Generalized Hydrodynamics on an Atom Chip

Schemmer, Max; Bouchoule, Isabelle; Doyon, Benjamin; Dubail, Jérôme

doi:10.1103/physrevlett.122.090601

Cited by 244 publications

(301 citation statements)

References 67 publications

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“…The resulting generalized hydrodynamics of integrable systems has been thoroughly verified through numerical simulation of a wide range of quantum and classical systems, and in a cold-atom realization of the Lieb-Liniger gas (see e.g. [15] and references therein).…”

mentioning

confidence: 96%

Kardar-Parisi-Zhang universality from soft gauge modes

Bulchandani

2020

Phys. Rev. B

126

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The emergence of superdiffusive spin dynamics in integrable classical and quantum magnets is well established by now, but there is no generally valid theoretical explanation for this phenomenon. A fundamental difficulty is that the hydrodynamic fluctuations of conserved quasiparticle modes are purely diffusive. We propose a "hydrodynamic Higgs mechanism" in isotropic integrable magnets, which generates soft gauge modes that are decoupled from the quasiparticle sector. We show that the coarse-grained time evolution of these modes lies in the Kardar-Parisi-Zhang universality class of dynamics.

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mentioning

confidence: 96%

Kardar-Parisi-Zhang universality from soft gauge modes

Bulchandani

2020

Phys. Rev. B

126

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“…We hope that iFluid will be a help to both students and researchers, who wish to explore the numerical side of generalized hydrodynamics. Furthermore, the recent experimental evidence of GHD's ability to describe the dynamics of cold gas experiments [29] further increases the need for powerful numerical tools. Thus, iFluid represents a great step forward in making the theory more widely accessible, since no open-source software exist in the GHD community so far.…”

Section: Resultsmentioning

confidence: 99%

“…Since the inception of GHD several applications have been added to the framework, such as calculations of entanglement spreading [16][17][18][19], correlation functions [20][21][22], diffusive corrections [23,24], and many others [25][26][27][28]. Recently it has also been demonstrated to capture the dynamics of a cold Bose gas trapped on an atom-chip [29]. An especially appealing feature of the GHD framework is how the main equations can be universally applied to a large set of integrable models including the Lieb-Liniger model [14,[30][31][32], XXZ chain [15,[33][34][35], classical [36] and relativistic [14] sinh-Gordon, and many more [37][38][39][40].…”

Section: Introductionmentioning

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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“…However, though the caviton and constant solutions have the same constant specific entropy, they have different values of mass and energy (per unit length). For instance, the energy density (18) of an aerostatic caviton is less than that of the constant state:…”

Section: Exact Cavitons and Cnoidal Waves For γ =mentioning

confidence: 99%

Nonlinear dispersive regularization of inviscid gas dynamics

et al. 2020

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Ideal gas dynamics can develop shock-like singularities with discontinuous density. Viscosity typically regularizes such singularities and leads to a shock structure. On the other hand, in 1d, singularities in the Hopf equation can be non-dissipatively smoothed via KdV dispersion. In this paper, we develop a minimal conservative regularization of 3d ideal adiabatic flow of a gas with polytropic exponent γ . It is achieved by augmenting the Hamiltonian by a capillarity energy β(ρ)(∇ρ) 2 . The simplest capillarity coefficient leading to local conservation laws for mass, momentum, energy and entropy using the standard Poisson brackets is β(ρ) = β * /ρ for constant β * . This leads to a Korteweg-like stress and nonlinear terms in the momentum equation with third derivatives of ρ , which are related to the Bohm potential and Gross quantum pressure. Just like KdV, our equations admit sound waves with a leading cubic dispersion relation, solitary waves and periodic traveling waves. As with KdV, there are no steady continuous shock-like solutions satisfying the Rankine-Hugoniot conditions. Nevertheless, in 1d, for γ = 2 , numerical solutions show that the gradient catastrophe is averted through the formation of pairs of solitary waves which can display approximate phase-shift scattering. Numerics also indicate recurrent behavior in periodic domains. These observations are related to an equivalence between our regularized equations (in the special case of constant specific entropy potential flow in any dimension) and the defocussing nonlinear Schrödinger equation (cubically nonlinear for γ = 2 ), with β * playing the role of 2 . Thus, our regularization of gas dynamics may be viewed as a generalization of both the single field KdV and nonlinear Schrödinger equations to include the adiabatic dynamics of density, velocity, pressure and entropy in any dimension.

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Generalized Hydrodynamics on an Atom Chip

Cited by 244 publications

References 67 publications

Kardar-Parisi-Zhang universality from soft gauge modes

Kardar-Parisi-Zhang universality from soft gauge modes

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

Nonlinear dispersive regularization of inviscid gas dynamics

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