Generalized hydrodynamics in strongly interacting 1D Bose gases

Malvania, Neel; Zhang, Yicheng; Le, Yuan; Dubail, Jérôme; Rigol, Marcos; Weiss, David S.

doi:10.1126/science.abf0147

Cited by 116 publications

(89 citation statements)

References 49 publications

(36 reference statements)

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“…The rate equations (11) generalise those already obtained for a one-dimensional bosonic gas trapped in a lattice and described by the Bose-Hubbard model [36]. The derivation of the equations is given here below and it is obtained by regularising the problem onto a lattice.…”

Section: Rate Equations For the Dissipative Dynamicsmentioning

confidence: 73%

“…In order to derive the rate equations (11), we regularise the original problem introducing a short-length cutoff, a, that is the shortest length-scale of the problem. In this way, the original master equation is turned into a lattice problem.…”

Section: Derivation Of the Rate Equationsmentioning

confidence: 99%

“…[2][3][4]. Restricting our focus to one-dimensional Bose gases that at low temperature are described by the Lieb-Liniger model [5,6], several developments, among which the generalised hydrodynamics [7,8], have produced a theoretical framework that successfully describes the experiments where bosonic gases are put out of equilibrium via a quantum quench of the external potential [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

2022

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We study the dynamics of a one-dimensional Bose gas in presence of strong two-body losses. In this dissipative quantum Zeno regime, the gas fermionises and its dynamics can be described with a simple set of rate equations. Employing the local density approximation and a Boltzmann-like dynamical equation, the description is extended to take into account an external potential. We show that in the absence of confinement the population is depleted in an anomalous way and that the gas behaves as a low-temperature classical gas. The harmonic confinement accelerates the depopulation of the gas and introduces a novel decay regime, which we thoroughly characterise.

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Section: Rate Equations For the Dissipative Dynamicsmentioning

confidence: 73%

Section: Derivation Of the Rate Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

2022

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“…the form of which follows from the Casimir function, see Eqs. ( 9), (12). Two imporatnt remarks are in order at this stage: (I) in the easy-plane regime (with → iγ and F iγ (s)), Eq.…”

Section: Sklyanin Lax Matrixmentioning

confidence: 99%

“…Amidst recent experimental breakthroughs with cold-atom technologies [7,8], there has been an upsurge of interest in the study of out-of-equilibrium phenomena. Nowadays, optical lattices not only enable manufacturing of tailor-made nanodevices for processing quantum information, but also offer a versatile platform to directly probe the relaxation process at finite energy density in the systems both near and far from equilibrium [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Landau-Lifshitz model in discrete space-time

et al. 2021

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We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.

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Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

Doyon

2022

Commun. Math. Phys.

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One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space and time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the $$C^*$$ C ∗ algebra description of statistical mechanics by the Gelfand–Naimark–Segal construction. Using Araki’s exponential clustering and the Lieb–Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states.

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Generalized hydrodynamics in strongly interacting 1D Bose gases

Cited by 116 publications

References 49 publications

The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

Anisotropic Landau-Lifshitz model in discrete space-time

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

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