Related papers: Nonperturbative Stochastic Quantization of the Hel…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
I review the realistic interpretation of several typically quantum phenomena using a heuristic approach that rests on the assumption that the electromagnetic quantum vacuum is a stochastic field. I include the particle behaviour of light,…
This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…
The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…
We propose a simple stochastic model of cascading transport in wave number space to clarify the origin of intermittent behavior of fully-developed fluid turbulence. In spite of lack of nonlinearity and viscosity the model gives non-Gaussian…
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this…
This letter presents a non-parametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion…
One challenge in developing a statistical field theory of turbulence is the analysis of the functional equations that govern the complete statistics of the flow field. Simplified models of turbulence may help to develop such a statistical…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
We consider traffic flow models at different scales of observation. Starting from the well known hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models using…
Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical…
We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit shape as the mesh size tends to 0. We further…
We develop a unified stochastic framework in which a velocity- and helicity-reversing Poisson process gives rise to the Telegrapher's equation. Analytic continuation to the complex plane results in Dirac-like evolution equations for…
A geometric approach to the friction phenomena is presented. It is based on the holographic view which has recently been popular in the theoretical physics community. We see the system in one-dimension-higher space. The heat-producing…
Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties…
A geometric approach to some quantum statistical systems (including the harmonic oscillator) is presented. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum…
We apply the modified triplectic formalism for quantizing several popular gauge models - non-abelian antisymmetric tensor field model, W2-gravity and two-dimensional gravity with dynamical torsion. The explicit solutions are obtained for…
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an…
We construct a new model for relativistic particle on the noncommutative surface in $(2+1)$ dimensions, using the symplectic formalism of constrained systems and embedding the model on an extended phase space. We suggest a short cut to…
The procedure of nonperturbative quantization \`a la Heisenberg is considered. A few applications, features, perspectives, problems, and so on are considered. The comparison with turbulence modeling is performed.