Related papers: Interior-Boundary Conditions for Schrodinger Opera…
Classical electromagnetic boundary conditions (EMBCs) fail to describe quantum interface phenomena at nanoscale. Here, we construct the interface model with a transition layer describing the electromagnetic field inhomogeneity across the…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
We consider the Laplacian in a tubular neighbourhood of a hyperplane subjected to non-self-adjoint $\mathcal{PT}$-symmetric Robin boundary conditions. Its spectrum is found to be purely essential and real for constant boundary conditions.…
Dealing with boundary conditions in Smoothed Particle Hydrodynamics (SPH) poses significant difficulties, indeed being one of the SPHERIC Grand Challenges. In particular, wall boundary conditions have been pivotal in SPH model development…
We analyze the interior controllability problem for a nonlocal Schr\"odinger equation involving the fractional Laplace operator $(-\Delta)^s$, $s\in(0,1)$, on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The controllability from…
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…
This paper presents the spectral analysis of 1-dimensional Schroedinger operator on the half-line whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. The coupling constants are allowed to be…
We describe a new approach to derive numerical approximations of boundary conditions for high-order accurate finite-difference approximations. The approach, called the Local Compatibility Boundary Condition (LCBC) method, uses boundary…
We consider the initial-boundary value problem in the quarter space for the system of equations of ideal Magneto-Hydrodynamics for compressible fluids with perfectly conducting wall boundary conditions. On the two parts of the boundary the…
We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in ${\mathbb R}^n $ with non-coercive boundary conditions. In this case there is a loss of smoothness of the…
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of…
In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a…
In this paper, we introduced the local and global mixed Morrey-type spaces, and some properties of these spaces are also studied. After that, the necessary conditions of the boundedness of fractional integral operators $I_{\alpha}$ are…
Schroedinger developed an operator method for solving quantum mechanics. While this technique is overshadowed by his more familiar differential equation approach, it has found wide application as an illustration of supersymmetric quantum…
We give explicit analytic criteria for two problems associated with the Schr\"odinger operator $H = -\Delta + Q$ on $L^2(\R^n)$ where $Q\in D'(\R^n)$ is an arbitrary real- or complex-valued potential. First, we obtain necessary and…
The paper studies properties of acoustic operators in bounded Lipschitz domains $\Omega$ with m-dissipative generalized impedance boundary conditions. We prove that such acoustic operators have a compact resolvent if and only if the…
We recently constructed type-IIB compactifications to four dimensions depending on a single additional coordinate, where a five-form flux $\Phi$ on an internal torus leads to a constant string coupling. Supersymmetry is fully broken when…
It is known that Fourier integral operators arising when solving Schr\"odinger-type operators are bounded on the modulation spaces $\cM^{p,q}$, for $1\leq p=q\leq\infty$, provided their symbols belong to the Sj\"ostrand class…
We derive equations for evaluating differential operators in transparent boundary conditions (TBCs) for a certain class of hyperbolic systems of second-order equations. This local part of TBCs can be used as approximate nonreflecting…
It is shown that natural boundary conditions for non-relativistic wave functions are of periodic or of homogeneous Robin type. Using asymptotic central symmetry of Hamiltonian and theory of singular differential equations the many-electron…