相关论文: Exact relativistic time evolution for a step poten…
We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle, starting in a convex set $X\subset\mathbb{R}^d$ at $t=0$, to…
We consider a Fokker-Planck equation which is coupled to an externally given time-dependent constraint on its first moment. This constraint introduces a Lagrange-multiplier which renders the equation nonlocal and nonlinear. In this paper we…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…
We consider the Klein-Gordon equation in the non-relativistic limit regime, i.e. the speed of light c tending to infinity. We construct an asymptotic expansion for the solution with respect to the small parameter depending on the inverse of…
The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e. supporting an infinite electric field), of height U> E + m - due to the many-body nature of the Dirac equation…
We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is governed by a free boundary problem. The particles evolve…
Highly localized explicit solutions to multidimensional wave and Klein--Gordon--Fock equations are presented. Their Fourier transform is also found explicitly. Solutions depend on a set of parameters, and demonstrate astigmatic properties.…
We show that space-time modulation of electromagnetic potentials enables Klein tunneling far below the static threshold. The derived kinematics reveal oblique transitions that can connect opposite-energy continua without requiring their…
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the…
We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism…
We investigate Klein tunneling through finite potential barriers with space-time resolved solutions to relativistic quantum field equations. We find that no particle actually tunnels through a finite supercritical barrier, even in the case…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component…
We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski-Maliborski on the existence of time periodic solutions to the spherically symmetric…
A family of travelling wave solutions to the Fisher-KPP equation with speeds $c=\pm 5/\sqrt{6}$ can be expressed exactly using Weierstrass elliptic functions. The well-known solution for $c=5/\sqrt{6}$, which decays to zero in the…
Consider the Navier-Stokes flow past a rotating obstacle with a general time-dependent angular velocity and a time-dependent outflow condition at infinity. After rewriting the problem on a fixed domain, one obtains a non-autonomous system…
While the constant radial acceleration problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to a time parameter, has eluded…
In this paper we present the power series solution of the Klein-Gordon equation in the spacetime background of a gravitational wave with amplitude that decays with distance from the source. The resulting solution describes the interaction…