Hydrodynamic equations and correlation functions

Leo P. Kadanoff, Paul C. Martin

Alexander G. Abanov

Pavlo Shygorin, Svidzynsky

Starting from the first principles of statistical mechanics, the two-fluid hydrodynamics of superconductor in ideal approximation is constructed.The system of equations of motion for normal and anomalous correlation functions is used for hydrodynamic description.Transition to equations of hydrodynamics is performed using an expansion of equations of motion for correlation functions in terms of a small parameter.

Eldad Bettelheim, Alexander G. Abanov, Paul B. Wiegmann

Abstract. We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1, 2, 3, 4] and provide vital tools to study nonequilibrium dynamics of electronic systems. The method we developed is based only on Wick’s theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form. Quantum hydrodynamics and nonlinear differential equations... 2 1.

Guido Mazzuca

Abstract In recent years, a lot of effort has been put in describing the hydrodynamic behavior of integrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics (GHDs) to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the GHDs equations develops shocks at ξ 0 = x t ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued by this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ 0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.

Norman Henry March