Physics and Mathematics of Calogero particles

Abstract

We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.

Version to appear in Special Issue of Journal of Physics A: Mathematical and General

References in corpus (50)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• Exact operator solution of the Calogero-Sutherland model
• Explicit Solution to the N-Body Calogero Problem
• Quantum Hall states as matrix Chern-Simons theory
• Lattice Integrable Systems of Haldane-Shastry Type
• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• On Models with Inverse-Square Exchange
• Integrable Systems for Particles with Internal Degrees of Freedom
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Quantum Hall Physics = Noncommutative Field Theory
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Dynamical correlation functions in the Calogero-Sutherland model
• Spectrum of a spin chain with inverse square exchange
• Interacting Fermion Systems from Two Dimensional QCD
• Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
• Invariants of the Haldane-Shastry $SU(N)$ Chain
• Density Correlation Functions in Calogero Sutherland Models
• Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions
• Finite Noncommutative Chern-Simons with a Wilson Line and the Quantum Hall Effect
• Exact Solution of the Sutherland Model with arbitrary symmetry
• Orthogonal basis for the energy eigenfunctions of the Chern-Simons matrix model
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• Supersymmetric Polychronakos Spin Chain: Motif, Distribution Function, and Character
• Solitons in the Calogero-Sutherland Collective-Field Model
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Generalized Calogero models through reductions by discrete symmetries
• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Collective field theory of the matrix-vector model
• Spin Calogero models associated with Riemannian symmetric spaces of negative curvature
• Multidimensional Calogero systems from matrix models
• Matrix Model Description of Laughlin Hall States
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Charge and Current in the Quantum Hall Matrix Model
• Fractional quantum Hall effect on the two-sphere: a matrix model proposal
• Yangian-invariant field theory of matrix-vector models
• New Integrable Systems from Unitary Matrix Models
• Solvable scalar and spin models with near-neighbors interactions
• Generalized Calogero-Sutherland systems from many-matrix models
• Novel integrable spin-particle models from gauge theories on a cylinder
• Description of identical particles via gauged matrix models : a generalization of the Calogero-Sutherland system
• Conserved charges of non-yangian type for the Frahm-Polychronakos spin chain
• SU(ν) Generalization of Twisted Haldane-Shastry Model
• Explicit computations of low lying eigenfunctions for the quantum trigonometric Calogero-Sutherland model related to the exceptional algebra E7

Cited by in corpus (160)

• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• On the Singularities of the Magnon S-matrix
• Supersymmetric Calogero models by gauging
• Superconformal mechanics
• Hidden symmetries of integrable conformal mechanical systems
• Calogero models and nonlocal conformal transformations
• Systems of coupled PT-symmetric oscillators
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
• Cuboctahedric Higgs oscillator from the Calogero model
• A class of Calogero type reductions of free motion on a simple Lie group
• Harmonically confined particles with long-range repulsive interactions
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• Interacting systems and wormholes
• Nonlinear supersymmetry in the quantum Calogero model
• Notes on Matrix Models
• High spin limits and non-abelian T-duality
• The spherical sector of the Calogero model as a reduced matrix model
• Effective action and phase transitions of scalar field on the fuzzy sphere
• Integer Partitions and Exclusion Statistics
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Correlation functions and representation bases in free N=4 Super Yang-Mills
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Exactly solvable D_N-type quantum spin models with long-range interaction
• $\mathcal{N}$-extended supersymmetric Calogero models
• Lobachevsky geometry of (super)conformal mechanics
• Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
• R-matrix-valued Lax pairs and long-range spin chains
• Edge fluctuations and third-order phase transition in harmonically confined long-range systems
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Invariants of the spherical sector in conformal mechanics
• Poisson-Lie analogues of spin Sutherland models
• Dynamical fluctuations in the Riesz gas
• Holomorphic representation of quantum computations
• Free particles from Brauer algebras in complex matrix models
• Runge-Lenz vector in Calogero-Coulomb problem
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Notes on Collective Field Theory of Matrix and Spin Calogero Models
• Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
• Gauged spinning models with deformed supersymmetry
• Generalized model of interacting integrable tops
• Supersymmetric many-body Euler-Calogero-Moser model
• Some connections between the Classical Calogero-Moser model and the Log Gas
• Rational deformations of conformal mechanics
• Truncated Calogero-Sutherland models
• Hidden symmetries of rationally deformed superconformal mechanics
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
• On R-matrix valued Lax pairs for Calogero-Moser models
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Solitons in a continuous classical Haldane-Shastry spin chain
• Klein four-group and Darboux duality in conformal mechanics
• The classical hydrodynamics of the Calogero-Sutherland model
• Extended supersymmetric Calogero model
• Mapping the Calogero model on the Anyon model
• Particles confined in arbitrary potentials with a class of finite-ranged interactions
• Solving field equations in non-isometric coset CFT backgrounds
• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• Harmonically confined long-ranged interacting gas in the presence of a hard wall
• Yangian-invariant spin models and Fibonacci numbers
• The action-angle dual of an integrable Hamiltonian system of Ruijsenaars--Schneider--van Diejen type
• The spin Sutherland model of D_N type and its associated spin chain
• Soliton solutions of Calogero model in harmonic potential
• Emergence of Calogero family of models in external potentials: Duality, Solitons and Hydrodynamics
• A Calogero formulation for four-dimensional black-hole micro states
• The structure of invariants in conformal mechanics
• Unusual ergodic and chaotic properties of trapped hard rods
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction
• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Relativistic interacting integrable elliptic tops
• Orthogonality catastrophe and fractional exclusion statistics
• Remarks on Multi-Dimensional Conformal Mechanics
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Detecting dimensional crossover and finite Hilbert space through entanglement entropies
• Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps
• Superconformal Quantum Mechanics from M2-branes
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Symmetry and Integrability of Non-Singlet Sectors in Matrix Quantum Mechanics
• On an approach for computing the generating functions of the characters of simple Lie algebras
• Spin chains of Haldane-Shastry type and a generalized central limit theorem
• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models
• Duality in a hyperbolic interaction model integrable even in a strong confinement: Multi-soliton solutions and field theory
• Noncommutative Fluids
• Composing arbitrarily many $SU(N)$ fundamentals
• Fluctuations in the active Dyson Brownian motion and the overdamped Calogero-Moser model
• Integrability, intertwiners and non-linear algebras in Calogero models
• $1/f^{\alpha }$ noise and integrable systems
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• Dunkl symplectic algebra in generalized Calogero models
• Waves and Solitons in the Calogero Model - Revisited
• Nonlinear supersymmetry as a hidden symmetry
• Sutherland Models for Complex Reflection Groups
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• Veneziano amplitudes, spin chains and Abelian reduction of QCD
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Phase transitions in the decomposition of $SU(N)$ representations
• On the Lieb-Liniger model in the infinite coupling constant limit
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Limit shape of minimal difference partitions and fractional statistics
• Effective short distance interaction in Calogero-Sutherland quantum fluids
• New Super Calogero Models and OSp(4|2) Superconformal Mechanics
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• The virial expansion of a classical interacting system
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Exchange interactions, Yang-Baxter relations and transparent particles
• Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
• Generalizations of MICZ-Kepler system
• Poisson reductions of master integrable systems on doubles of compact Lie groups
• On symmetries of generalized Calogero model and Polychronakos-Frahm chain
• Convexity properties of superpositions of degenerate bipartite eigenstates
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Veneziano Amplitudes, Spin Chains and String Models
• New strings for old Veneziano amplitudes IV.Connections with spin chains and other stochastic systems
• Crossover in densities of confined particles with finite range of interaction
• Integrable many-body systems of Calogero-Ruijsenaars type
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• A Casimir operator for a Calogero $W$ algebra
• Quantum dynamics of the effective field theory of the Calogero-Sutherland model
• Equivalence of two sets of Hamiltonians associated with the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• An SLE approach to four dimensional black hole microstate entropy
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• Generalized spin Sutherland systems revisited
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians
• Supersymmetric Calogero models from superfield gauging
• A note on limit shapes of minimal difference partitions
• Expansion into the vacuum of stochastic gases with long-range interactions
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
• Echoes and defects in the Calogero model
• Hydrodynamics of spin transport in the Haldane-Shastry chain
• Poisson-Lie analogues of spin Sutherland models revisited
• Coupling and particle number intertwiners in the Calogero model
• Totally classical Calogero model
• A superintegrable quantum field theory
• Jack polynomials with prescribed symmetry and some of their clustering properties
• Macroscopic fluctuation theory of interacting Brownian particles
• Dynamical symmetries of the Calogero-Coulomb model
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance
• $T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction
• Lax random matrices from Calogero systems
• On the derivation of Darboux form for the action-angle dual of trigonometric BC(n) Sutherland system
• Calogero-like model without rearrangement symmetry
• Quantum Algebra of Chern-Simons Matrix Model and Large $N$ Limit
• Relativistic generalization of the rational Calogero model
• Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type