Related papers: Exact relativistic time evolution for a step poten…
In the present letter, the solutions of the Klein Gordon equation in the space time of an infinite domain wall is studied. It is shown that the horizon is an special region, where initial conditions (scattering conditions) at asymptotic…
We present a new axially symmetric monochromatic free-space solution to the Klein-Gordon equation propagating with a superluminal group velocity and show that it gives rise to an imaginary part of the causal propagator outside the light…
In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine-Gordon equation and the non-integrable $\phi^4$ model. We focus, in particular, on two of their prototypical solutions, namely the kink-like…
For the first time the exact vortex solution of the Cauchy problem in unbounded space is obtained for the three-dimensional Euler-Helmholtz (EH) equation in the case of a nonzero-divergence velocity field for an ideal compressible medium.…
We discuss the non-relativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, highlighting and clarifying several subtleties. We study the following topics: (a)…
It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically,…
We test the validity of Isaacson's formula which states that high frequency and low amplitude gravitational waves behave as a radiation fluid on average. For this purpose, we numerically construct a solution of the vacuum Einstein equations…
The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a single-particle relativistic quantum mechanical equation that defines unique time-like particle trajectories. The particle trajectories are determined by the…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients we derive an evolution equation for the discontinuity front of the…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
We consider random walks in Dirichlet environment (RWDE) on $\Z ^d$, for $ d \geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, ..., \alpha_{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We…
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…
Starting from the local-in-time classical solution to the compressible Euler system with impermeable boundary condition in half-space, by employing the coupled weak viscous layers (governed by linearized compressible Prandtl equations with…
In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…
We derive a uniform exponential decay of the total energy for the nonlinear Klein-Gordon equation with a damping around spatial infinity in the whole space or in the exterior of a star shaped obstacle.
Time-dependent analytical solutions to Schr\"{o}dinger's equation with quantum shutter initial conditions are used to investigate the issue of the tunneling time of forerunners in rectangular potential barriers. By using a time-frequency…
Consider a non-relativistic quantum particle with wave function inside a region $\Omega\subset \mathbb{R}^3$, and suppose that detectors are placed along the boundary $\partial \Omega$. The question how to compute the probability…