Related papers: A multispecies Calogero model
We consider a $A_{N-1}$ type of spin dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as…
We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We restrict our attention to states where one atom is excited and the other is in the ground state, in…
We study the impact of the inter-level energy constraints imposed by Haldane Exclusion Statistics on relaxation processes in 1-dimensional systems coupled to a bosonic bath. By formulating a second-quantized description of the relevant Fock…
We consider the spherical reduction of the rational Calogero model (of type $A_{n-1}$, without the center of mass) as a maximally superintegrable quantum system. It describes a particle on the $(n{-}2)$-sphere in a very special potential. A…
This article introduces the "Goldilocks model" for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. The Goldilocks model shares features with two…
The Fock-Darwin system is analysed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its…
A complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence classes, have been obtained. We will re-examine two…
We study the "mixed spin" isotropic ladder system having S=1 spins on one leg and S=1/2 spins on the other, with general-type exchange interactions between spins on neighboring rungs. A set of model Hamiltonians with exact ground states in…
We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered ground states as the strength of the longer range interactions is…
Many body models undergoing a quantum phase transition to a broken-symmetry phase that survives up to a critical temperature must possess, in the ordered phase, symmetric as well as non-symmetric eigenstates. We predict, and explicitly show…
We analyze in detail the quantum phase transitions that arise in models based on the $u(2)$ algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians…
We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional…
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland…
We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
Many-body localized systems in which interactions and disorder come together defy the expectations of quantum statistical mechanics: In contrast to ergodic systems, they do not thermalize when undergoing nonequilibrium dynamics. What is…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
Quasi-Stationary States of long-range interacting systems have been studied at length over the last fifteen years. It is known that the collisional terms of the Balescu-Lenard and Landau equations vanish for one-dimensional systems in…
The dynamics of homogeneous Robertson--Walker cosmological models with a self-interacting scalar field source is examined here in full generality, requiring only the scalar field potential to be bounded from below and divergent when the…
We study in some detail an interacting cosmological model based on two canonical scalar fields starting from a Lagrangian description. Contrary to other more phenomenological approaches where non-relativistic matter and dark energy are…