Related papers: Curing the Self-Force Runaway Problem in Finite-Di…
We develop a comprehensive framework in which the existence of solutions to the semiclassical Einstein equation (SCE) in cosmological spacetimes is shown. Different from previous work on this subject, we do not restrict to the conformally…
We consider the self-force acting on a pointlike (electromagnetic or conformal-scalar) charge held fixed on a spacetime with a spherically-symmetric mass distribution of constant density (the Schwarzschild star). The Schwarzschild interior…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…
The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
The paper addresses an escape of a classical particle from a potential well under harmonic forcing. Most dangerous/efficient escape dynamics reveals itself in conditions of 1:1 resonance and can be described in the framework of isolated…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
In cosmological first-order phase transitions, the microscopic interaction of the phase transition fronts with non-equilibrium plasma particles manifests itself macroscopically as friction forces. In general, it is a nontrivial problem to…
This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Land\'e--Thomas, and Podolsky. We rigorously derive a world-line integral expression for the…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
We present the coisotropic embedding theorem as a tool to provide a solution for the inverse problem of the calculus of variations for a particular class of implicit differential equations, namely the equations of motion of free…
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are…
We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation,…
We study the exit-time from a domain of a self-interacting diffusion, where the Brownian motion is replaced by $\sigma B_t$ for a constant $\sigma$. The first part of this work consists in showing that the rate of convergence (of the…
We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes…
Solving large-scale eigenvalue problems poses a significant challenge due to the computational complexity and limitations on the parallel scalability of the orthogonalization operation, when many eigenpairs are required. In this paper, we…
We compute the electromagnetic self-force acting on a charged particle held in place at a fixed position r outside a five-dimensional black hole described by the Schwarzschild-Tangherlini metric. Using a spherical-harmonic decomposition of…
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous…