619 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
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
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
Gravitational effects on defect formation in melt grown photorefractive materials : bismuth silicate
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003.Includes bibliographical references (leaves 206-213).Photorefractivity is the modulation of index of refraction due to nonuniform illumination, and numerous applications have been demonstrated utilizing this nonlinear optical property. However, commercial production is seriously impeded by the inability to produce bulk material with the homogeneity of opto-electronic properties that is required for device applications. Bismuth Silicate, Bi12SiO20, (BSO) is a photorefractive material with outstanding properties including a fast response time and high sensitivity is studied. Its photorefractivity is due to a native defect whose exact nature and origin have not been unambiguously determined. Motivation for current research arose from unexplained optical variations observed in BSO that implicate convective interference as playing a role in native defect formation. Microgravity growth experiments are proposed in order to establish a controlled, convection-free environment to study the origin and nature of the critical native defect. This work aims at resolving critical aspects of performing quantitative microgravity growth experiments that include the interaction of BSO melts with its confinement material; development and characterization of a vertical Bridgman-Stockbarger growth system with a quantifiable, reproducible, and controllable thermal environment; and Bridgman-Stockbarger growth experiments. A comparative analysis of crystals was done in order to establish the relationship between variations in opto-electronic properties as a function of changes in growth conditions. Wetting experiments revealed the sessile drop method to be inappropriate for the BSO-platinum system due to grain boundary pinning. No fundamental difference between the wetting behavior in a terrestrial and a low gravity environment was observed.(cont.) Results from the comparative analysis indicate a lower defect concentration in Bridgman-Stockbarger material as compared to Czochralski material. The ambient atmosphere during processing and high temperature annealing was found affect material response, including removal of the photochromic response and decrease of carrier lifetime. The lack of the critical defect in hydrothermal BSO, and its existence in all melt grown material indicates that the melt plays a fundamental role in its formation. Clustering in the melt is implicated in the literature from nonlinear melt properties. It is therefore hypothesized that these clusters in the melt act as precursors for native defect formation and subject to gravitationally induced convection. The support of the National Aeronautics and Space Administration is gratefully acknowledged.by Michaela E.K. Wiegel.Ph.D
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
Some approximate analytical methods in the study of the self-avoiding loop model with variable bending rigidity and the critical behaviour of the strong coupling lattice Schwinger model with Wilson fermions
Some time ago Salmhofer demonstrated the equivalence of the strong coupling
lattice Schwinger model with Wilson fermions to a certain 8-vertex model which
can be understood as a self-avoiding loop model on the square lattice with
bending rigidity and monomer weight . The
present paper applies two approximate analytical methods to the investigation
of critical properties of the self-avoiding loop model with variable bending
rigidity, discusses their validity and makes comparison with known MC results.
One method is based on the independent loop approximation used in the
literature for studying phase transitions in polymers, liquid helium and cosmic
strings. The second method relies on the known exact solution of the
self-avoiding loop model with bending rigidity . The present
investigation confirms recent findings that the strong coupling lattice
Schwinger model becomes critical for . The phase
transition is of second order and lies in the Ising model universality class.
Finally, the central charge of the strong coupling Schwinger model at
criticality is discussed and predicted to be .Comment: 22 pages LaTeX, 6 Postscript figure
Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time
In this paper we show that the existence of a primarily discrete space-time
may be a fruitful assumption from which we may develop a new approach of
statistical thermodynamics in pre-relativistic conditions. The discreetness of
space-time structure is determined by a condition that mimics the Heisenberg
uncertainty relations and the motion in this space-time model is chosen as
simple as possible. From these two assumptions we define a path-entropy that
measures the number of closed paths associated with a given energy of the
system preparation. This entropy has a dynamical character and depends on the
time interval on which we count the paths. We show that it exists an
like-equilibrium condition for which the path-entropy corresponds exactly to
the usual thermodynamic entropy and, more generally, the usual statistical
thermodynamics is reobtained. This result derived without using the Gibbs
ensemble method shows that the standard thermodynamics is consistent with a
motion that is time-irreversible at a microscopic level. From this change of
paradigm it becomes easy to derive a . A comparison with the
traditional Boltzmann approach is presented. We also show how our approach can
be implemented in order to describe reversible processes. By considering a
process defined simultaneously by initial and final conditions a well defined
stochastic process is introduced and we are able to derive a Schroedinger
equation, an example of time reversible equation.Comment: latex versio
Entangled Polymer Rings in 2D and Confinement
The statistical mechanics of polymer loops entangled in the two-dimensional
array of randomly distributed obstacles of infinite length is discussed. The
area of the loop projected to the plane perpendicular to the obstacles is used
as a collective variable in order to re-express a (mean field) effective theory
for the polymer conformation. It is explicitly shown that the loop undergoes a
collapse transition to a randomly branched polymer with .Comment: 17 pages of Latex, 1 ps figure now available upon request, accepted
for J.Phys.A:Math.Ge
Why is the DNA Denaturation Transition First Order?
We study a model for the denaturation transition of DNA in which the
molecules are considered as composed of a sequence of alternating bound
segments and denaturated loops. We take into account the excluded-volume
interactions between denaturated loops and the rest of the chain by exploiting
recent results on scaling properties of polymer networks of arbitrary topology.
The phase transition is found to be first order in d=2 dimensions and above, in
agreement with experiments and at variance with previous theoretical results,
in which only excluded-volume interactions within denaturated loops were taken
into account. Our results agree with recent numerical simulations.Comment: Revised version. To appear in Phys. Rev. Let
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