相关论文: Stability of good quantum numbers in ground states

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues $\mu_k$ satisfying $\mu_{k+1}-\mu_k \geq \Delta >0$. Perturbations are considered in…

We study the Schr\"odinger operators ${H}_{\lambda\mu}(K)$ with $K\in\mathbb{T}^2$ being the fixed quasimomentum of a pair of particles, associated with a system of two arbitrary particles on a two-dimensional lattice $\mathbb{Z}^2$ with…

We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $\sigma_0$ and $\sigma_1$. Let $V$ be a bounded operator on $\fH$, off-diagonal and $J$-self-adjoint with…

Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed…

We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator $H$, with respect to an auxiliary operator $A$ that is conjugate to $H$ in the sense of Mourre. We work within the framework of singular…

We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrically local commuting projectors on a…

We study perturbations of a self-adjoint positive operator $T$, provided that a perturbation operator $B$ satisfies "local" subordinate condition $\|B\varphi_k\|\leqslant b\mu_k^{\beta}$ with some $\beta <1$ and $b>0$. Here…

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J.…

The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates…

In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and…

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…

We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators…

We study the Schr\"odinger operators $H_{\gamma \lambda \mu}(K)$, $K\in\T$ being a fixed (quasi)momentum of the particles pair, associated with a system of two identical bosons on the one-dimensional lattice $\mathbb{Z}$, where the real…

This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…

In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…

Although the physical Hamiltonian operator can be constructed in the deparameterized model of loop quantum gravity coupled to a scalar field, its property is still unknown. This open issue is attacked in this paper by considering an…

We consider a non-self-adjoint $H$ given as the perturbation of a self-adjoint operator $H_0$. We suppose that $H$ is of the form $H=H_0+CWC$ where $C$ is a bounded, positive definite and relatively compact with respect to $H_0$, and $W$ is…

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below…