相关论文: A Schr\"odinger Operator Approach to Higher Spin X…
This paper deals with the approximation of a magnetic Schr\"odinger operator with a singular $\delta$-potential that is formally given by $(i \nabla + A)^2 + Q + \alpha \delta_\Sigma$ by Schr\"odinger operators with regular potentials in…
We study periodic approximations of aperiodic Schr\"odinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems that have been recently introduced in this setting. We…
In this paper we first establish the theory of a magnetic Sobolev space $H^1_A(\mathcal{G},\mathbb{C})$ on metric graphs $\mathcal{G}$ and we prove the self-adjointness of its corresponding magnetic Schr\"odinger operator. Then, in this…
The spectrum of the integrable spin-S Heisenberg chains is completely characterized in terms of spin-1/2 spinons. In the continuum limit they form a quasi-particle basis to the higher level SU(2) Wess-Zumino-Witten (WZW) models. Enumerating…
The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave…
We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…
We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on…
We study the problem of minimizing or maximizing the fundamental spectral gap of Schr\"odinger operators on metric graphs with either a convex potential or a ``single-well'' potential on an appropriate specified subset. (In the case of…
We consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We obtain two-sided estimates of the total bandwidth for the Schr\"odinger operators in terms of…
We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. A main result in this paper is that the spectral density function of DMLs…
We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the…
We consider discrete Schr\"odinger operators with periodic potentials on periodic graphs perturbed by guided non-positive potentials, which are periodic in some directions and finitely supported in other ones. The spectrum of the…
We consider discrete Schr\"odinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of these operators is always connected. This result is…
We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level…
We investigate the limit properties of a family of Schr\"odinger operators of the form $H_\varepsilon= -\frac{\mathrm{d}^2}{\mathrm{d}x^2}+ \frac{\lambda(\varepsilon)}{\varepsilon^2}Q \big(\frac{x}{\varepsilon}\big)$ acting on $n$-edge star…
In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…
We show that if we start from a symmetric lower semi-bounded Schr\"odinger operator $\mathcal{H}$ on finitely supported functions on a discrete weighted graph (satisfying certain conditions), apply the Friedrichs construction to get a…
We study in a semiclassical regime a two-dimensional magnetic periodic Schr\"odinger operator. We first review some results for the square (Harper), triangular and hexagonal (case of the graphene) lattices. Then we study the case considered…
In this paper, we introduce a novel first-order derivative for functions on a lattice graph, which extends the discrete Laplacian and generalizes the theory of discrete PDEs on lattices. First, we establish the well-posedness of generalized…