Hydrodynamics beyond local equilibrium: application to electron gas

Generalized hydrodynamic theory, which does not rest on the requirement of a local equilibrium, is derived in the long-wave limit of a kinetic equation. The theory bridges the whole frequency range between the quasistatic (Navier-Stokes) hydrodynamics and the high frequency (Vlasov) collisionless limit. In addition to pressure and velocity the theory includes new macroscopic tensor variables. In a linear approximation these variables describe an effective shear stress of a liquid and the generalized hydrodynamics recovers the Maxwellian theory of highly viscous fluids - the media behaving as solids on a short time scale, but as viscous fluids on long time intervals. It is shown that the generalized hydrodynamics can be applied to the Landau theory of Fermi liquid. Illustrative results for collective modes in confined systems are given, which show that nonequilibrium effects qualitatively change the collective dynamics in comparison with the predictions of the heuristic Bloch's hydrodynamics. Earlier improvements of the Bloch theory are critically reconsidered.Comment: 15 pages, RevTeX, to appear in Phys.Rev.B (2000

Online Coloring and a New Type of Adversary for Online Graph Problems

We introduce a new type of adversary for online graph problems. The new adversary is parameterized by a single integer $\kappa$, which upper bounds the number of connected components that the adversary can use at any time during the presentation of the online graph $G$. We call this adversary "$\kappa$ components bounded", or $\kappa$-CB for short. On one hand, this adversary is restricted compared to the classical adversary because of the $\kappa$-CB constraint. On the other hand, we seek competitive ratios parameterized only by $\kappa$ with no dependence on the input length $n$, thereby giving the new adversary power to use arbitrarily large inputs. We study online coloring under the $\kappa$-CB adversary. We obtain finer analysis of the existing algorithms $FirstFit$ and $CBIP$ by computing their competitive ratios on trees and bipartite graphs under the new adversary. Surprisingly, $FirstFit$ outperforms $CBIP$ on trees. When it comes to bipartite graphs $FirstFit$ is no longer competitive under the new adversary, while $CBIP$ uses at most $2\kappa$ colors. We also study several well known classes of graphs, such as $3$-colorable, $C_k$-free, $d$-inductive, planar, and bounded treewidth, with respect to online coloring under the $\kappa$-CB adversary. We demonstrate that the extra adversarial power of unbounded input length outweighs the restriction on the number of connected components leading to non existence of competitive algorithms for these classes

Different scenarios of topological phase transitions in homogeneous neutron matter

We study different scenarios of topological phase transitions in the vicinity of the \pi^0 condensation point in neutron matter. The transitions occur between the Fermi-liquid state and a topologically different one with two sheets of the Fermi surface. Two possibilities of a rearrangement of quasiparticle degrees of freedom are shown: the first-order topological phase transition and the second-order one. The order of the phase transition is found to be strongly dependent on the value of the critical wave vector of the soft \pi^0 mode. The thermodynamics of the system is also studied. It is shown that the topology of the quasiparticle momentum distribution is mainly determined by the neutron matter density, while the temperature T is essential in a narrow density region. A simple explanation of the first-order topological phase transition at T=0 is given.Comment: 8 pages, 11 figures. The English of the text was revised; 2 references were added; minor changes in figures were made; all results remained unchange

Phonon-particle coupling effects in odd-even mass differences of semi-magic nuclei

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on a direct solving the Dyson equation with PC corrected mass operator, is used for finding the odd-even mass difference between 18 even Pb isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather high accuracy of the predictions for these mass differences already on the mean-field level, with the average deviation from the existing experimental data equal to 0.389 MeV. It is only a bit worse than the corresponding value of 0.333 MeV for the Skyrme EDF HFB-17 which belongs to a family of Skyrme EDFs with the highest overall accuracy in describing the nuclear masses. Account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ significantly diminishes the deviation of the theory from the data till 0.218 MeV.Comment: 6 pages, 3 figures, 3 table

Including particle-vibration coupling in the Fayans functional. Odd-even mass differences of semi-magic nuclei

