Related papers: Curvature induced toroidal bound states

We make a spectral analysis of the massive Dirac operator in a tubular neighborhood of an unbounded planar curve,subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and…

A theoretical framework is presented for the computation of rovibrational polaritonic states of a molecule in a lossless infrared (IR) microcavity. In the proposed approach the quantum treatment of the rotational and vibrational motion of…

We study the time evolution of the wave function of a particle bound by an attractive $\delta$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this…

We consider two two-level quantum emitters (QEs) with separations on the order of the wavelength which are chirally coupled to a one-dimensional (1D) waveguide, and the electromagnetic field of the 1D waveguide has a direction-dependent…

The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of…

In this work, we use the warped \( \mu \)-bubble method to study the consequences of a spectral curvature bound. In particular, with a lower spectral Ricci curvature bound and a lower spectral scalar curvature bound, we show that the band…

New upper and lower limits are given for the number of S-wave bound states yielded by an attractive (monotonic) potential in the context of the Schrodinger or Klein-Gordon equation.

For mathematical models of quantum wave guides we show that in some situations two interacting particles can be trapped more easily than a single particle. In particular, we give an example of a wave guide that can not bind a single…

We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…

Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher…

Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in…

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…

A well known result of Da Rios and Levi-Civita says that a closed planar curve is elastic if and only if it is stationary under the localized induction (or smoke ring) equation, where stationary means that the evolution under the localized…

We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…

Mathematically rigorous derivation of the hadron matter equation of state within the induced surface and curvature tensions approach is worked out. Such an equation of state allows one to go beyond the Van der Waals approximation for the…

Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…

Wave functions and electron potentials of laterally-confined surface states are determined experimentally by means of photoemission from stepped Au(111) surfaces. Using an iterative formalism borrowed from x-ray diffraction, we retrieve the…

Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A (2009) in press], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We…

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…

We give three lower bounds for the Morse index of a constant mean curvature torus in Euclidean 3-space in terms of its spectral genus g. The first two lower bounds grow linearly in g and are stronger for smaller values of g, while the third…