相关论文: Scattering Theory from a Bohmian Perspective

A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…

We consider deterministic self-propelled particles with anti-alignment interactions. An asymptotically exact kinetic theory for particle scattering at low densities is constructed by a non-local closure of the BBGKY-hierarchy, involving…

Harmonic generation in the scattered fields produced by a dielectric sphere coated with a time-varying conductive shell is studied using a Mie theory approach hybridized with conversion matrix methods. Analytic results are derived for plane…

The violation of Bell type inequalities in quantum systems manifests that quantum states cannot be described by classical probability distributions. Yet, Bohmian mechanics is a realistic, non-local theory of classical particle trajectories…

Quantum mechanics is the most successful theory to describe microscopic phenomena. It was derived in different ways over the past 100 years by Heisenberg, Schr\"{o}dinger, and Feynman. At the same time, other interpretations have been…

A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.

Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the…

It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is…

The small angle scattering (by a gravitational field) of classical and quantum particles is considered and compared. It is suggested that the differences in small angle scattering of particles with spin 0, 1, 2 are due to the nonzero…

Bohmian mechanics is a deterministic theory of quantum mechanics that is based on a set of n velocity functions for n particles, where these functions depend on the wavefunction from the n-body time-dependent Schroedinger equation. It is…

It is shown that quantum entanglement is the only force able to maintain the fourth state of matter, possessing fixed shape at an arbitrary volume. Accordingly, a new relativistic Schrodinger equation is derived and transformed further to…

The paper presents an inquiry into the question regarding the compatibility of Bohmian mechanics, intended as a non-local theory of moving point-like particles, with background independence. This issue is worth being investigated because,…

Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…

Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…

In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical…

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…

"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…

We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…

We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…

The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…