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

Møller, Frederik Trier; Schmiedmayer, Jörg

doi:10.21468/scipostphys.8.3.041

Cited by 47 publications

(47 citation statements)

References 47 publications

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“…The main prerequisite to use the MD is therefore the nondegeneracy of the system, which is necessary to allow for the classical description of centerof-mass trajectories of individual molecules in a simulation. Alternatively, one could describe the system using the recently developed theory of generalized hydrodynamics (GHD), which has been proposed to describe dynamics of 1D quantum gases at or close to the integrable point [27,[39][40][41][42][43]. Unlike other methods, GHD takes into account interactions between particles and remains across all phases of the Lieb-Liniger model.…”

Section: Introductionmentioning

confidence: 99%

Relaxation of bosons in one dimension and the onset of dimensional crossover

Zhou

Mazets

et al. 2020

SciPost Phys.

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We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

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Section: Introductionmentioning

confidence: 99%

Relaxation of bosons in one dimension and the onset of dimensional crossover

Zhou

Mazets

et al. 2020

SciPost Phys.

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“…We have made the implementation of our numerical scheme public as a module of the iFluid framework for GHD calculations [79,94].…”

Section: Resultsmentioning

confidence: 99%

“…Although the theory of generalized hydrodynamics is still relatively young, several works have provided reviews, see for example Refs. [78,79] and the lecture notes [48]. In this Section we simply reiterate some of the central concepts of GHD, which later will be relevant for computing dynamical correlation functions.…”

Section: Summary Of Ghdmentioning

confidence: 99%

“…In this Section we simply reiterate some of the central concepts of GHD, which later will be relevant for computing dynamical correlation functions. Note that various notational conventions have been used in the literature; here we will follow that of [79].…”

Section: Summary Of Ghdmentioning

confidence: 99%

“…Lastly, Eq. (5) admits a solution by a characteristic function, U(x, t; λ), encoding the inverse trajectories of the quasi-particles [52,79,91]. Given the characteristic, one can directly relate the evolved state to the initial state via the relation…”

Section: Summary Of Ghdmentioning

confidence: 99%

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Euler-scale dynamical correlations in integrable systems with fluid motion

et al. 2020

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We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationary, inhomogeneous situations, when motion occurs at the Euler-scale of hydrodynamics. In such situations, in interacting systems, the simple correlations due to fluid modes propagating with the flow receive subtle corrections, which we test. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard-rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time-scales, thus providing the first demonstration of validity for the expressions derived in Ref. [1]. We also observe the onset of the Euler-scale limit for the dynamical correlations.

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Generalised hydrodynamics of particle creation and decay

Castro-Alvaredo

Fazio

Doyon

et al. 2022

J. High Energ. Phys.

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Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the spectrum whilst the scattering matrix is diagonal and solves the usual bootstrap equations. In the standard scattering picture, unstable particles result from complex poles of the S-matrix located in the unphysical sheet of rapidity space. Since they are not part of the asymptotic spectrum, their presence is only felt through the effect they have on physical quantities associated either to the theory as a whole (i.e. scaling functions, correlation functions) or to the stable particles themselves (i.e. energy/particle density). In two recent publications, the effect of unstable particles in different out-of-equilibrium settings has been studied. It has been shown that their presence is associated with specific signatures in many quantities of physical interest. A good way to select those quantities is to adopt the generalised hydrodynamic approach and to consider the effective velocities and particle densities of the stable particles in the theory. For an initial state given by a spacial gaussian profile of temperatures peaked at the origin, time evolution gives rise to particle and spectral particle densities that exhibit hallmarks of the creation and decay of unstable particles. While these signatures have been observed numerically elsewhere, this paper explores their quantitative and qualitative dependence on the parameters of the problem. We also consider other initial states characterised by “inverted gaussian” and “double gaussian” temperature profiles.

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

Cited by 47 publications

References 47 publications

Relaxation of bosons in one dimension and the onset of dimensional crossover

Relaxation of bosons in one dimension and the onset of dimensional crossover

Euler-scale dynamical correlations in integrable systems with fluid motion

Generalised hydrodynamics of particle creation and decay

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