Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model

Abstract

We examine a collection of particles interacting with inverse-square two-body potentials in the thermodynamic limit. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed as coherent states of either solitons or phonons. Therefore, either solitons or phonons can be considered as the fundamental excitations. The generic wave is shown to correspond to a two-band state in the quantum description of the system, while the limiting cases of solitons and phonons correspond to particle and hole excitations.

Version to appear in Physical Rerview Letters; contains some new results and explanations

References in corpus (1)

• Density Correlation Functions in Calogero Sutherland Models

Cited by in corpus (65)

• Physics and Mathematics of Calogero particles
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
• Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
• Cuboctahedric Higgs oscillator from the Calogero model
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• Integrable Hierarchy of the Quantum Benjamin-Ono Equation
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Oscillons in hyperbolic models
• Exact solutions of an elliptic Calogero--Sutherland model
• Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems
• Equilibration in one-dimensional quantum hydrodynamic systems
• Dissipationless kinetics of one dimensional interacting fermions
• Sekiguchi-Debiard operators at infinity
• Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
• Applications of the Collective Field Theory for the Calogero-Sutherland Model
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
• Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type
• Solitons and giants in matrix models
• Solitons in a continuous classical Haldane-Shastry spin chain
• The classical hydrodynamics of the Calogero-Sutherland model
• Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases
• Soliton solutions of Calogero model in harmonic potential
• Emergence of Calogero family of models in external potentials: Duality, Solitons and Hydrodynamics
• The Whitham approach to Generalized Hydrodynamics
• Solvable scalar and spin models with near-neighbors interactions
• Cold Fermi-gas with long range interaction in a harmonic trap
• The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics
• Balancing long-range interactions and quantum pressure: solitons in the HMF model
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Nonlinear dynamics of spin and charge in spin-Calogero model
• Solitons in the Calogero model for distinguishable particles
• Solitons and excitations in the duality-based matrix model
• Duality and quasiparticles in the Calogero-Sutherland model: Some exact results
• The Quantum Hydrodynamics of the Sutherland Model
• Multiple algebraisations of an elliptic Calogero-Sutherland model
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Solitons in fluctuating hydrodynamics of diffusive processes
• The non-chiral intermediate Heisenberg ferromagnet equation
• Duality in a hyperbolic interaction model integrable even in a strong confinement: Multi-soliton solutions and field theory
• Noncommutative Fluids
• Waves and Solitons in the Calogero Model - Revisited
• Duality and interacting families in models with the inverse-squared interaction
• Solitons and fractional statistics
• Traveling waves & finite gap potentials for the Calogero-Sutherland Derivative nonlinear Schrödinger equation
• Exact Bohr-Sommerfeld Conditions for the Quantum Periodic Benjamin-Ono Equation
• Matrix-model dualities in the collective field formulation
• Fluctuations around Periodic BPS-Density Waves in the Calogero Model
• Emptiness Formation in Polytropic Quantum Liquids
• Effective short distance interaction in Calogero-Sutherland quantum fluids
• Modulation theory of quantum tunneling into a Calogero-Sutherland fluid
• N=2 supersymmetric extensions of relativistic Toda lattice
• Multi-vortex solution in the Sutherland model
• Hydrodynamics of the Chiral Dirac Spectrum
• Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics
• Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills
• Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions
• Dynamic structure factor of Calogero-Sutherland fluids
• Totally classical Calogero model
• Bosonic Bogoliubov transformations as Lorentz boosts in $(c,\overline{c})=(1,1)$ conformal field theories with marginal $J\overline{J}$ deformations
• Solitons in the duality-based matrix model