315 research outputs found
Level spacings and periodic orbits
Starting from a semiclassical quantization condition based on the trace
formula, we derive a periodic-orbit formula for the distribution of spacings of
eigenvalues with k intermediate levels. Numerical tests verify the validity of
this representation for the nearest-neighbor level spacing (k=0). In a second
part, we present an asymptotic evaluation for large spacings, where consistency
with random matrix theory is achieved for large k. We also discuss the relation
with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for
two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of
validity of asymptotic evaluation clarifie
Ellipticity of Structures in CMB Sky Maps
We study the ellipticity of contour lines in the sky maps of the cosmic
microwave background (CMB) as well as other measures of elongation. The
sensitivity of the elongation on the resolution of the CMB maps which depends
on the pixelization and the beam profile of the detector, is investigated. It
is shown that the current experimental accuracy does not allow to discriminate
between cosmological models which differ in curvature by Delta Omega_tot=0.05.
Analytical expressions are given for the case that the statistical properties
of the CMB are those of two-dimensional Gaussian random fields
The Topology and Size of the Universe from the Cosmic Microwave Background
We study the possibility that the universe has compact topologies T^3, T^2 x
R^1, or S^1 x R^2 using the seven-year WMAP data. The maximum likelihood 95%
confidence intervals for the size L of the compact direction are 1.7 < L/L_0 <
2.1, 1.8 < L/L_0 < 2.0, 1.2 < L/L_0 < 2.1 for the three cases, respectively,
where L_0=14.4 Gpc is the distance to the last scattering surface. An infinite
universe is compatible with the data at 4.3 sigma. We find using a Bayesian
analysis that the most probable universe has topology T^2 x R^1, with
L/L_0=1.9.Comment: Additional checks, Monte-Carlo skies, and study of dipole
contamination added. References added. 13 pages, 11 figure
Nodal domains statistics - a criterion for quantum chaos
We consider the distribution of the (properly normalized) numbers of nodal
domains of wave functions in 2- quantum billiards. We show that these
distributions distinguish clearly between systems with integrable (separable)
or chaotic underlying classical dynamics, and for each case the limiting
distribution is universal (system independent). Thus, a new criterion for
quantum chaos is provided by the statistics of the wave functions, which
complements the well established criterion based on spectral statistics.Comment: 4 pages, 5 figures, revte
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
Quintessence and the Curvature of the Universe after WMAP
We study quintessence models with a constant (effective) equation of state.
It is investigated whether such quintessence models are consistent with a
negative spatial curvature of the Universe with respect to the anisotropy of
the cosmic microwave background radiation measured by the WMAP mission. If the
reionization is negligibly small, it is found that such models with negative
curvature are admissible due to a geometrical degeneracy. However, a very high
optical depth tau to the surface of last scattering, as indicated by the
polarization measurements of WMAP, would rule out such models.Comment: enlarged version which includes a discussion of reionizatio
Nodal domains on quantum graphs
We consider the real eigenfunctions of the Schr\"odinger operator on graphs,
and count their nodal domains. The number of nodal domains fluctuates within an
interval whose size equals the number of bonds . For well connected graphs,
with incommensurate bond lengths, the distribution of the number of nodal
domains in the interval mentioned above approaches a Gaussian distribution in
the limit when the number of vertices is large. The approach to this limit is
not simple, and we discuss it in detail. At the same time we define a random
wave model for graphs, and compare the predictions of this model with analytic
and numerical computations.Comment: 19 pages, uses IOP journal style file
Simulating Cosmic Microwave Background maps in multi-connected spaces
This article describes the computation of cosmic microwave background
anisotropies in a universe with multi-connected spatial sections and focuses on
the implementation of the topology in standard CMB computer codes. The key
ingredient is the computation of the eigenmodes of the Laplacian with boundary
conditions compatible with multi-connected space topology. The correlators of
the coefficients of the decomposition of the temperature fluctuation in
spherical harmonics are computed and examples are given for spatially flat
spaces and one family of spherical spaces, namely the lens spaces. Under the
hypothesis of Gaussian initial conditions, these correlators encode all the
topological information of the CMB and suffice to simulate CMB maps.Comment: 33 pages, 55 figures, submitted to PRD. Higher resolution figures
available on deman
Lipase Secretion and Citric Acid Production in Yarrowia lipolytica Yeast Grown on Animal and Vegetable Fat
The aim of the study was to investigate the potentiality of the utilization of raw agro- -industrial fat for the biotechnological production of valuable products (lipase and citric acid) by the yeast Yarrowia (Candida) lipolytica. Thirty strains of the aforementioned species were investigated for their capability of lipase secretion and citric acid production on media containing animal fat or rapeseed oil as a sole carbon and energy source. Strain Y. lipolytica 704, exhibiting the highest lipase activity on rapeseed oil (2760 U/mL), was selected for the study of biochemical peculiarities of cell growth, and strain Y. lipolytica 187/1, exhibiting the maximum citric acid synthesis, was selected for the subsequent studies on citric acid production. A relationship between lipase production and residual rapeseed oil concentration was studied. The essential factor for lipase production was found to be the concentration of rapeseed oil in the medium, which should be no less than 5 g/L. Under optimal conditions of cultivation, citric acid production by rapeseed-oil-grown yeast Yarrowia lipolytica 187/1 amounted to 135 g/L; specific rate of citric acid production reached m(CA)/m(cell)=127 mg/(g·h); mass yield (YCA) and energy yield (hCA) were 1.55 and 0.41, respectively
On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds
Asymptotic laws for mean multiplicities of lengths of closed geodesics in
arithmetic hyperbolic three-orbifolds are derived. The sharpest results are
obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o)
and some congruence subgroups. Similar results hold for cocompact arithmetic
quaternion groups, if a conjecture on the number of gaps in their length
spectra is true. The results related to the groups above give asymptotic lower
bounds for the mean multiplicities in length spectra of arbitrary arithmetic
hyperbolic three-orbifolds. The investigation of these multiplicities is
motivated by their sensitive effect on the eigenvalue spectrum of the
Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as
the Hamiltonian of a three-dimensional quantum system being strongly chaotic in
the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT
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