JeanSébastien Caux, Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura
SciPost Phys. 6, 070 (2019) ·
published 20 June 2019

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Describing and understanding the motion of quantum gases out of equilibrium
is one of the most important modern challenges for theorists. In the
groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss,
Nature 440, 900, 2006], quasionedimensional cold atom gases were observed
with unprecedented accuracy, providing impetus for many developments on the
effects of low dimensionality in outofequilibrium physics. But it is only
recently that the theory of generalized hydrodynamics has provided the adequate
tools for a numerically efficient description. Using it, we give a complete
numerical study of the time evolution of an ultracold atomic gas in this setup,
in an interacting parameter regime close to that of the original experiment. We
evaluate the full evolving phasespace distribution of particles. We simulate
oscillations due to the harmonic trap, the collision of clouds without
thermalization, and observe a small elongation of the actual oscillation period
and cloud deformations due to manybody dephasing. We also analyze the effects
of weak anharmonicity. In the experiment, measurements are made after release
from the onedimensional trap. We evaluate the gas density curves after such a
release, characterizing the actual time necessary for reaching the asymptotic
state where the integrable quasiparticle momentum distribution function
emerges.
SciPost Phys. 6, 023 (2019) ·
published 15 February 2019

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We, for the first time, report a firstprinciple proof of the equations of
state used in the hydrodynamic theory for integrable systems, termed
generalized hydrodynamics (GHD). The proof makes full use of the graph
theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed
recently. This approach is purely combinatorial and relies only on common
structures shared among Bethe solvable models, suggesting universal
applicability of the method. To illustrate the idea of the proof, we focus on
relativistic integrable quantum field theories with diagonal scatterings and
without bound states such as strings.
Alvise Bastianello, Benjamin Doyon, Gerard Watts, Takato Yoshimura
SciPost Phys. 4, 045 (2018) ·
published 30 June 2018

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Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of
classical integrable field theory. Classical field GHD is based on a known
formalism for Gibbs ensembles of classical fields, that resembles the
thermodynamic Bethe ansatz of quantum models, which we extend to generalized
Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic
and radiative modes of classical fields. We observe that the quasiparticle
formulation of GHD remains valid for radiative modes, even though these do not
display particlelike properties in their precise dynamics. We point out that
because of a UV catastrophe similar to that of black body radiation, radiative
modes suffer from divergences that restrict the set of finiteaverage
observables; this set is larger for GGEs with higher conserved charges. We
concentrate on the sinhGordon model, which only has radiative modes, and study
transport in the domainwall initial problem as well as Eulerscale
correlations in GGEs. We confirm a variety of exact GHD predictions, including
those coming from hydrodynamic projection theory, by comparing with Metropolis
numerical evaluations.
SciPost Phys. 2, 014 (2017) ·
published 22 April 2017

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Generalized hydrodynamics (GHD) was proposed recently as a formulation of
hydrodynamics for integrable systems, taking into account infinitelymany
conservation laws. In this note we further develop the theory in various
directions. By extending GHD to all commuting flows of the integrable model, we
provide a full description of how to take into account weakly varying force
fields, temperature fields and other inhomogeneous external fields within GHD.
We expect this can be used, for instance, to characterize the nonequilibrium
dynamics of onedimensional Bose gases in trap potentials. We further show how
the equations of state at the core of GHD follow from the continuity relation
for entropy, and we show how to recover Eulerlike equations and discuss
possible viscosity terms.
SciPost Phys. 2, 014 (2017) ·
published 22 April 2017

· pdf
Generalized hydrodynamics (GHD) was proposed recently as a formulation of
hydrodynamics for integrable systems, taking into account infinitelymany
conservation laws. In this note we further develop the theory in various
directions. By extending GHD to all commuting flows of the integrable model, we
provide a full description of how to take into account weakly varying force
fields, temperature fields and other inhomogeneous external fields within GHD.
We expect this can be used, for instance, to characterize the nonequilibrium
dynamics of onedimensional Bose gases in trap potentials. We further show how
the equations of state at the core of GHD follow from the continuity relation
for entropy, and we show how to recover Eulerlike equations and discuss
possible viscosity terms.