Generalized Gibbs Ensembles of the Classical Toda Chain

Spohn, Herbert

doi:10.1007/s10955-019-02320-5

Cited by 75 publications

(91 citation statements)

References 37 publications

(49 reference statements)

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“…Acknowledgments. We thank Herbert Spohn for illuminating discussions and for sharing his results prior to their publication in [29]. We acknowledge support from…”

mentioning

confidence: 94%

Kinetic theory of quantum and classical Toda lattices

Bulchandani¹,

Cao²,

Moore³

2019

J. Phys. A: Math. Theor.

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We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the kinetic theory depends smoothly on Planck's constant, and explicitly characterise the leading quantum corrections to classical behaviour. The classical kinetic theory is compared with direct numerical simulations and shows excellent agreement. Finally, we connect the Bethe-Boltzmann approach with the classical inverse scattering method, by identifying conserved quasiparticles with the spectrum of the Lax matrix.

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“…Acknowledgments. We thank Herbert Spohn for illuminating discussions and for sharing his results prior to their publication in [29]. We acknowledge support from…”

mentioning

confidence: 94%

Kinetic theory of quantum and classical Toda lattices

Bulchandani¹,

Cao²,

Moore³

2019

J. Phys. A: Math. Theor.

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“…In our paper we investigate the collision rate assumption for the classical Toda lattice [20,21,22]. The Toda lattice has several simplifying features.…”

Section: Introduction Collision Rate Assumptionmentioning

confidence: 99%

The GGE averaged currents of the classical Toda chain

Cao

Bulchandani

Spohn

2019

J. Phys. A: Math. Theor.

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The Toda chain with random initial data is studied. Of particular interest are generalized Gibbs ensembles, their averaged conserved fields, and the averages of the corresponding currents. While averaged fields are well-understood, the description of averaged currents has hitherto relied on the collision-rate assumption. For the Toda chain, the rate assumption can be investigated numerically. Here, we provide convincing evidence for the validity of the rate assumption. This lends further support to the idea that generalized Euler-type equations have a structure common to all integrable extensive systems.arXiv:1905.04548v1 [cond-mat.stat-mech]

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“…One can rewrite the dressing equations into a system of linear equations, which can be solved by the standard routines of Matlab. Thus, the dressing is achieved by solving h k i = j l δ ij δ kl + w l j T kl ij ϑ l j (h dr ) l j (39)…”

Section: A Thermodynamic Bethe Ansatz Of Implemented Modelsmentioning

confidence: 99%

Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

Møller

Schmiedmayer

2020

SciPost Phys.

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We present an open-source Matlab framework, titled iFluid, for simulating the dynamics of integrable models using the theory of generalized hydrodynamics (GHD). The framework provides an intuitive interface, enabling users to define and solve problems in a few lines of code. Moreover, iFluid can be extended to encompass any integrable model, and the algorithms for solving the GHD equations can be fully customized. We demonstrate how to use iFluid by solving the dynamics of three distinct systems: (i) The quantum Newton's cradle of the Lieb-Liniger model, (ii) a gradual field release in the XXZ-chain, and (iii) a partitioning protocol in the relativistic sinh-Gordon model. 8 4.2 Charges and currents of XXZ model 13 4.3 Partitioning protocol in relativistic sinh-Gordon 15 5 Conclusion 17 A Thermodynamic Bethe ansatz of implemented models 18 A.1 Lieb-Liniger model 18 A.2 XXZ spin chain model 19 A.3 Relativistic sinh-Gordon model 19 B Numerical implementation of GHD equations 20 1 arXiv:2001.02547v1 [cond-mat.stat-mech] 8 Jan 2020 SciPost Physics Submission B.1 Tensor representation and index conventions 20 B.2 Discretized GHD equations 21 References 22

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Generalized Gibbs Ensembles of the Classical Toda Chain

Cited by 75 publications

References 37 publications

Kinetic theory of quantum and classical Toda lattices

Kinetic theory of quantum and classical Toda lattices

The GGE averaged currents of the classical Toda chain

Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

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