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Register a new userEquations of state in generalized hydrodynamics
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We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.
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We utilize a generalized Irving-Kirkwood procedure to derive the hydrodynamic equations of an active matter suspension with internal structure and driven by internal torque. The internal structure and torque of the active Brownian particles give rise to a balance law for internal angular momentum density, making the hydrodynamic description a polar theory of continuum mechanics. We derive exact microscopic expressions for the stress tensor, couple stress tensor, internal energy density, and heat flux vector. Unlike passive matter, the symmetry of the stress tensor is broken explicitly due to active internal torque and the antisymmetric component drives the internal angular momentum density. These results provide a molecular basis to understand the transport characteristics and collectively provide a strategy to develop the theory of linear irreversible thermodynamics of active matter.
We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts entropy increase and thermal states as the only stationary states. The equation applies to any hydrodynamic system with any number of local, PT-symmetric conserved quantities, in arbitrary dimension. It is fully expressed in terms of elements of an extended Onsager matrix. In integrable systems, this matrix admits an expansion in the density of excitations. We evaluate exactly its 2-particle-hole contribution, which dominates at low density, in terms of the scattering phase and dispersion of the quasiparticles, giving a lower bound for the extended Onsager matrix and entropy production. We conclude with a molecular dynamics simulation, demonstrating thermalisation over diffusive time scales in the Toda interacting particle model with an inhomogeneous energy field.
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.
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is derived in terms of a Kinetic Theory based on the Non-Equilibrium Statistical Ensemble Formalism. The general system of coupled evolution equations is derived. Maxwell times - which are of large relevance to determine the character of the motion - are derived. They also have a quite important role for the choice of the contraction of description (limitation in the number of fluxes to be retained) in the study of the hydrodynamic motion. In a description of order 1 it is presented an analysis of the technological process of thermal prototyping.
We provide a pure state formulation for hydrodynamic dynamics of isolated quantum many-body systems. A pure state describing quantum systems in local thermal equilibrium is constructed, which we call a local thermal pure quantum ($ell$TPQ) state. We show that the thermodynamic functional and the expectation values of local operators (including a real-time correlation function) calculated from the $ell$TPQ state converge to those from a local Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we investigate a one-dimensional spin chain and observe the hydrodynamic relaxation obeying the Fouriers law. We further prove the second law of thermodynamics and the quantum fluctuation theorem, which are also validated numerically. The $ell$TPQ formulation gives a useful theoretical basis to describe the emergent hydrodynamic behavior of quantum many-body systems furnished with a numerical efficiency, being applicable to both the non-relativistic and relativistic regimes.
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