Related papers: Stable Boundary Conditions and Discretization for …
We consider a microscopic model of an inhomogeneous environment where an arbitrary quantum system is locally coupled to a harmonic bath via a finite-range interaction. We show that in the overdamped regime the position distribution obeys a…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
In the framework of instantaneous approximations to the Bethe-Salpeter formalism for the description of bound states within quantum field theories, depending on the Lorentz structure of the Bethe-Salpeter interaction kernel the solutions of…
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…
By integrating the pressure equation at the surface of a self coupled curvilinear boundary, one may obtain asymptotic estimates of energy shifts, which is especially useful in lattice QCD studies of nonrelativistic bound states. Energy…
The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…
We obtain the squeezed coherent states (SCS) for a free particle with exponentially time-varying mass. We write these states in terms of the squeeze and displacement parameters on the time-independent Fock states. Thus, we find a condition…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
The Schr\"odinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a $C^1$ bounded domain, subject to a large external potential $\Phi(x)$…
The paper presents an analytical approach for predicting the safe basins (SB) in a plane of initial conditions (IC) for escape of classical particle from the potential well under harmonic forcing. The solution is based on the approximation…
The observation of Planckian scattering, often inferred from Drude fits in strongly correlated metals, raises the question of how to extract an intrinsic timescale from measurable quantities in a model-independent way. We address this by…
The two-fermion bound system is an attractive subject of atomic and sub-atomic physics. Despite these systems are rather simple the study of two-particle bound states is challenging and still remains a source of progress in quantum theory.…
In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out…
Continuum models are particularly appealing for theoretical studies of bound states, due to simplicity of their bulk Hamiltonians. The main challenge on this path is a systematic description of the boundary, which comes down to determining…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…