7,854 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
Estimates for parameters and characteristics of the confining SU(3)-gluonic field in an -meson
The confinement mechanism proposed earlier by the author is applied to
estimate the possible parameters of the confining SU(3)-gluonic field in an
-meson. For this aim the electric form factor of an
-meson is nonperturbatively computed in an explicit analytic form.
The estimates obtained are also consistent with the width of the
electromagnetic decay . The corresponding estimates of
the gluon concentrations, electric and magnetic colour field strengths are also
adduced for the mentioned field at the scales of the meson under consideration.Comment: 20 pages, LaTe
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