Related papers: Quantum Dissipation versus Classical Dissipation f…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
This note derives the stochastic differential equations and partial differential equation of general hybrid quantum--classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this…
In this paper we study Doob's transform of fractional Brownian motion (FBM). It is well known that Doob's transform of standard Brownian motion is identical in law with the Ornstein-Uhlenbeck diffusion defined as the solution of the…
This note is answering an old questioning about the F\'{e}nyes-Nelson stochastic mechanics. The Brownian nature of the quantum fluctuations, which are associated to this mechanics, is deduced from Feynman's interpretation of the Heisenberg…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
We examine spectral equilibration of quantum chaotic spectra to universal statistics, in the context of the Brownian motion model. Two competing time scales, proportional and inversely proportional to the classical relaxation time, jointly…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
The Langevin equation with multiplicative noise and state-dependent transport coefficient has to be always complemented with the proper interpretation rule of the noise, such as the Ito and Stratonovich conventions. Although the…
Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion…
An equation for the reduced density matrix which describes a free particle, that is interacting with a linearly dissipative medium, is derived using the total Hamiltonian, and without resorting to any artificial model. A Master equation is…
The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
We use the stochastic quantization method to construct a supersymmetric version of the quantum spherical model. This is based on the equivalence between the Brownian motion described by a Langevin equation and the supersymmetric quantum…