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on the direct solution of the Dyson equation with PC corrected mass operator, is presented. It is used for finding the odd-even mass difference between even Pb and Sn isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather highly accurate predictions for these mass differences already at the mean-field level. In the case of the lead chain, account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ makes agreement of the theory with the experimental data significantly better. For the tin chain, the situation is not so definite. In this case, the PC corrections make agreement better in the case of the addition mode but they spoil the agreement for the removal mode. We discuss the reason of such a discrepancy.Comment: 10 pages, 3 figures, 11 tables. arXiv admin note: substantial text overlap with arXiv:1710.0915

Master equation approach to the theory of diffusion in alloys and calculations of enhancement factors for tracer solvent and tracer solute diffusion in FCC alloys

The earlier-suggested master equation approach is used to develop the consistent statistical theory of diffusion in alloys using the five-frequency model of FCC alloys as an example. Expressions for the Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are presented. We discuss methods of calculations of these averages using both the mean-field and the pair-cluster approximation to describe influence of vacancy-solute and solute-solute interactions, and both the nearest-neighbor and the second-shell approximation to describe vacancy correlation effects. The methods developed are used for calculations of enhancement factors which determine the concentration dependence of tracer self-diffusion and tracer solute diffusion in dilute FCC alloys. For the tracer self-diffusion, we show that some significant contribution to the enhancement factor related to the thermodynamic activity of vacancies was missed in the previous treatments of this problem. It implies that the most of existing estimates of parameters of the five-frequency model for real alloys should be revised. For the tracer solute diffusion, the expression for the enhancement factor seems to be presented for the first time. The results obtained are used to estimate the microscopic parameters important for diffusion, including the vacancy-solute interaction, in several FCC alloys for which necessary experimental data are available.Comment: 18 page, 3 jpg figures, LaTe

Specific Features of Motion of Cations and Anions in Electrolyte Solutions

The nature of mobility of ions and water molecules in dilute aqueous solutions of electrolytes (at most fifteen water molecules per ion) is investigated. It is shown that the behavior of the mobility coefficients of water molecules and ions, as well as the self-diffusion coefficients of water molecules, are determined by the radii of their hard shells rather than by the effect of the hydrogen bond network. It is established that the influence of hydration effects on the density of the system and the self-diffusion coefficients of water molecules does not exceed several per cent. Based on microscopic concepts, it is shown that the different behaviors of a $\rm K^{+}$ cation and an $\rm F^{-}$ anion with equal rigid radii are in good agreement with specific features of the intermolecular interaction described by the generalized Stillinger--David potential.Comment: 9 pages, 3 figure

Master equation approach to configurational kinetics of non-equilibrium alloys and its application to studies of L1_0 type orderings

We review a series of works where the fundamental master equation is used to develop a microscopical description of evolution of non-equilibrium atomic distributions in alloys. We describe exact equations for temporal evolution of local concentrations and their correlators as well as approximate methods to treat these equations, such as the kinetic mean-field and the kinetic cluster methods. We also describe an application of these methods to studies of kinetics of L1_0 type orderings in FCC alloys which reveal a number of peculiar microstructural effects, many of them agreeing well with experimental observations.Comment: 11 pages, 5 figures (figures look much better in PS than in PDF). Presented at the NATO ARW (Advanced Research Workshop) "New kinds of phase transitions: Transformations in disordered substances", Moscow, Russia, Volga River ship, May 24-28, 200

Semi-microscopic model of pairing in nuclei

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab intio BCS gap equation with Argonne v18 force and the self-consistent Energy Density Functional Method basis characterized with the bare nucleon mass. The BCS theory is formulated in terms of the model space S0 with the effective pairing interaction calculated from the first principles in the subsidiary space S0. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei confirm the validity of the model. The role of the self-consistent basis is stressed.Comment: 22 pages, 9 figures, 3 table

On limits of ab initio calculations of pairing gap in nuclei

A brief review of recent microscopic calculations of nuclear pairing gap is given. A semi-microscopic model is suggested in which the ab-initio effective pairing interaction is supplemented with a small phenomenological addendum. It involves a parameter which is universal for all medium and heavy nuclei. Calculations for several isotopic and isotonic chains of semi-magic nuclei confirm the relevance of the model.Comment: 16 pages, 6 fig