相关论文: Asymptotics for the number of eigenvalues of three…

We study the self-adjoint Hamiltonian that models the quantum dynamics of a one-dimensional (1D) three-body system consisting of a light particle interacting with two heavy ones through a zero-range force. For an attractive interaction we…

We consider a three-particle quantum system in dimension three composed of two identical fermions of mass one and a different particle of mass $m$. The particles interact via two-body short range potentials. We assume that the Hamiltonians…

We prove the existence of two-and three-particle bound states of the Schr\"odinger operators $h_\mu(k),k\in \T^d$ and $H_\mu(K),K\in \T^d$ associated to Hamiltonians $\mathrm{h}_{\mu}$ and $\mathrm{H}_{\mu}$ of a system of two and three…

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…

In this paper, we investigate the bound states of $2+1$ fermionic trimers on a three-dimensional lattice at strong coupling. Specifically, we analyze the discrete spectrum of the associated three-body discrete Schr\"odinger operator…

We study the discrete spectrum of the two-particle Schr\"odinger operator $\hat H_{\mu\lambda}(K),$ $K\in\mathbb{T}^2,$ associated to the Bose-Hubbard Hamiltonian $\hat {\mathbb H}_{\mu\lambda}$ of a system of two identical bosons…

A model operator $H$ corresponding to the energy operator of a system with non-conserved number $n\leq 3$ of particles is considered. The precise location and structure of the essential spectrum of $H$ is described. The existence of…

This work continues \cite{bib1} where the construction of Hamiltonian $H$ for the system of three quantum particles is considered. Namely the system consists of two fermions with mass $1$ and another particle with mass $m>0$. In the present…

A model operator $H_\mu,$ $\mu>0$ associated to a system of three particles on the three-dimensional lattice $ \mathbb{Z}^3$ that interact via nonlocal pair potentials is considered. We study the case where the parameter function $w$ has a…

We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $ m $, where each fermion interacts via a zero-range force with the different particle. In particular we…

An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra…

We consider three fermions with two spin components interacting on a lattice model with an infinite scattering length. Low lying eigenenergies in a cubic box with periodic boundary conditions, and for a zero total momentum, are calculated…

In this note we discuss the quantum mechanical three-body problem with pairwise zero-range interactions in dimension three. We review the state of the art concerning the construction of the corresponding Hamiltonian as a self-adjoint…

We consider $N$-body Schr\"odinger operators with a virtual level at the threshold of the essential spectrum. We show that in the case of $N\geq 3$ particles in dimension $n\geq3$ virtual levels correspond to eigenvalues of the system and…

We consider the discrete spectrum of the two-dimensional Hamiltonian $H=H_0+V$, where $H_0$ is a Schr\"odinger operator with a non-constant magnetic field $B$ that depends only on one of the spatial variables, and $V$ is an electric…

We show that in d>1 dimensions the N-particle kinetic energy operator with periodic boundary conditions has symmetric eigenfunctions which vanish at particle encounters, and give a full description of these functions. In two and three…

In the limit $\hbar\to 0$, we analyze a class of Schr\"odinger operators $H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}$ acting on sections of a vector bundle $\mathcal{Eh}$ over a Riemannian manifold $M$ where $L$ is a Laplace type…

We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body systems consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation,…

We briefly summarize the most relevant steps in the search of rigorous results about the properties of quantum systems made of three bosons interacting with zero-range forces. We also describe recent attempts to solve the unboundedness…

The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…