228 research outputs found
Conformal Turbulence with Boundary
Based upon the formalism of conformal field theory with a boundary, we give a
description of the boundary effect on fully developed two dimensional
turbulence. Exact one and two point velocity correlation functions and energy
power spectrum confined in the upper half plane are obtained using the image
method. This result enables us to address the infrared problem of the theory of
conformal turbulence.Comment: 10pages, KHTP-93-01, SNUCTP-93-0
Realistic Electron-Electron Interaction in a Quantum Wire
The form of an effective electron-electron interaction in a quantum wire with
a large static dielectric constant is determined and the resulting properties
of the electron liquid in such a one-dimensional system are described. The
exchange and correlation energies are evaluated and a possibility of a
paramagnetic-ferromagnetic phase transition in the ground state of such a
system is discussed. Low-energy excitations are briefly described.Comment: 10 pages, 6 figure
On Fields with Finite Information Density
The existence of a natural ultraviolet cutoff at the Planck scale is widely
expected. In a previous Letter, it has been proposed to model this cutoff as an
information density bound by utilizing suitably generalized methods from the
mathematical theory of communication. Here, we prove the mathematical
conjectures that were made in this Letter.Comment: 31 pages, to appear in Phys.Rev.
Statistical Mechanics of the Self-Gravitating Gas: I. Thermodynamic Limit and Phase Diagram
We provide a complete picture to the selfgravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations, analytic mean field methods
(MF) and low density expansions. The system is shown to possess an infinite
volume limit in the grand canonical (GCE), canonical (CE) and microcanonical
(MCE) ensembles when(N, V) --> infinity, keeping N/ V^{1/3} fixed. We compute
the equation of state (we do not assume it as is customary), as well as the
energy, free energy, entropy, chemical potential, specific heats, compressibi-
lities and speed of sound;we analyze their properties, signs and singularities.
All physical quantities turn out to depend on a single variable eta = G m^2 N/
[V^{1/3} T] that is kept fixed in the N--> infinity and V --> infinity limit.
The system is in a gaseous phase for eta < eta_T and collapses into a dense
objet for eta > \eta_T in the CE with the pressure becoming large and negative.
At eta simeq eta_T the isothermal compressibility diverges. Our Monte Carlo
simulations yield eta_T simeq 1.515. PV/[NT] = f(eta) and all physical magni-
tudes exhibit a square root branch point at eta = eta_C > eta_T. The MF for
spherical symmetry yields eta_C = 1.561764.. while Monte Carlo on a cube yields
eta_C simeq 1.540.The function f(eta) has a second Riemann sheet which is only
physically realized in the MCE.In the MCE, the collapse phase transition takes
place in this second sheet near eta_MC = 1.26 and the pressure and temperature
are larger in the collapsed phase than in the gas phase.Both collapse phase
transitions (CE and MCE) are of zeroth order since the Gibbs free energy jumps
at the transitions. f(eta), obeys in MF a first order non-linear differential
equation of first kind Abel's type.The MF gives an extremely accurate picture
in agreement with Monte Carlo both in the CE and MCE.Comment: Latex, 51 pages, 15 .ps figures, to appear in Nucl. Phys.
Superfluid Flow Past an Array of Scatterers
We consider a model of nonlinear superfluid flow past a periodic array of
point-like scatterers in one dimension. An application of this model is the
determination of the critical current of a Josephson array in a regime
appropriate to a Ginzburg-Landau formulation. Here, the array consists of short
normal-metal regions, in the presence of a Hartree electron-electron
interaction, and embedded within a one-dimensional superconducting wire near
its critical temperature, . We predict the critical current to depend
linearly as , while the coefficient depends sensitively on the
sizes of the superconducting and normal-metal regions and the strength and sign
of the Hartree interaction. In the case of an attractive interaction, we find a
further feature: the critical current vanishes linearly at some temperature
less than , as well as at itself. We rule out a simple
explanation for the zero value of the critical current, at this temperature
, in terms of order parameter fluctuations at low frequencies.Comment: 23 pages, REVTEX, six eps-figures included; submitted to PR
Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r
The MCMC analysis of the CMB+LSS data in the context of the Ginsburg-Landau
approach to inflation indicated that the fourth degree double--well inflaton
potential best fits the present CMB and LSS data. This provided a lower bound
for the ratio r of the tensor to scalar fluctuations and as most probable value
r = 0.05, within reach of the forthcoming CMB observations. We systematically
analyze here the effects of arbitrary higher order terms in the inflaton
potential on the CMB observables: spectral index ns and ratio r. Furthermore,
we compute in close form the inflaton potential dynamically generated when the
inflaton field is a fermion condensate in the inflationary universe. This
inflaton potential turns to belong to the Ginsburg-Landau class too. The
theoretical values in the (ns,r) plane for all double well inflaton potentials
in the Ginsburg-Landau approach (including the potential generated by fermions)
turn to be inside a universal banana-shaped region B. The upper border of the
banana-shaped region B is given by the fourth order double--well potential and
provides an upper bound for the ratio r.The lower border of B is defined by the
quadratic plus an infinite barrier inflaton potential and provides a lower
bound for the ratio r. For example, the current best value of the spectral
index ns = 0.964, implies r is in the interval: 0.021 < r < 0.053.
Interestingly enough, this range is within reach of forthcoming CMB
observations.Comment: 24 pages, 10 figures. Presentation improved. To appear in Annals of
Physic
Strings in Homogeneous Background Spacetimes
The string equations of motion for some homogeneous (Kantowski-Sachs, Bianchi
I and Bianchi IX) background spacetimes are given, and solved explicitly in
some simple cases. This is motivated by the recent developments in string
cosmology, where it has been shown that, under certain circumstances, such
spacetimes appear as string-vacua.
Both tensile and null strings are considered. Generally, it is much simpler
to solve for the null strings since then we deal with the null geodesic
equations of General Relativity plus some additional constraints.
We consider in detail an ansatz corresponding to circular strings, and we
discuss the possibility of using an elliptic-shape string ansatz in the case of
homogeneous (but anisotropic) backgrounds.Comment: 25 pages, REVTE
Minimal energy for the traveling waves of the Landau-Lifshitz equation
We consider nontrivial finite energy traveling waves for the Landau-Lifshitz
equation with easy-plane anisotropy. Our main result is the existence of a
minimal energy for these traveling waves, in dimensions two, three and four.
The proof relies on a priori estimates related with the theory of harmonic maps
and the connection of the Landau-Lifshitz equation with the kernels appearing
in the Gross-Pitaevskii equation.Comment: submitte
Asymptotics for the Fredholm Determinant of the Sine Kernel on a Union of Intervals
In the bulk scaling limit of the Gaussian Unitary Ensemble of Hermitian
matrices the probability that an interval of length contains no eigenvalues
is the Fredholm determinant of the sine kernel over
this interval. A formal asymptotic expansion for the determinant as tends
to infinity was obtained by Dyson. In this paper we replace a single interval
of length by where is a union of intervals and present a proof
of the asymptotics up to second order. The logarithmic derivative with respect
to of the determinant equals a constant (expressible in terms of
hyperelliptic integrals) times , plus a bounded oscillatory function of
(zero of , periodic if , and in general expressible in terms of the
solution of a Jacobi inversion problem), plus . Also determined are the
asymptotics of the trace of the resolvent operator, which is the ratio in the
same model of the probability that the set contains exactly one eigenvalue to
the probability that it contains none. The proofs use ideas from orthogonal
polynomial theory.Comment: 24 page
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