1,511 research outputs found
Fluctuations in the level density of a Fermi gas
We present a theory that accurately describes the counting of excited states
of a noninteracting fermionic gas. At high excitation energies the results
reproduce Bethe's theory. At low energies oscillatory corrections to the
many--body density of states, related to shell effects, are obtained. The
fluctuations depend non-trivially on energy and particle number. Universality
and connections with Poisson statistics and random matrix theory are
established for regular and chaotic single--particle motion.Comment: 4 pages, 1 figur
Level density of a Fermi gas: average growth and fluctuations
We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur
On the Quantum Invariant for the Brieskorn Homology Spheres
We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev
invariant for the Brieskorn homology spheres by use of
properties of the modular form following a method proposed by Lawrence and
Zagier. Key observation is that the invariant coincides with a limiting value
of the Eichler integral of the modular form with weight 3/2. We show that the
Casson invariant is related to the number of the Eichler integrals which do not
vanish in a limit . Correspondingly there is a
one-to-one correspondence between the non-vanishing Eichler integrals and the
irreducible representation of the fundamental group, and the Chern-Simons
invariant is given from the Eichler integral in this limit. It is also shown
that the Ohtsuki invariant follows from a nearly modular property of the
Eichler integral, and we give an explicit form in terms of the L-function.Comment: 26 pages, 2 figure
Rademacher's infinite partial fraction conjecture is (almost certainly) false
In his book \emph{Topics in Analytic Number Theory}, Hans Rademacher
conjectured that the limits of certain sequences of coefficients that arise in
the ordinary partial fraction decomposition of the generating function for
partitions of integers into at most parts exist and equal particular values
that he specified. Despite being open for nearly four decades, little progress
has been made toward proving or disproving the conjecture, perhaps in part due
to the difficulty in actually computing the coefficients in question.
In this paper, we provide a fast algorithm for calculating the Rademacher
coefficients, a large amount of data, direct formulas for certain collections
of Rademacher coefficients, and overwhelming evidence against the truth of the
conjecture. While the limits of the sequences of Rademacher coefficients do not
exist (the sequences oscillate and attain arbitrarily large positive and
negative values), the sequences do get very close to Rademacher's conjectured
limits for certain (predictable) indices in the sequences
The Lyapunov exponent in the Sinai billiard in the small scatterer limit
We show that Lyapunov exponent for the Sinai billiard is with where
is the radius of the circular scatterer. We consider the disk-to-disk-map
of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho
Molecular Mechanism of the pH-Dependent Calcium Affinity in Langerin
The C-type lectin receptor langerin plays a vital role in the mammalian defense against invading pathogens. Its function hinges on the affinity to its co-factor Ca2+ which in turn is regulated by the pH. We studied the structural consequences of pro-tonating the allosteric pH-sensor histidine H294 by molecular dynamics simulations (total simulation time: about 120 μs) and Markov models. We discovered a mechanism in which the signal that the pH has dropped is transferred to the Ca2+-binding site without transferring the initial proton. Instead, protonation of H294 unlocks a conformation in which a protonated lysine side-chain forms a hydrogen bond with a Ca2+-coordinating aspartic acid. This destabilizes Ca2+ in the binding pocket, which we probed by steered molecular dynamics. After Ca2+-release, the proton is likely transferred to the aspartic acid and stabilized by a dyad with a nearby glutamic acid, triggering a conformational transition and thus preventing Ca2+-rebinding
Quantum Invariants, Modular Forms, and Lattice Points II
We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert
fibered homology spheres with M-exceptional fibers. We show that the WRT
invariant can be written in terms of (differential of) the Eichler integrals of
modular forms with weight 1/2 and 3/2. By use of nearly modular property of the
Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in
the large-N limit. We further reveal that the number of the gauge equivalent
classes of flat connections, which dominate the asymptotics of the WRT
invariant in N ->\infinity, is related to the number of integral lattice points
inside the M-dimensional tetrahedron
Laser performance of perylenebis (dicarboximide) dyes with long secondary alkyl chains
The laser performance and related photophysical properties of two very soluble perylene dyes with long chain secondary alkyl groups were investigated in cyclohexane solution. With a dye laser as pump source a tuning range of 555–580 nm was obtained at an optimum concentration of 3×10–4 M. The quantum efficiencies (=0.29 and 0.21) were better than 1/2 that of rhodamine 6G. No photodegradation was observed over an excitation period of several hours
Зміна роздільної здатності зображень на основі власних векторів матриць-операторів індукованих з піксельних наборів
The method of problem solving increase resolution image sets provided that the
dimension of the set. The method is to build a matrix operator and find its
eigenvectors. Using sets of eigenvectors and matrix color images developed a practical set of algorithm changes the resolution
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