Generalized Hydrodynamics Approach Research Articles

Finite temperature spin diffusion in the Hubbard model in the strong coupling limit

We investigate finite temperature spin transport in one spatial dimension by considering the spin-spin correlation function of the Hubbard model in the limiting case of infinitely strong repulsion. We find that in the absence of a magnetic field the transport is diffusive, and derive the spin diffusion constant. Our approach is based on asymptotic analysis of a Fredholm determinant representation. The obtained results are in agreement with Generalized Hydrodynamics approach.

Delocalization of Longitudinal Acoustic-Like Excitations in DNA Due to Structural Effects

Terahertz-frequency phonon-like modes in DNA have been widely studied both experimentally and theoretically in recent years. However, current theoretical models turn out to fail to reproduce some basic properties of these modes. Using a generalized hydrodynamics approach and the results of inelastic X-ray scattering measurements, we propose a model to describe structural effects due to wavenumber dependence of the static structure factor in the dynamics of longitudinal acoustic-like excitations in DNA. Our analysis qualitatively suggests that on a length scale corresponding to a wavenumber region between the positions of the maximum and the minimum of the dispersion relation for the excitation frequency, structural effects may induce a tendency of delocalization of the dynamics. This proposal is consistent with the recent experimental observations of delocalized terahertz-frequency DNA phonon-like modes that seem to be relevant to biological function.

The Whitham approach to the c → 0 limit of the Lieb–Liniger model and generalized hydrodynamics

The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial conditions. A similarly powerful approach has recently emerged that is applicable to quantum integrable systems, namely the generalized hydrodynamics approach. This paper aims at showing that the Whitham approach is the semiclassical limit of the generalized hydrodynamics approach by connecting the two formal methods explicitly on the example of the Lieb–Liniger model on the quantum side to the non-linear Schrödinger equation on the classical side in the c → 0 limit, c being the interaction parameter. We show how quantum expectation values may be computed in this limit based on the connection established here which is mentioned above.

Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb-Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

Dressed excitations, thermodynamics and relaxation in the XXZ Heisenberg model

In this note, we discuss the low and high temperature contribution of thermodynamic Bethe ansatz (TBA) dressed excitations in the thermodynamics and energy-magnetization relaxation within the generalized hydrodynamics approach in the linear response regime. In particular, we show how the temperature dependent dispersions of the excitations reproduce well known behavior of the specific heat, magnetic susceptibility, spin and energy Drude weights. In this context, we derive a further formulation of the Drude weights from the finite wavevector relaxation. Furthermore, we contrast the TBA description of thermodynamics and dynamics in terms of a multitude of string excitations to that in terms of a single quasi-particle in low energy effective theories.

Long-range strain correlations in 3D quiescent glass forming liquids

Recent two-dimensional computer simulations and experiments indicate that even supercooled liquids exhibit long-lived, long-range strain correlations expected only in solids. Here we investigate this issue in three dimensions via Newtonian molecular-dynamics simulations, by a generalized hydrodynamics approach, and by experiments on Brownian hard-sphere colloids. Both in the glassy state and in liquid regimes, strain correlations are predicted to decay with a power law, reminiscent of elastic fields around an inclusion. In contrast, the temporal evolution of the correlation amplitude is distinct in the liquid state, where it grows linearly with time, and in the glass, where it reaches a time-independent plateau. These predictions are assessed via molecular-dynamics simulations and experiments. In simple liquids, the size of the cooperative strain patterns is of the order of the distance traveled by (high-frequency) transverse sound prior to structural relaxation. This length is of the order of nanometers in a normal liquid and grows to macroscale upon approaching the glass transition.

Local exchange-correlation vector potential with memory in time-dependent density functional theory: The generalized hydrodynamics approach

Using Landau Fermi liquid theory we derive a nonlinear non-adiabatic approximation for the exchange-correlation (xc) vector potential defined by the xc stress tensor. The stress tensor is a local nonlinear functional of two basic variables - the displacement vector and the second-rank tensor which describes the evolution of momentum in a local frame moving with Eulerian velocity. For irrotational motion and equilibrium initial state the dependence on the tensor variable reduces to that on a metrics generated by a dynamical deformation of the system.

Impulsive stimulated light scattering from glass-forming liquids. I. Generalized hydrodynamics approach

The generalized hydrodynamics equations, including nonlocal behavior in time, are used to calculate density response functions for impulsive stimulated light scattering (ISS) from glass-forming liquids. Single-exponential relaxation dynamics are considered first, and then the results are generalized to account for complex relaxation. Thermal diffusion, acoustic, and relaxation modes are described. The time dependence of both acoustic and relaxation modes yields the structural relaxation dynamics. In addition, the relative amplitudes of the modes in ISS data yield the Debye–Waller factor fq, called the nonergodicity parameter in mode-coupling theory (MCT) of glass-forming liquids, in the limit of low wave vector q. This permits testing of MCT predictions of a square-root cusp in fq→0(T) at a crossover temperature Tc. The information which can be obtained through ISS is compared in theoretical and practical terms to that obtainable through low-frequency light scattering spectroscopy.

