相关论文: Quantum Dynamics as a Stochastic Process

The Heisenberg equations of motion for a quantum particle of mass $m$ are deduced from the infinitesimal qr-number equations of motion for the particle. The infinitesimal qr-number equations, and hence the standard quantum mechanical…

The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…

Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…

A particle subjected to a fluctuating force originated from its interaction with an external quantum system undergoes quantum Brownian motion. This phenomenon is investigated in detail for the case of a particle confined by a harmonic…

The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…

A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…

We explore analytically the quantum dynamics of a point mass pendulum using the Heisenberg equation of motion. Choosing as variables the mean position of the pendulum, a suitably defined generalised variance and a generalised skewness, we…

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…

Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been…

Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…

The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…

The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…

The simple algorithm for the simulation and visualization of non relativistic quantum dynamics is proposed that is based on a collective behavior of classical particles. Any quantum particle is represented as the swarm of its classical…

Stochastic phenomena occurring within charged particle beams can be handled using the Vlasov-Fokker-Planck generalization of the Vlasov equation. In particular, this non-deterministic approach can deal with effects due to Coulomb scattering…

Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…

In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special…

Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation…

The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…