Related papers: Boundary conditions in the envelope function appro…
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…
This article is concerned with maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
It is conjectured that the coefficients of the Jones polynomial can be computed by counting solutions of the KW equations on a four-dimensional half-space, with certain boundary conditions that depend on a knot. The boundary conditions are…
We analyse the dynamics of an open membrane, both for the free case and when it is coupled to a background three-form, whose boundary is attached to $p$-branes. The role of boundary conditions and constraints in the Nambu-Goto and Polyakov…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly…
A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…
The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…
We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire's…
A change in boundary conditions (BC) from uniform Dirichlet to non-identical BC on the edges of a triangular billiard often brings about a dramatic change in quantum spectral fluctuations. We provide a theory for this based on periodic…
We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the…
A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the…