相关论文: Spectral Gaps for Periodic Elliptic Operators with…
We deal with a spectral problem for the Laplace-Beltrami operator posed on a stratified set $\Omega$ which is composed of smooth surfaces joined along a line $\gamma$, the junction. Through this junction we impose the Kirchhoff-type vertex…
Using the strong coupling diagram technique equations are derived for hole Green's functions of the three-band Hubbard model, which describes Cu-O planes of high-$T_c$ cuprates. The equations are self-consistently solved in the…
We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a…
We theoretically study electronic states in graded-gap junctions of IV-VI compounds with band inversion. Using a two-band model within the ${\bf k}\cdot{\bf p}$ approximation and assuming that the gap and the gap centre present linear…
We obtain a perturbative proof of localization for quasiperiodic operators on $\ell^2(\Z^d)$ with one-dimensional phase space and monotone sampling functions, in the regime of small hopping. The proof is based on an iterative scheme which…
The equilibrium properties and interminiband transitions for Hartree-interacting two-dimensional electron gas in a one-dimensional chain of planar quantum rings subjected to a transverse homogeneous magnetic field are examined theoretically…
The many-body theory of interacting electrons poses an intrinsically difficult problem that requires simplifying assumptions. For the determination of electronic screening properties of the Coulomb interaction, the Random Phase…
Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…
We give a precise and complete description on the spectrum for a class of non-self-adjoint quasi-periodic operators acting on $\ell^2(\mathbb{Z}^d)$ which contains the Sarnak's model as a special case. As a consequence, one can see various…
We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as…
The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type…
In this paper we address the question how to design photonic crystals that have photonic band gaps around a finite number of given frequencies. In such materials electromagnetic waves with these frequencies can not propagate; this makes…
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
The aim of this paper is to offer an original and comprehensive spectral theoretical approach to the study of convergence to equilibrium, and in particular of the hypocoercivity phenomenon, for contraction semigroups in Hilbert spaces. Our…
We consider a hybrid diffusion process that is a combination of two Ornstein-Uhlenbeck processes with different restraining forces. This process serves as the heavy-traffic approximation to the Markovian many-server queue with abandonments…
We investigate the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized electron systems in the quantum regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner…
In this paper we deal with the so-called "spectral inequalities", which yield a sharp quantification of the unique continuation for the spectral family associated with the Schr\"odinger operator in $ \mathbb{R}^d$ \begin{equation*} H_{g,V}…
We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectral components can be computed by simple algebraic operations…
We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schr\"odinger type operators on what we call "$N$-particle graphs with maximal local occupation…
We show, that in contrast to the free electron model (standard BCS model), a particular gap in the spectrum of multiband superconductors opens at some distance from the Fermi energy, if conduction band is composed of hybridized atomic…