相关论文: Stochastic Processes and the Dirac Equation with E…

The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…

Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the…

In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…

We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here.…

In this paper we address the one-dimensional problem of stochastic renewal in different damping environments. An ensemble of particles with some specified initial distribution in phase space are allowed to evolve stochastically till a…

An overview is given of recent developments in the field of Dirac equations generalized to curved space-times. An illustrative discussion is provided. We conclude with a variation of Dirac's large-number hypothesis which relates a number of…

The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary timescale, and the corresponding equilibrium free energy difference, is generalized to quantum systems. Using the…

Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…

When pressure is not negligible in comparison with energy density, the external gravitational field and the motion of particles in it are modified. For spherically symmetric body two effective mass parameters determine the external…

A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…

Transport of a particle in a spatially periodic harmonic potential under the influence of a slowly time-dependent unbiased periodic external force is studied. The equations of motion are the same as in the problem of a slowly forced…

We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…

We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…

The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…

We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional and the rates are equal to the…

We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We…

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave…