相关论文: Levy Flights over Quantum Paths
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal…
We show that the Bergman, Szego, and Poisson kernels associated to a finitely connected domain in the plane are all composed of finitely many easily computed functions of one variable. The new formulas give rise to new methods for computing…
Quantum electrodynamics predicts x-ray diffractions under a high-intensity laser field via virtual charged particles, and this phenomenon is called as vacuum diffraction (VD). In this paper, we derive a new formula to describe VD in a…
We prove a product formula for the remaining cases of the weighted enumeration of self-complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the…
We discuss correlations between two particles in jets at high energy colliders and exactly solve the MLLA evolution equations in the small x limit. We thus extend the Fong-Webber analysis to the region away from the hump of the single…
A kink-based expression for the canonical partition function is developed using Feynman's path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on…
For a refracted spectrally negative Levy process, we find some new and fantastic formulas for its q-potential measures without killing. Unlike previous results, which are written in terms of the known q-scale functions, our formulas are…
The logical consistency of a description of Quantum Theory in the context of General Relativity, which includes Minimal Coupling Principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will…
We review some recent developments in white noise analysis and quantum probability. We pay a special attention to spaces of test and generalized functionals of some L\'evy white noises, as well as as to the structure of quantum white noise…
We demonstrate the non-spreading behavior of Airy wave packets utilizing the Feynman path integral formulation of a linear potential, the Airy functions' zeros correspondence to heavy-meson mass spectroscopy, and their implications to the…
We find kernel functions of the $q$-Heun equation and its variants. We apply them to obtain $q$-integral transformations of solutions to the $q$-Heun equation and its variants. We discuss special solutions of the $q$-Heun equation from the…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
Linear combination of Hamiltonian simulation (LCHS) connects the general linear non-unitary dynamics with unitary operators and serves as the mathematical backbone of designing near-optimal quantum linear differential equation algorithms.…
Accurate description of deformed atomic nuclei by the orbital-free density functional theory has been a longstanding textbook challenge, due to the difficulty in accounting for the intricate quantum shell effects that are present in such…
We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…
We study symmetric L\'evy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the L\'evy process. Incorporating the boundary…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions…
In relativistic heavy-ion collisions, studying jet correlations and their dependence on the angle of emission with respect to the reaction plane can be used to shed light on the path length dependence of the energy lost by the jet. In this…