Related papers: The Pauli equation with complex boundary condition…
We discuss the problem of constructing self-adjoint and lower bounded Hamiltonians for a system of $n>2$ non-relativistic quantum particles in dimension three with contact (or zero-range or $\delta$) interactions. Such interactions are…
We compare the solutions of two one-dimensional Poisson problems on an interval with Robin boundary conditions, one with given data, and one where the data has been symmetrized. When the Robin parameter is positive and the symmetrization is…
In PT quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
We use an n-spin system with permutation symmetric zz-interaction for simulating arbitrary pair-interaction Hamiltonians. The calculation of the required time overhead is mathematically equivalent to a separability problem of n-qubit…
Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem…
We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that…
On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions.…
Let $\Omega \subset \mathbb{R}^n$ be an open, bounded and Lipschitz set. We consider the Poisson problem for the $p-$Laplace operator associated to $\Omega$ with Robin boundary conditions. In this setting, we study the equality case in the…
We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli…
We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…
In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the problem as a non-autonomous Dirichlet-to-Neumann operator and…
We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…
In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we…
A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of Spin-Orbit interaction is presented. Emphasis is made on the non trivial construction of the correct Hamiltonian in polar coordinates, the…
We study the Pauli--Schr\"odinger equation in a uniformly rotating frame of reference to describe a coupling of spins and mechanical rotations. The explicit form of the spin-orbit interaction (SOI) with the inertial effects due to the…
We consider a free boundary problem for the $p$-Laplace operator which is related to the so-called Bernoulli free boundary problem. In this formulation, the classical boundary gradient condition is replaced by a condition on the distance…
In this article, we define the Pauli Hamiltonian function for twist-deformed N-enlarged Newton-Hooke space-time provided in article [12]. Further, we derive its energy spectrum, i.e., we find the corresponding eigenvalues as well as the…
We consider finite-dimensional nonlinear systems with linear part described by a parity-time (PT-) symmetric operator. We investigate bifurcations of stationary nonlinear modes from the eigenstates of the linear operator and consider a…
In the last decades comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the results obtained in arXiv:1909.11950 to the case of p-Laplace…