8,703 research outputs found
Cluster ensembles, quantization and the dilogarithm
Cluster ensemble is a pair of positive spaces (X, A) related by a map p: A ->
X. It generalizes cluster algebras of Fomin and Zelevinsky, which are related
to the A-space. We develope general properties of cluster ensembles, including
its group of symmetries - the cluster modular group, and a relation with the
motivic dilogarithm. We define a q-deformation of the X-space. Formulate
general duality conjectures regarding canonical bases in the cluster ensemble
context. We support them by constructing the canonical pairing in the finite
type case.
Interesting examples of cluster ensembles are provided the higher Teichmuller
theory, that is by the pair of moduli spaces corresponding to a split reductive
group G and a surface S defined in math.AG/0311149.
We suggest that cluster ensembles provide a natural framework for higher
quantum Teichmuller theory.Comment: Version 7: Final version. To appear in Ann. Sci. Ecole Normale. Sup.
New material in Section 5. 58 pages, 11 picture
Limits of structure stability of simple liquids revealed by study of relative fluctuations
We analyse the inverse reduced fluctuations (inverse ratio of relative volume
fluctuation to its value in the hypothetical case where the substance acts an
ideal gas for the same temperature-volume parameters) for simple liquids from
experimental acoustic and thermophysical data along a coexistence line for both
liquid and vapour phases. It has been determined that this quantity has a
universal exponential character within the region close to the melting point.
This behaviour satisfies the predictions of the mean-field (grand canonical
ensemble) lattice fluid model and relates to the constant average structure of
a fluid, i.e. redistribution of the free volume complementary to a number of
vapour particles. The interconnection between experiment-based fluctuational
parameters and self-diffusion characteristics is discussed. These results may
suggest experimental methods for determination of self-diffusion and structural
properties of real substances.Comment: 5 pages, 4 figure
Dirac Monopoles in the Ernst--Schwarzschild Spacetime
It is discussed that the Ernst--Schwarzschild metric describing a nonrotating
black hole in the external magnetic field admits the solutions of the Dirac
monopole types for the corresponding Maxwell equations. The given solutions are
obtained in explicit form and a possible influence of the conforming Dirac
monopoles on Hawking radiation is also outlined.Comment: Int. Journal of Modern Physics A, vol. 18 (2003), 2153-215
Asymptotic normalization coefficients for mirror virtual nucleon decays in a microscopic cluster model
It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that
charge symmetry of nucleon-nucleon interactions relates the Asymptotic
Normalization Coefficients (ANCs) of proton and neutron virtual decays of
mirror nuclei. This relation is given by a simple analytical formula which
involves proton and neutron separation energies, charges of residual nuclei and
the range of their strong interaction with the last nucleon. Relation between
mirror ANCs, if understood properly, can be used to predict astrophysically
relevant direct proton capture cross sections using neutron ANCs measured with
stable beams. In this work, we calculate one-nucleon ANCs for several light
mirror pairs, using microscopic two-, three- and four-cluster models, and
compare the ratio of mirror ANCs to the predictions of the simple analytic
formula. We also investigate mirror symmetry between other characteristics of
mirror one-nucleon overlap integrals, namely, spectroscopic factors and
single-particle ANCs.Comment: 12 pages, submitted to Phys. Rev.
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