Abstract We review the recent theoretical and experimental progress regarding the generalized hydrodynamics (GHD) behavior of the one-dimensional (1D) Bose gas with contact repulsive interactions, also known as the Lieb–Liniger gas. In the first section, we review the theory of the Lieb–Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb–Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb–Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results of GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atom experiments: the experimental realization of the Lieb–Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions.
Abstract We review the recent theoretical and experimental progress regarding the generalized hydrodynamics (GHD) behavior of the one-dimensional (1D) Bose gas with contact repulsive interactions, also known as the Lieb–Liniger gas. In the first section, we review the theory of the Lieb–Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb–Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb–Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results of GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atom experiments: the experimental realization of the Lieb–Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions.
The results of benchmarks of the recent theory of generalized hydrodynamics (GHD) in the context of the dynamics of the 1D Bose gas described by the Lieb-Liniger model are reported. Through comparisons against several alternative, well-established computational approaches, the range of applicability of GHD in some of the most challenging out-of-equilibrium scenarios, such as propagation of quantum shock waves and collisional relaxation, is verified and validated and, additionally, some of the methods limitations are pointed out.
Generalized hydrodynamics (GHD) is a recent theoretical approach that is becoming a go-to tool for characterizing out-of-equilibrium phenomena in integrable and near-integrable quantum many-body systems. Here, we benchmark its performance against an array of alternative theoretical methods, for an interacting one-dimensional Bose gas described by the Lieb-Liniger model. In particular, we study the evolution of both a localized density bump and dip, along with a quantum Newton's cradle setup, for various interaction strengths and initial equilibrium temperatures. We find that GHD generally performs very well at sufficiently high temperatures or strong interactions. For low temperatures and weak interactions, we highlight situations where GHD, while not capturing interference phenomena on short lengthscales, can describe a coarse-grained behaviour based on convolution averaging that mimics finite imaging resolution in ultracold atom experiments. In a quantum Newton's cradle setup based on a double-well to single-well trap quench, we find that GHD with diffusive corrections demonstrates excellent agreement with the predictions of a classical field approach.
We theoretically investigate the effect of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K K -body losses ( K=1,2,3,\dots K = 1 , 2 , 3 , … ) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion – where the gas behaves like an ideal Bose gas – and hard-core repulsion – where the gas is mapped to a non-interacting Fermi gas –, we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.
Abstract This article reviews the recent developments in the theory of generalised hydrodynamics (GHD) with emphasis on the repulsive one-dimensional Bose gas. We discuss the implications of GHD on the mechanisms of thermalisation in integrable quantum many-body systems as well as its ability to describe far-from-equilibrium behaviour of integrable and near-integrable systems in a variety of quantum quench scenarios. We outline the experimental tests of GHD in cold-atom gases and its benchmarks with other microscopic theoretical approaches. Finally, we offer some perspectives on the future direction of the development of GHD.
The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics-thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures.