Related papers: Classical and quantum concepts of probability appl…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
Liouville transformations map in a rigorous manner one Schr\"odinger equation into another, with a changed scattering potential. They are used here to transform quantum reflection of an atom on an attractive well into reflection of the atom…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as…
We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our…
We extend the recently developed classical theory for the optical response of a single-layer crystal to bilayers. We account for the interaction between the two atomic planes and the multiple reflections inside the crystals. We show how to…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing)…
We consider classical dynamics of a 1D system of $N$ particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…
We analyze statistical probability distributions of intensities collected by diffraction techniques like Low-Energy Electron Diffraction. A simple theoretical model based in hard-sphere potentials and LEED formalism is investigated for…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…
We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment.…
The X-ray radiation delay law dependence on the diffraction asymmetry parameters is analyzed. It is shown that the use of subpicosecond pulses allows to observe the time delay of pulse in crystal phenomenon and to investigate the delay law…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix…