Multiple solutions of the quasirelativistic Choquard equation

We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential

Evolution of a Network of Vortex Loops in HeII. Exact Solution of the "Rate Equation"

Evolution of a network of vortex loops in HeII due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function $n(l)$ of number of loops of length $l$ proposed by Copeland with coauthors. By using the special ansatz in the ''collision'' integral we have found the exact power-like solution of ''kinetic equation'' in stationary case. That solution is the famous equilibrium distribution $n(l)\varpropto l^{-5/2}$ obtained earlier in numerical calculations. Our result, however, is not equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of the vortex loop sizes. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of order of interline space. We also obtain that the decay of the vortex tangle obeys the Vinen equation, obtained earlier phenomenologically. We evaluate also the full rate of reconnection events. PACS-number 67.40Comment: 4 pages, submitted to PR

Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor

Single polymer adsorption in shear: flattening versus hydrodynamic lift and corrugation effects

The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of flexible polymers. Surface friction due to small-wavelength surface potential corrugations is argued to weaken the surface attraction as well.Comment: 6 pages, 4 figure

Path Integral Approach to the Non-Relativistic Electron Charge Transfer

A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement collisions is formulated in terms of influence functionals. It has been shown that the electron charge transfer process can be treated either as electron transition problem or as elastic scattering of ion and atom in the some effective potential field. The first-order Born approximation for the electron charge transfer cross section has been reproduced to prove the adequacy of the path integral approach for this problem.Comment: 19 pages, 1 figure, to appear in Journal of Physics B: Atomic, Molecular & Optical, vol.34, 200

Threefold onset of vortex loops in superconductors with a magnetic core

A magnetic inclusion inside a superconductor gives rise to a fascinating complex of {\it vortex loops}. Our calculations, done in the framework of the Ginzburg-Landau theory, reveal that {\it loops always nucleate in triplets} around the magnetic core. In a mesoscopic superconducting sphere, the final superconducting state is characterized by those confined vortex loops and the ones that eventually spring to the surface of the sphere, evolving into {\it vortex pairs} piercing through the sample surface.Comment: 6 pages, 6 figures (low resolution), latex2

Diffusion of Inhomogeneous Vortex Tangle and Decay of Superfluid Turbulence

The theory describing the evolution of inhomogeneous vortex tangle at zero temperature is developed on the bases of kinetics of merging and splitting vortex loops. Vortex loops composing the vortex tangle can move as a whole with some drift velocity depending on their structure and their length. The flux of length, energy, momentum etc. executed by the moving vortex loops takes a place. Situation here is exactly the same as in usual classical kinetic theory with the difference that the "carriers" of various physical quantities are not the point particles, but extended objects (vortex loops), which possess an infinite number of degrees of freedom with very involved dynamics. We offer to fulfill investigation basing on supposition that vortex loops have a Brownian structure with the only degree of freedom, namely, lengths of loops $l$. This conception allows us to study dynamics of the vortex tangle on the basis of the kinetic equation for the distribution function $n(l,t)$ of the density of a loop in the space of their lengths. Imposing the coordinate dependence on the distribution function n(l,\mathbf{% r},t) and modifying the "kinetic" equation with regard to inhomogeneous situation, we are able to investigate various problem on the transport processes in superfluid turbulence. In this paper we derive relation for the flux of the vortex line density $\mathcal{L}(x,t)$. The correspoding evolution of quantity $\mathcal{L}(x,t)$ obeys the diffusion type equation as it can be expected from dimensional analysis. The according diffusion coefficient is evaluated from calculation of the (size dependent) free path of the vortex loops. We use this equation to describe the decay of the vortex tangle at very low temperature. We compare that solution with recent experiments on decay of the superfluid turbulence.Comment: 7 pages, 6 figure

Quench Induced Vortices in the Symmetry Broken Phase of Liquid 4^4He

Motivated by the study of cosmological phase transitions, our understanding of the formation of topological defects during spontaneous symmetry-breaking and the associated non-equilibrium field theory has recently changed. Experiments have been performed in superfluid $^4$He to test the new ideas involved. In particular, it has been observed that a vortex density is seen immediately after pressure quenches from just below the $\lambda$ transition. We discuss possible interpretations of these vortices, conclude they are consistent with our ideas of vortex formation and propose a modification of the original experiments.Comment: 29 pages, RevTeX with one EPS figur