Related papers: Calogero Models for Distinguishable Particles
A method of storing and retrieving quantum states of radiation fields using the ground-state coherences is discussed. We demonstrate the generation of multiparticle entangled states starting from atoms prepared in a coherent state. Use is…
Bipartite entanglement entropies are calculated for the ground state of the two-excitation subspace in a two-site coupled cavity model. Each region in the phase diagram (atomic insulator, polaritonic insulator, photonic superfluid, and…
We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the…
Through an algebraic method using the Dunkl--Cherednik operators, the multivariable Hermite and Laguerre polynomials associated with the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles are…
In quantum information W states are a central class of multipartite entangled states because of their robustness against noise and use in many quantum processes. Their generation however remains a demanding task whose difficulty increases…
The present article is an extended version of the paper {\it Phys. Rev.} {\bf B 59}, R2490 (1999), where, we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach…
We describe a class of the singular solutions to the multicomponent analogs of the Lam{\'e} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
We define a Chern- Simons Lagrangian for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. We propose exact N-body eigenstates, set up a…
A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J_1 between the first…
Motivated by the growing attention devoted to the Quantum Chromodynamics sector of the Standard Model, and the recent observations of non-standard hadronic states, a possible substructure of quarks $q_{f}\equiv C_{ij}|k_{i}k_{j}\rangle $ in…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
Explicit solutions for one completely-integrable system of Calogero-Moser type in external fields are found in case of three and four interacting particles. Relation between coupling constant, initial values of coordinates and time of…
Suppose we have a natural Hamiltonian $H$ of $n$ particles on the line, centre of mass momentum $P$ and a further independent quantity $Q$, cubic in the momenta. If these are each $S_{n}$ invariant and mutually Poisson commute we have the…
We present an analytically solvable model of $P$ colinear, two-dimensional quantum dots, each containing two electrons. Inter-dot coupling via the electron-electron interaction gives rise to sets of entangled ground states. These ground…
We consider a charged quantum particle in a random magnetic field with Gaussian, delta-correlated statistics. We show that although the single particle properties are peculiar, two particle quantities such as the diffusion constant can be…
Here we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) which never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…