Light-scattering study of the liquid-glass transition in propylene carbonate.

Depolarized light-scattering spectra of propylene carbonate were obtained in the frequency range 0.2 GHz--4 THz at temperatures from 350 to 135 K. Analysis of the resulting susceptibility spectra revealed reasonable agreement with the predictions of the idealized mode coupling theory, yielding critical exponents a=0.29, b=0.50, and an exponent parameter \ensuremath{\lambda}=0.78\ifmmode\pm\else\textpm\fi{}0.05. A scaling analysis demonstrated critical slowing down of the scaling frequencies from both above and below ${\mathit{T}}_{\mathit{C}}$, with the scaling frequency extrapolating to zero at ${\mathit{T}}_{\mathit{C}}$=187\ifmmode\pm\else\textpm\fi{}5 K. The \ensuremath{\alpha}-relaxation peak was fit to a Kohlrausch function, which gave \ensuremath{\beta}=0.77\ifmmode\pm\else\textpm\fi{}0.05 for 210\ensuremath{\le}T\ensuremath{\le}350 K with no sign of systematic temperature dependence. An extended mode coupling theory analysis was also carried out which corroborated the results obtained with the idealized version. Polarized Brillouin spectra were also obtained, and were analyzed with a generalized hydrodynamics approach using low-frequency sound velocity values determined separately in an ultrasonics experiment. The results indicate that the Cole-Davidson function is not an adequate model for the structural relaxation due to the neglect of \ensuremath{\beta}-relaxation processes, so that this analysis cannot provide a meaningful estimate of ${\mathit{T}}_{\mathit{C}}$. Furthermore, the \ensuremath{\alpha}-relaxation time associated with Brillouin scattering was found to be about five times shorter than that probed by depolarized light scattering.

Generalized hydrodynamics approach to the Knudsen problem.

It is shown that the Knudsen problem (``paradox'') can be resolved by the flow-rate formula for a non-Newtonian fluid flowing under a pressure gradient in a circular tube, as reported elsewhere. The flow-rate formula exhibits a minimum in the low-pressure regime but gives the Hagen-Poiseuille linear dependence on pressure in the high-pressure regime. Since the generalized hydrodynamic equations used for the derivation of the flow-rate formula are derived from the Boltzmann equation, the present solution of the Knudsen problem is well founded on the kinetic theory of gases. The nonlinear transport processes, which increasingly manifest themselves as the gas density decreases, are the cause for the emergence of a minimum in the flow rate for rarefied gases in circular tube flow. The entropy production and also the drag coefficient are calculated as a function of pressure difference, Reynolds number, and other parameters characteristic of the system.

On the memory functions in simple classical liquids

The relation between the two memory function formalisms for correlation functions in classical liquids is discussed. It is found that the kinetic equation formalism of Duderstadt and Akcasu with a simple exponential memory function can account for the double Gaussian form of the memory function in the generalized-hydrodynamics approach. The former therefore gives reasonably good results for the coherent scattering function S(k, ω), as is shown for the case of liquid Rb at 315 K in the range 1.25 ⩽k ⩽ 5.5 A−.

Kinetic theory of rough sphere fluids: Density fluctuations

We construct a kinetic equation for the phase space density correlation function (PSDCF) in a rough sphere fluid (at the generalized Enskog level) which is valid for arbitrary wave number and frequency. The kinetic equation yields the first two kinetic sum rules exactly; also the density–density correlation function implied by it has the correct first four sum rules exactly. We use the short time behavior of PSDCF and the generalized hydrodynamics approach to construct approximate interpolation formulas for a variety of space–time dependent correlation functions related to conserved variables in the fluid. The coupling of modes described by these correlation functions to the test particle density fluctuations is responsible for the known asymptotic power law decay in the linear and angular velocity correlation functions. As a by-product of this study, we also obtain expressions for various (bare) transport coefficients in a dense rough sphere fluid.

Internal Relaxation in Chemically Reacting Fluids

The coupling of an internal relaxation to both the chemical reaction and diffusion processes is investigated for a fluid mixture. A microscopic approach beginning with a generalized Langevin equation is used to derive relaxation equations for the concentration fluctuations of the species in specified internal states as well as total concentration fluctuations. These equations are used to calculate the matrix of concentration correlation functions which are then related to the intensity of the light scattered from the fluid. The circumstances under which such a generalized hydrodynamics approach must be used are examined. The possibility of extracting information about both the chemical and internal relaxation processes from a measurement of the width of the polarized component of the Rayleigh line is considered.