相关论文: Explicit Solution of the Time Evolution of the Wig…

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in…

The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical…

We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…

We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…

Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The…

We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a…

We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…

New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…

The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner…

As a profound example of spontaneous motion, we analyze the motion of a camphor particle on a water surface. The motion is modeled as an initial-boundary value problem for a coupled nonlinear system of a diffusion equation and an ordinary…

The Wiener-Hopf equations are a Toeplitz system of linear equations that naturally arise in several applications in time series. These include the update and prediction step of the stationary Kalman filter equations and the prediction of…

The extended Weber location problem is a classical optimization problem that has inspired some new works in several machine learning scenarios recently. However, most existing algorithms may get stuck due to the singularity at the data…

We study the Wigner kernel and the Gabor matrix associated with the propagators of a broad class of linear evolution equations, including the complex heat, wave, and Hermite equations. Within the framework of time-frequency analysis, we…

In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong…

The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…

A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…

In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed…

It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space…

We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…