317 research outputs found
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 of number of loops
of length 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 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 . This
conception allows us to study dynamics of the vortex tangle on the basis of the
kinetic equation for the distribution function 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
. The correspoding evolution of quantity
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 He
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 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 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
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