minkowski space is related to a quantum correction to the vacuum expectation value of the energy-momentum tensor in a…
We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argument uses a relation between integrals of special functions,…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
In this work, the notion of spacetime of maximal proper acceleration is motivated as a weak form to implement general covariance and a generalized form of Einstein's equivalence principle from a physical point of view and the fundamental…
We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in…
Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative…
Observation of the Brownian motion of a small probe interacting with its environment is one of the main strategies to characterize soft matter. Essentially two counteracting forces govern the motion of the Brownian particle. First, the…
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…
For every $d\geq 1$, we consider the $d$-dimensional Hermitian fractional Brownian motion (HfBm), that is the process with values in the space of $(d\times d)$-Hermitian matrices and with upper-diagonal entries given by complex fractional…