Related papers: Brownian Motion and Quantum Mechanics
We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
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, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Quantum brownian motion is a fundamental model for a proper understanding of open quantum systems in different contexts such as chemistry, condensed matter physics, bio-physics and opto- mechamics. In this paper we propose a novel approach…
Brownian oscillator, i.e. a micron-sized or smaller particle trapped in a thermally fluctuating environment is studied. The confining harmonic potential can move with a constant velocity. As distinct from the standard Langevin theory, the…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
The dynamics of a kicked quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is…
In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the…
Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy.…
Quantum mechanics introduces the possibility for particles to move in a direction opposite to their momentum -- a counter-intuitive and classically impossible phenomenon known as quantum backflow. The magnitude of this effect is relatively…
Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…
We study stochastic thermodynamics of over-damped Brownian motion in a flowing fluid. Unlike some previous works, we treat the effects of the flow field as a non-conservational driving force acting on the Brownian particle. This allows us…
We present a translation of the 1933 paper by R. F\"urth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. This paper opened in some sense the way to the stochastic methods of quantization…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…
We establish that the exact quantum dynamics of a Brownian particle in the Caldeira-Leggett model can be mapped, at any temperature, onto a classical, non-Markovian stochastic process in phase space. Starting from a correlated thermal…
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…