Generalized hydrodynamics of the KdV soliton gas

Bonnemain, Thibault; Doyon, Benjamin; El, Gennady

doi:10.1088/1751-8121/ac8253

Cited by 22 publications

(17 citation statements)

References 92 publications

(187 reference statements)

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“…However, one can try to reparameterize λ → f (λ) or change the definition of P (λ). (In the GHD context, the momentum function P (λ) is not physically accessible, which means that it is some 'gauge' degree of freedom [55]). Both actions change the scattering phase shift, and it may be possible to obtain a T (λ, µ) that depends only on the difference.…”

Section: Stationary Ghd Equation In Normal Modesmentioning

confidence: 99%

Mesoscopic impurities in generalized hydrodynamics

Hübner

2024

J. Stat. Mech.

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This study focuses on the impurities in integrable models from the viewpoint of generalized hydrodynamics (GHD). An impurity can be thought of as a boundary condition for the GHD equation, relating the states on the left and right sides. It was found that, in interacting models, it is not possible to disentangle the incoming and outgoing states, which means that it is not possible to think of scattering as a mapping that maps the incoming state to the outgoing state. A novel class of impurities, dubbed mesoscopic impurities, was then introduced, whose spatial size is mesoscopic (i.e. their size L m i c r o ≪ L i m p ≪ L is much larger than the microscopic length scale L m i c r o but much smaller than the macroscopic scale L). Because of their large size, it is possible to describe mesoscopic impurities via GHD. This simplification allows one to study these impurities both analytically and numerically. These impurities show interesting non-perturbative scattering behavior, such as the nonuniqueness of the solutions and a nonanalytic dependence on the impurity strength. In models with one quasi-particle species and a scattering phase shift that depends only on the difference in momenta, the scattering can be described using an effective Hamiltonian. This Hamiltonian is dressed due to the interaction between the particles and satisfies a self-consistency fixed-point equation. In the example of the hard-rod model, it was demonstrated how this fixed-point equation can be used to find almost explicit solutions to the scattering problem by reducing it to a two-dimensional system of equations that can be solved numerically.

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Section: Stationary Ghd Equation In Normal Modesmentioning

confidence: 99%

Mesoscopic impurities in generalized hydrodynamics

Hübner

2024

J. Stat. Mech.

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“…In GHD, one in fact forgoes the set of explicit, extensive conserved charges, and describes the relaxed states more universally in terms of distributions of asymptotic states, see [3]. GHD has been observed in recent experiments on cold atomic gases [66][67][68], and it is also the framework at the heart of the theory of soliton gases, structures observed in water-wave and light-guide experiments [69][70][71].…”

Section: Numerical Checks: Integrable Systemsmentioning

confidence: 99%

Ballistic macroscopic fluctuation theory

Doyon,

Perfetto,

Sasamoto

et al. 2023

SciPost Phys.

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We introduce a new universal framework describing fluctuations and correlations in quantum and classical many-body systems, at the Euler hydrodynamic scale of space and time. The framework adapts the ideas of the conventional macroscopic fluctuation theory (MFT) to systems that support ballistic transport. The resulting “ballistic MFT” (BMFT) is solely based on the Euler hydrodynamics data of the many-body system. Within this framework, mesoscopic observables are classical random variables depending only on the fluctuating conserved densities, and Euler-scale fluctuations are obtained by deterministically transporting thermodynamic fluctuations via the Euler hydrodynamics. Using the BMFT, we show that long-range correlations in space generically develop over time from long-wavelength inhomogeneous initial states in interacting models. This result, which we verify by numerical calculations, challenges the long-held paradigm that at the Euler scale, fluid cells may be considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation theorem for non-equilibrium ballistic transport follows purely from time-reversal invariance of the Euler hydrodynamics. We check the validity of the BMFT by applying it to integrable systems, and in particular the hard-rod gas, with extensive simulations that confirm our analytical results.

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“…I fact, it is often useful to go back to the classical realm, in order to disentangle classical form quantum effects. In this special issue, contributions developed the hydrodynamic theory of integrable systems either quite generally [9,13], or by focussing on gases of particles [6,24], quantum spin systems [27], quantum and classical field theories [2,16,19], and even cellular automata [15,17,18,21,23] and ensembles of classical solitons of integrable partial differential equations [5,28]. Third, of particular interest in one-dimensional quantum systems is their often very peculiar or anomalous transport properties.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics of low-dimensional quantum systems

Abanov,

Doyon,

Dubail

et al. 2023

J. Phys. A: Math. Theor.

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Generalized hydrodynamics of the KdV soliton gas

Cited by 22 publications

References 92 publications

Mesoscopic impurities in generalized hydrodynamics

Mesoscopic impurities in generalized hydrodynamics

Ballistic macroscopic fluctuation theory

Hydrodynamics of low-dimensional quantum systems

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