Related papers: Soliton gases and generalized hydrodynamics
The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs…
This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of…
Upon breaking the integrability, the equations of generalized hydrodynamics (GHD) are supplemented by a Boltzmann collision term. Such terms are typically complicated and stem from a perturbative treatment of integrability-breaking terms in…
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and…
We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time…
In the spirit of Sakharov's `metric elasticity' proposal, we draw a loose analogy between general relativity and the hydrodynamic state of a quantum gas. In the `top-down' approach, we examine the various conditions which underlie the…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
We study non-homogeneous quantum quenches in a one-dimensional gas of repulsive spin-$1/2$ fermions, as described by the integrable Yang-Gaudin model. By means of generalized hydrodynamics (GHD), we analyze in detail the real-time evolution…
Hydrodynamics and quantum mechanics have many elements in common, as the density field and velocity fields are common variables that can be constructed in both descriptions. Starting with the Schroedinger equation and the Klein-Gordon for a…
Equations of fluid dynamics are formulated, which hold invariant under the action of the l-conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a…
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes…
A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the…
We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of…
Macroscopic dynamics of soliton gases can be analytically described by the thermodynamic limit of the Whitham equations, yielding an integro-differential kinetic equation for the density of states. Under a delta-functional ansatz, the…
We consider a new geometric approach to Madelung's quantum hydrodynamics (QHD) based on the theory of gauge connections. In particular, our treatment comprises a constant curvature thereby endowing QHD with intrinsic non-zero holonomy. In…
The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport…
The generalized hydrodynamics (GHD) formalism has become an invaluable tool for the study of spatially inhomogeneous quantum quenches in (1+1)-dimensional integrable models. The main paradigm of the GHD is that at late times local…
We investigate a lattice model representing a granular gas in a thin channel. We deduce the hydrodynamic description for the model from the microscopic dynamics in the large system limit, including the lowest finite-size corrections. The…
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…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…