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New Classical Integrable Systems from Generalized TT[over ¯]-Deformations.

Benjamin Doyon1, Friedrich Hübner1, Takato Yoshimura2,3

  • 1Department of Mathematics, <a href="https://ror.org/0220mzb33">King's College London</a>, Strand, London WC2R 2LS, United Kingdom.

Physical Review Letters
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Summary
This summary is machine-generated.

We introduce novel classical integrable many-body systems using generalized TT deformations. These systems exhibit factorized scattering and novel dynamics, with thermodynamics described by the thermodynamic Bethe ansatz.

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Area of Science:

  • Classical mechanics
  • Integrable systems
  • Many-body physics

Background:

  • Classical integrable systems are fundamental in physics.
  • Understanding their dynamics and thermodynamics is crucial.
  • Existing models have limitations in describing diverse scattering behaviors.

Purpose of the Study:

  • Introduce a novel class of classical integrable many-body systems.
  • Explore their unique scattering properties and short-scale dynamics.
  • Describe their thermodynamic behavior and large-scale emergent phenomena.

Main Methods:

  • Generalized TT deformations of free particle systems.
  • Analysis of deformation terms involving densities and currents.
  • Investigation of many-body scattering factorization and two-body scattering shifts.
  • Application of thermodynamic Bethe ansatz equations.

Main Results:

  • Factorized many-body scattering processes.
  • Arbitrary two-body scattering shifts as a function of momenta.
  • Novel short-scale dynamics including particle-pair creation/annihilation.
  • Thermodynamic description via Bethe ansatz equations.
  • Emergence of generalized hydrodynamics at large scales.

Conclusions:

  • The proposed "semiclassical Bethe systems" offer a new framework for classical integrable models.
  • These systems display rich dynamics and versatile scattering properties.
  • They provide a platform for studying emergent phenomena like generalized hydrodynamics.