Generalized hydrodynamics of the attractive non-linear Schrӧdinger equation

@article{Koch2022GeneralizedHO,
  title={Generalized hydrodynamics of the attractive non-linear Schrӧdinger equation},
  author={Rebekka Koch and Jean-S{\'e}bastien Caux and Alvise Bastianello},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2022},
  volume={55}
}
We study the generalized hydrodynamics of the one-dimensional classical non linear Schrӧdinger equation in the attractive phase. We thereby show that the thermodynamic limit is entirely captured by solitonic modes and radiation is absent. Our results are derived by considering the semiclassical limit of the quantum Bose gas, where the Planck constant has a key role as a regulator of the classical soliton gas. We use our result to study adiabatic interaction changes from the repulsive to the… 

References

SHOWING 1-10 OF 104 REFERENCES
Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation
  • H. Spohn
  • Mathematics
    Journal of Mathematical Physics
  • 2022
Ablowitz and Ladik discovered a discretization that preserves the integrability of the nonlinear Schrödinger equation in one dimension. We compute the generalized free energy of this model and
Correlation functions and transport coefficients in generalised hydrodynamics
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights,
Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects
We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in
Bose–Einstein Condensation and Superfluidity
This book on Bose–Einstein condensation (BEC) and superfluidity, is an extended version of the notable work by the pioneering researchers Sandro Stringari and Lev Pitaevskii, which first appeared in
Thermodynamics of One-Dimensional Solvable Models
Part I. Thermodynamics of Non-Interacting Systems and Ground States on Interacting Systems: 1. Free energy and correlation functions of XY models 2. Systems with delta-function potential 3. Isotropic
Quantum Inverse Scattering Method and Correlation Functions
One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral
Form Factors in Completely Integrable Models of Quantum Field Theory
Completely integrable models of quantum field theory the space of physical states the necessary properties of form factors the local commutativity theorem soliton form factors in SG model the
Theory of Solitons: The Inverse Scattering Method
Physical Review B 103
  • 165121
  • 2021
SciPost Phys
  • 9, 2
  • 2020
...
1
2
3
4
5
...