Related papers: Bound States in Mildly Curved Layers
We consider the quantum optics of a single photon interacting with a system of two level atoms. This leads to the study of a nonlinear eigenproblem for a system of nonlocal partial differential equations. Two classes of solutions to these…
We present a new linked cluster expansion for calculating properties of multiparticle excitation spectra to high orders. We use it to obtain the two-particle spectra for systems of coupled spin-half dimers. We find that even for weakly…
We consider a non relativistic particle on the surface of a semi-infinite cylinder of circumference $L$ submitted to a perpendicular magnetic field of strength $B$ and to the potential of impurities of maximal amplitude $w$. This model is…
In this paper we investigate quantum fields propagating on given, static, spherically symmetric spacetimes, which are isometric to a part of the Schwarzschild spacetime. Without specifying the internal geometry we show, that there exist…
We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
For the structure of the thin electrical double layer~(EDL) and the property related to the EDL capacitance, we analyze boundary layer solutions (corresponding to the electrostatic potential) of a non-local elliptic equation which is a…
We demonstrate existence of positive bound and ground states for a system of coupled nonlinear Schr\"odinger--Korteweg-de Vries equations. More precisely, we prove there is a positive radially symmetric ground state if either the coupling…
The spatial characteristics and structure of an axisymmetric turbulent boundary layer under strong adverse pressure gradient and weak transverse curvature are investigated using incompressible large-eddy simulation. The boundary layer is on…
On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus bounds. This area bound implies…
We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
We consider the cubic nonlinear Schr\"{o}dinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result…
With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…
We consider a straight three dimensional quantum layer with singular potential supported on a straight wire which is localized perpendicularly to the walls and connects them. We prove that the infinite number of embedded eigenvalues appears…
Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any…
Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous…
The most popular 3-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states within quantum field theory is the Salpeter equation, found as the instantaneous limit of the Bethe-Salpeter framework if allowing,…
We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension (1D) for both positive and negative signs of the nonlinear term, as…