Frederik S. Møller, Gabriele Perfetto, Benjamin Doyon, Jörg Schmiedmayer
SciPost Phys. Core 3, 016 (2020) ·
published 22 December 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.
Chen Li, Tianwei Zhou, Igor Mazets, Hans-Peter Stimming, Frederik S. Møller, Zijie Zhu, Yueyang Zhai, Wei Xiong, Xiaoji Zhou, Xuzong Chen, Jörg Schmiedmayer
SciPost Phys. 9, 058 (2020) ·
published 22 October 2020
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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.
SciPost Phys. 8, 041 (2020) ·
published 13 March 2020
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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.
Mr Møller: "We thank the Referee for the s..."
in Report on Euler-scale dynamical correlations in integrable systems with fluid motion