Related papers: Kramers' law: Validity, derivations and generalisa…
We develop a kinetic theory of Brownian particles with long and short range interactions. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean…
Computing reactive trajectories and free energy (FE) landscapes associated to rare event kinetics is key to understanding the dynamics of complex systems. The analysis of the FE surface on which the underlying dynamics takes place has…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
In this article we address the problem of quantum tunneling of a non-Markovian Brownian particle away from thermal equilibrium. We calculate the Kramers escape rate at low temperature (including the zero temperature case) in the…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
The generalized Langevin equation with an exponential kernel is used to analyze memory effects on the optimal work done by a Brownian particle in a heat bath and subjected to a harmonic moving potential. The generalized overdamping scenario…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
We investigate time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to whole fusion-fission dynamical process and can be…
In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems but also some $\lambda$-transient ones,…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
We show that the fraction of time a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by L\'evy for Brownian motion. Stochastic currents with long streaks above or below their average…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
We shall present a new strategy for handling mean field limits of quantum mechanical systems. The new method is simple and effective. It is simple, because it translates the idea behind the mean field description of a many particle quantum…
Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then…