Photon noise in a random laser amplifier with fluctuating properties

We study fluctuations of the number of photocounts measured by an ideal photodetector illuminated by light scattered in an amplifying disordered medium, below the threshold for random lasing. We show that the variance of fluctuations and their correlation function carry information about fluctuating properties of the medium. A direct link is established between the fluctuations of the number of photocounts due to the amplified spontaneous emission (ASE) and the dimensionless conductance g of the medium. Our results suggest a possibility of probing amplifying disordered media by analyzing statistics of their ASE, without illuminating them from outside by a probe beam.Comment: 14 pages, 9 figure

Gaussian modeling and Schmidt modes of SPDS biphoton states

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long

Structure and stability of chiral beta-tapes: a computational coarse-grained approach

We present two coarse-grained models of different levels of detail for the description of beta-sheet tapes obtained from equilibrium self-assembly of short rationally designed oligopeptides in solution. Here we only consider the case of the homopolymer oligopeptides with the identical sidegroups attached, in which the tapes have a helicoid surface with two equivalent sides. The influence of the chirality parameter on the geometrical characteristics, namely the diameter, inter-strand distance and pitch, of the tapes have been investigated. The two models are found to produceequivalent results suggesting a considerable degree of universality in conformations of the tapes.Comment: 24 pages, 5 PS figures. Accepted to J. Chem. Phy

Upper bounds for the number of orbital topological types of planar polynomial vector fields "modulo limit cycles"

The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To circumvent this obstacle we introduce the notion of equivalence modulo limit cycles. This paper is the continuation of the author's paper in [Mosc. Math. J. 1 (2001), no. 4] where the lower bound of the form 2^{cn^2} has been obtained. Here we obtain the upper bound of the same form. We also associate an equipped planar graph to every planar polynomial vector field, this graph is a complete invariant for orbital topological classification of such fields.Comment: 23 pages, 5 figure

Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)

For a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated to such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties. We also consider some special cases of the covering C -> E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of 3 different elliptic curves. Our description is accompanied with explicit numerical examples.Comment: 51 pages, 3 figures, 3 diagram

Eu3+ multicenter formation and luminescent properties of Ca3Sc2Si3O12:Eu and Ca2YScMgSiO12:Eu single crystalline films

The work is dedicated to the investigation of Eu3+ multicenter formation and luminescent properties of Ca3Sc2Si3O12:Eu (CSSG:Eu) and Ca2YScMgSiO12:Eu (CYMSSG:Eu) single crystalline film (SCF) phosphors, grown by liquid phase epitaxy method onto Gd3Ga2.5Al2.5O12 (GAGG) and Y3Al5O12 (YAG) substrates, respectively. We have found notable differences in the luminescent properties of CSSG:Eu and CYMSSG:Eu SCFs caused by the Eu3+ multicenter formation in both garnets due to the different local surrounding of Eu3+ ions in the dodecahedral positions by the non-isovalent Sc3+/Mg2+ and Si4+ cations in the octahedral and tetrahedral positions of garnet hosts, respectively. A feature of the Eu3+ center creation in CYMSSG:Eu garnet in comparison with CSSG:Eu counterpart is the possibility of localization of Eu3+ ions in dodecahedral sites of both Ca2+ and Y3+ cations. However, based on the obtained results, we have presupposed preferable localization of the Eu3+ ions mainly in the Y3+ positions of this garnet

Steklov-Lyapunov type systems

In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized Gaudin form with a rational spectral parameter. In the case of rank 2 orbits a corresponding 2×2 La x pair for the reduced systems enables us to perform a separation of variables