相关论文: Quantum Schroedinger bridges

We show that the Schr\"{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential…

Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between…

With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…

Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear…

The Schr\"odinger-Newton model describes self-gravitating quantum particles, and it is often cited to explain the gravitational collapse of the wave function and the localization of macroscopic objects. However, this model is completely…

A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of…

A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear stochastic wave equation.…

We modify the Schr\"{o}dinger equation in a way that preserves its main properties but makes use of higher order derivative terms. Although the modification represents an analogy to the Doebner-Goldin modification, it can differ from it…

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…

In this paper we are interested in unraveling the mathematical connections between the stochastic derivation of Schr\"odinger equation and ours. It will be shown that these connections are given by means of the time-energy dispersion…

Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…

Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but…

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic…

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…

It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…

The Schr\"odinger-Newton (SN) equation introduces a nonlinear self-gravitational term to the standard Schr\"odinger equation, offering a paradigmatic model for semiclassical gravity. However, the small deviations it predicts from standard…

A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from…