Generalized Hydrodynamics (GHD) has recently been devised as a method to solve the dynamics of integrable quantum many-body systems beyond the mean-field approximation. In its original form, a major limitation is the inability to predict equal-time correlations. Here we present a new method to treat thermal fluctuations of a 1D bosonic degenerate gas within the GHD framework. We show how the standard results using the thermodynmaic Bethe ansatz can be obtained through sampling of collective bosonic excitations, revealing the connection or duality between GHD and effective field theories such as the standard hydrodynamic equations. As an example, we study the damping of a coherently excited density wave and show how equal-time phase correlation functions can be extracted from the GHD evolution. Our results present a conceptually new way of treating fluctuations beyond the linearized regime of GHD.
Generalized Hydrodynamics (GHD) has recently been devised as a method to solve the dynamics of integrable quantum many-body systems beyond the mean-field approximation. In its original form, a major limitation is the inability to predict equal-time correlations. Here we present a new method to treat thermal fluctuations of a 1D bosonic degenerate gas within the GHD framework. We show how the standard results using the thermodynmaic Bethe ansatz can be obtained through sampling of collective bosonic excitations, revealing the connection or duality between GHD and effective field theories such as the standard hydrodynamic equations. As an example, we study the damping of a coherently excited density wave and show how equal-time phase correlation functions can be extracted from the GHD evolution. Our results present a conceptually new way of treating fluctuations beyond the linearized regime of GHD.
Physical systems made of many interacting quantum particles can often be described by Euler hydrodynamic equations in the limit of long wavelengths and low frequencies. Recently such a classical hydrodynamic framework, now dubbed generalized hydrodynamics (GHD), was found for quantum integrable models in one spatial dimension. Despite its great predictive power, GHD, like any Euler hydrodynamic equation, misses important quantum effects, such as quantum fluctuations leading to nonzero equal-time correlations between fluid cells at different positions. Focusing on the one-dimensional gas of bosons with delta repulsion, and on states of zero entropy, for which quantum fluctuations are larger, we reconstruct such quantum effects by quantizing GHD. The resulting theory of quantum GHD can be viewed as a multicomponent Luttinger liquid theory, with a small set of effective parameters that are fixed by the thermodynamic Bethe ansatz. It describes quantum fluctuations of truly nonequilibrium systems where conventional Luttinger liquid theory fails.
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. It offers a full and efficient framework to capture the long-wavelengths nonequilibrium dynamics in experimentally realizable one-dimensional systems, like Bose gases with delta repulsion. In this letter, we study the nonlinear sound waves emanating from initial density accumulations in the zero-temperature Bose gas. We numerically confirm the emergence of GHD by comparing its predictions with a full quantum simulation performed using the NRG-TSA-ABACUS algorithm. We prove that at zero temperature, GHD is equivalent to conventional Galilean hydrodynamics with nontrivial equations of state. We further predict, at long wavelengths and large densities, the appearance of sharp profiles in finite times, that immediately dissolve (no sustained shocks). The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to the leading contribution with one particle-hole pair on a finite energy-density background. The thermodynamic bootstrap program (TBP) formalism was recently introduced as an axiomatic approach to computing such finite-energy-density form factors for integrable field theories. We derive a new axiom within the TBP formalism from which we easily recover the predicted GHD Eulerian correlators. We also compute higher form factor contributions, with more particle-hole pairs, within the TBP, allowing for the computation of correlation functions in the diffusive, and beyond, GHD regimes. The two particle-hole form factors agree with expressions recently conjectured within the GHD.
Abstract We present steps towards an ab initio derivation of generalized hydrodynamics (GHD) in quantum integrable models, starting from the Bethe wave functions, and explained on the example of the repulsive Lieb–Liniger model. This includes an identification of the GHD quasi-particles as wave packets in the quantum model. These wave packets evolve according to a classical particle model and collect two-particle scattering shifts similar to solitons in integrable PDEs. We then discuss potential routes to obtain the GHD equation for average conserved densities in long-wavelength states from this description. As part of this, we provide an explicit formula for the action of the spectral phase-space density operator on Bethe wave functions, and show that it generates local conserved densities.
Generalised hydrodynamics (GHD) is a recent and powerful framework to study many-body integrable systems, quantum or classical, out of equilibrium. It has been applied to several models, from the delta Bose gas to the XXZ spin chain, the KdV soliton gas and many more. Yet it has only been applied to (1+1)-dimensional systems and generalisation to higher dimensions of space is non-trivial. We study the Boussinesq equation which, while generally considered to be less physically relevant than the KdV equation, is interesting as a stationary reduction of the (boosted) Kadomtsev-Petviashvili (KP) equation, a prototypical and universal example of a nonlinear integrable PDE in (2+1) dimensions. We follow a heuristic approach inspired by the Thermodynamic Bethe Ansatz in order to construct the GHD of the Boussinesq soliton gas. Such approach allows for a statistical mechanics interpretation of the Boussinesq soliton gas that comes naturally with the GHD picture. This is to be seen as a first step in the construction of the KP soliton gas, yielding insight on some classes of solutions from which we may be able to build an intuition on how to devise a more general theory. This also offers another perspective on the construction of anisotropic bidirectional soliton gases previously introduced phenomenologically by Congy et al (2021).
Generalised hydrodynamics (GHD) is a recent and powerful framework to study many-body integrable systems, quantum or classical, out of equilibrium. It has been applied to several models, from the delta Bose gas to the XXZ spin chain, the KdV soliton gas and many more. Yet it has only been applied to (1+1)-dimensional systems and generalisation to higher dimensions of space is non-trivial. We study the Boussinesq equation which, while generally considered to be less physically relevant than the KdV equation, is interesting as a stationary reduction of the (boosted) Kadomtsev-Petviashvili (KP) equation, a prototypical and universal example of a nonlinear integrable PDE in (2+1) dimensions. We follow a heuristic approach inspired by the Thermodynamic Bethe Ansatz in order to construct the GHD of the Boussinesq soliton gas. Such approach allows for a statistical mechanics interpretation of the Boussinesq soliton gas that comes naturally with the GHD picture. This is to be seen as a first step in the construction of the KP soliton gas, yielding insight on some classes of solutions from which we may be able to build an intuition on how to devise a more general theory. This also offers another perspective on the construction of anisotropic bidirectional soliton gases previously introduced phenomenologically by Congy et al (2021).