Nonlocal hydrodynamic description of quantized field models

A procedure is considered for passing to the hydrodynamic limit for a quantized multiparticle system having N local conservation laws. A non-equilibrium statistical-operator method is used. A general form is derived for the hydrodynamic equations containing sources in the linear approximation with respect to deviations from the global equilibrium state, which involve Green's functions for the currents. The hydrodynamic model in general is nonlocal in time and space. The corresponding material relations are given.Earth Physics Institute, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 70–75, July, 1994.     

On Dissipative Phenomena of the Interaction of Hamiltonian Systems

The dynamics is under study of a composite Hamiltonian system that is the union of a finite-dimensional nonlinear system and an infinite-dimensional linear system with quadratic interaction Hamiltonian. The dynamics of the finite-dimensional subsystem is determined by a nonlinear integro-differential equation with a relaxation kernel. We prove existence and uniqueness theorems and find a priori estimates for a solution. Under some assumptions on the form of interaction, the solution to the finite-dimensional subsystem converges to one of the critical points of the effective Hamiltonian.     

Nonlocal hydrodynamics in the quantum field modelϕ 4

The procedure of passing from quantum statistical mechanics to the hydrodynamics previously developed by the author is now applied to the quantum field model ⁴. For a certain class of external forces, the equations of many-body systems in quantum theory appear to be equivalent to the equations of nonlocal hydrodynamics. The hydrodynamic nonlocalities arising in constituent relations are expressed through the Green's functions for currents. Some properties of the nonlocal kernels, in particular, the conditions related to dissipation and T-invariance of the model ⁴ (an analogue of Onsager's relations), are deduced from the general symmetry properties. In hydrodynamics, nonlocality allows causality and dissipativity to be consistently combined. The connection between the classical transport coefficients and the hydrodynamic kernels is established. An algorithm for calculating constituent relations by perturbation theory, using the technique of temperature Green's functions, is described.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 1, pp. 50–68, July, 1996.     

Gas-condensate flow in the vicinity of a hydraulic fracture

The problem of gas-condensate flow in the vicinity of a production well with a hydraulic fracture is considered. In the matrix, the flow is assumed to be three-dimensional, and at the fracture, it is assumed to be two-dimensional. It is shown that, for steady-state flow, the problem is split into a physicochemical problem (of phase transitions) and a filtration problem (of determining the pressure field). Numerical solutions are constructed for a rectangular fracture with finite and infinite conductivities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 128–136, May–June, 2008.     

Relaxation effects associated with the flow of a dense gas through a porous medium

Unsteady processes of gas and Newtonian liquid flow through porous media are usually described within the framework of the standard elastic regime model [1, 2]. At the same time, from general theoretical considerations it is clear that for fairly small characteristic times of variation of the pressure and the seepage velocity the elastic regime model loses its validity and more general relaxation flow models [3, 4] must be employed. It is therefore important to determine the limits of applicability of the elastic regime model. For this purpose the unsteady process of gas flow from one vessel to another through a porous medium has been investigated theoretically and experimentally for small pressure differences and absolute pressures up to 50 MPa. It is shown that the experimental results diverge sharply from the theoretical predictions based on the elastic regime model. It is therefore proposed that for unsteady processes a generalization of Darcy's law with a relaxation kernel be employed. From the results of the experiments it is possible to determine the parameters of the kernel characterizing the internal relaxation processes in the porous medium-dense gas system.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 105–113, January–February, 1991.     

Dissipation conditions in a system of coupled oscillators

A system of interacting oscillators with a quadratic Hamiltonian is investigated. The necessary and sufficient conditions are determined for the system to exhibit dissipative properties with respect to one designated oscillator. One of the necessary conditions is the existence of a continuous frequency spectrum in the system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 94–98, January, 1988.