478 research outputs found
Renormalization Effects in a Dilute Bose Gas
The low-density expansion for a homogeneous interacting Bose gas at zero
temperature can be formulated as an expansion in powers of ,
where is the number density and is the S-wave scattering length.
Logarithms of appear in the coefficients of the expansion. We show
that these logarithms are determined by the renormalization properties of the
effective field theory that describes the scattering of atoms at zero density.
The leading logarithm is determined by the renormalization of the pointlike scattering amplitude.Comment: 10 pages, 1 postscript figure, LaTe
Second-order corrections to mean field evolution for weakly interacting Bosons. I
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new
nonlinear Schr\"odinger equation that describes a second-order correction to
the usual tensor product (mean-field) approximation for the Hamiltonian
evolution of a many-particle system in Bose-Einstein condensation. We show that
our new equation, if it has solutions with appropriate smoothness and decay
properties, implies a new Fock space estimate. We also show that for an
interaction potential , where is
sufficiently small and , our program can be easily
implemented locally in time. We leave global in time issues, more singular
potentials and sophisticated estimates for a subsequent part (part II) of this
paper
Condensate fraction and critical temperature of a trapped interacting Bose gas
By using a mean field approach, based on the Popov approximation, we
calculate the temperature dependence of the condensate fraction of an
interacting Bose gas confined in an anisotropic harmonic trap. For systems
interacting with repulsive forces we find a significant decrease of the
condensate fraction and of the critical temperature with respect to the
predictions of the non-interacting model. These effects go in the opposite
direction compared to the case of a homogeneous gas. An analytic result for the
shift of the critical temperature holding to first order in the scattering
length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at
http://anubis.science.unitn.it/~oss/bec/BEC.htm
Elementary excitations of trapped Bose gas in the large-gas-parameter regime
We study the effect of going beyond the Gross-Pitaevskii theory on the
frequencies of collective oscillations of a trapped Bose gas in the large gas
parameter regime. We go beyond the Gross-Pitaevskii regime by including a
higher-order term in the interatomic correlation energy. To calculate the
frequencies we employ the sum-rule approach of many-body response theory
coupled with a variational method for the determination of ground-state
properties. We show that going beyond the Gross-Pitaevskii approximation
introduces significant corrections to the collective frequencies of the
compressional mode.Comment: 17 pages with 4 figures. To be published in Phys. Rev.
Bose condensates in a harmonic trap near the critical temperature
The mean-field properties of finite-temperature Bose-Einstein gases confined
in spherically symmetric harmonic traps are surveyed numerically. The solutions
of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for
the condensate and low-lying quasiparticle excitations are calculated
self-consistently using the discrete variable representation, while the most
high-lying states are obtained with a local density approximation. Consistency
of the theory for temperatures through the Bose condensation point requires
that the thermodynamic chemical potential differ from the eigenvalue of the GP
equation; the appropriate modifications lead to results that are continuous as
a function of the particle interactions. The HFB equations are made gapless
either by invoking the Popov approximation or by renormalizing the particle
interactions. The latter approach effectively reduces the strength of the
effective scattering length, increases the number of condensate atoms at each
temperature, and raises the value of the transition temperature relative to the
Popov approximation. The renormalization effect increases approximately with
the log of the atom number, and is most pronounced at temperatures near the
transition. Comparisons with the results of quantum Monte Carlo calculations
and various local density approximations are presented, and experimental
consequences are discussed.Comment: 15 pages, 11 embedded figures, revte
Number--conserving model for boson pairing
An independent pair ansatz is developed for the many body wavefunction of
dilute Bose systems. The pair correlation is optimized by minimizing the
expectation value of the full hamiltonian (rather than the truncated Bogoliubov
one) providing a rigorous energy upper bound. In contrast with the Jastrow
model, hypernetted chain theory provides closed-form exactly solvable equations
for the optimized pair correlation. The model involves both condensate and
coherent pairing with number conservation and kinetic energy sum rules
satisfied exactly and the compressibility sum rule obeyed at low density. We
compute, for bulk boson matter at a given density and zero temperature, (i) the
two--body distribution function, (ii) the energy per particle, (iii) the sound
velocity, (iv) the chemical potential, (v) the momentum distribution and its
condensate fraction and (vi) the pairing function, which quantifies the ODLRO
resulting from the structural properties of the two--particle density matrix.
The connections with the low--density expansion and Bogoliubov theory are
analyzed at different density values, including the density and scattering
length regime of interest of trapped-atoms Bose--Einstein condensates.
Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure
Limits on the gravity wave contribution to microwave anisotropies
We present limits on the fraction of large angle microwave anisotropies which
could come from tensor perturbations. We use the COBE results as well as
smaller scale CMB observations, measurements of galaxy correlations, abundances
of galaxy clusters, and Lyman alpha absorption cloud statistics. Our aim is to
provide conservative limits on the tensor-to-scalar ratio for standard
inflationary models. For power-law inflation, for example, we find T/S<0.52 at
95% confidence, with a similar constraint for phi^p potentials. However, for
models with tensor amplitude unrelated to the scalar spectral index it is still
currently possible to have T/S>1.Comment: 23 pages, 7 figures, accepted for publication in Phys. Rev. D.
Calculations extended to blue spectral index, Fig. 6 added, discussion of
results expande
Defective postsecretory maturation of MUC5B mucin in cystic fibrosis airways
In cystic fibrosis (CF), airway mucus becomes thick and viscous, and its clearance from the airways is impaired. The gel-forming mucins undergo an ordered "unpacking/maturation" process after granular release that requires an optimum postsecretory environment, including hydration and pH. We hypothesized that this unpacking process is compromised in the CF lung due to abnormal transepithelial fluid transport that reduces airway surface hydration and alters ionic composition. Using human tracheobronchial epithelial cells derived from non-CF and CF donors and mucus samples from human subjects and domestic pigs, we investigated the process of postsecretory mucin unfolding/maturation, how these processes are defective in CF airways, and the probable mechanism underlying defective unfolding. First, we found that mucins released into a normal lung environment transform from a compact granular form to a linear form. Second, we demonstrated that this maturation process is defective in the CF airway environment. Finally, we demonstrated that independent of HCO3- and pH levels, airway surface dehydration was the major determinant of this abnormal unfolding process. This defective unfolding/maturation process after granular release suggests that the CF extracellular environment is ion/water depleted and likely contributes to abnormal mucus properties in CF airways prior to infection and inflammation
Hamiltonian Study of Improved Lattice Gauge Theory in Three Dimensions
A comprehensive analysis of the Symanzik improved anisotropic
three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made.
Monte Carlo techniques are used to obtain numerical results for the static
potential, ratio of the renormalized and bare anisotropies, the string tension,
lowest glueball masses and the mass ratio. Evidence that rotational symmetry is
established more accurately for the Symanzik improved anisotropic action is
presented. The discretization errors in the static potential and the
renormalization of the bare anisotropy are found to be only a few percent
compared to errors of about 20-25% for the unimproved gauge action. Evidence of
scaling in the string tension, antisymmetric mass gap and the mass ratio is
observed in the weak coupling region and the behaviour is tested against
analytic and numerical results obtained in various other Hamiltonian studies of
the theory. We find that more accurate determination of the scaling
coefficients of the string tension and the antisymmetric mass gap has been
achieved, and the agreement with various other Hamiltonian studies of the
theory is excellent. The improved action is found to give faster convergence to
the continuum limit. Very clear evidence is obtained that in the continuum
limit the glueball ratio approaches exactly 2, as expected in a
theory of free, massive bosons.Comment: 13 pages, 15 figures, submitted to Phys. Rev.
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
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