Related papers: Threshold Singularities of the Spectral Shift Func…

We study the number $N_{<0}(H_s)$ of negative eigenvalues, counting multiplicities, of the fractional Schr\"odinger operator $H_s=(-\Delta)^s-V(x)$ on $L^2(\mathbb{R}^d)$, for any $d\ge1$ and $s\ge d/2$. We prove a bound on $N_{<0}(H_s)$…

We consider a compact perturbation $H_0 = S + K_0^* K_0$ of a self-adjoint operator $S$ with an eigenvalue $\lambda^\circ$ below its essential spectrum and the corresponding eigenfunction $f$. The perturbation is assumed to be "along" the…

In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators $P_a$ of order $2a$, with type and factorization index $a\in R_+$, restricted to compact sets with boundary; this includes…

We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in…

We prove an upper and a lower bound on the rank of the spectral projections of the Schr\"odinger operator $-\Delta + V$ in terms of the volume of the sublevel sets of an effective potential $\frac{1}{u}$. Here, $u$ is the `landscape…

The spectral shift function \xi_{L}(E) for a Schr\"odinger operator restricted to a finite cube of length L in multi-dimensional Euclidean space, with Dirichlet boundary conditions, counts the number of eigenvalues less than or equal to E…

For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schr\"{o}dinger operator $H=H_0+V$, where $H_0=(-\Delta)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We…

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V,\ V\ge 0,$ we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues (bound states), as the coupling parameter $\alpha$ tends to infinity.…

In this work, we use regularized determinant approach to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schr\"odinger operator $(-i\nabla - \textbf{\textup{A}})^{2} - b$ in…

We consider the dynamics of nonlinear Schr\"odinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the Landau…

We consider the Dirichlet problem for the focusing NLS equation on the half-line, with given Schwartz initial data and boundary data $q(0,t)$ equal to an exponentially decaying perturbation $u(t)$ of the periodic boundary data $ a…

We shall consider the Schr\"odinger operators on $\mathbf{R}^2$ with random $\delta$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $\delta$-fields, we prove the spectrum coincides with $[0,\infty)$ and…

We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a…

We investigate the onset of superconductivity in magnetic field for a clean two-dimensional multiple-band superconductor in the vicinity of the Lifshitz transition when one of the bands is very shallow. Due to small number of carriers in…

We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of…

The spectral properties of itinerant 2D systems with (nearly) ferromagnetic ground state are studied within the spin-fermion and the classical s-d exchange models. While the former model describes the effect of collective magnetic…

We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary conditions we obtain refined and new results about their…

By utilizing the twisted boundary conditions in the exact diagonalization method, we investigate the single-particle spectral function of the extended Peierls-Hubbard model at both half-filling and quarter filling. In one-dimensional (1D)…

Magneto-oscillations in two-dimensional systems with spin-orbit interaction are typically characterized by fast Shubnikov-de~Haas (SdH) oscillations and slower spin-orbit-related beatings. The characterization of the full SdH oscillatory…

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace…