Elliptic Schlesinger system and Painlev{\'e} VI

We construct an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the parameters in the moduli space of the complex structure). ESS is a non-autonomous Hamiltonian system with pair-wise commuting Hamiltonians. The system is bihamiltonian with respect to the linear and the quadratic Poisson brackets. The latter are the multi-color generalization of the Sklyanin-Feigin-Odeskii classical algebras. We give the Lax form of the ESS. The Lax matrix defines a connection of a flat bundle of degree one over the elliptic curve with first order poles at the marked points. The ESS is the monodromy independence condition on the complex structure for the linear systems related to the flat bundle. The case of four points for a special initial data is reduced to the Painlev{\'e} VI equation in the form of the Zhukovsky-Volterra gyrostat, proposed in our previous paper.Comment: 16 pages; Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Nonlinear QCD Evolution: Saturation without Unitarization

We consider the perturbative description of saturation based on the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK). Although the nonlinear corrections lead to saturation of the scattering amplitude locally in impact parameter space, we show that they do not unitarize the total cross section. The total cross section for the scattering of a strongly interacting probe on a hadronic target is found to grow exponentially with rapidity. The origin of this violation of unitarity is the presence of long range Coulomb fields away from the saturation region. The growth of these fields with rapidity is not tempered by the nonlinearity of the BK equation.Comment: 4 pages, RevTe

Internal thermal noise in the LIGO test masses : a direct approach

The internal thermal noise in LIGO's test masses is analyzed by a new technique, a direct application of the Fluctuation-Dissipation Theorem to LIGO's readout observable, $x(t)=$(longitudinal position of test-mass face, weighted by laser beam's Gaussian profile). Previous analyses, which relied on a normal-mode decomposition of the test-mass motion, were valid only if the dissipation is uniformally distributed over the test-mass interior, and they converged reliably to a final answer only when the beam size was a non-negligible fraction of the test-mass cross section. This paper's direct analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam sizes. In the domain of validity of the previous analysis, the two methods give the same answer for $S_x(f)$, the spectral density of thermal noise, to within expected accuracy. The new analysis predicts that thermal noise due to dissipation concentrated in the test mass's front face (e.g. due to mirror coating) scales as $1/r_0^2$, by contrast with homogeneous dissipation, which scales as $1/r_0$ ($r_0$ is the beam radius); so surface dissipation could become significant for small beam sizes.Comment: 6 pages, RevTex, 1 figur

Magnetic phase diagram and transport properties of FeGe_2

We have used resistivity measurements to study the magnetic phase diagram of the itinerant antiferromagnet FeGe_2 in the temperature range from 0.3->300 K in magnetic fields up to 16 T. In contrast to theoretical predictions, the incommensurate spin density wave phase is found to be stable at least up to 16 T, with an estimated critical field \mu _0H_c of ~ 30 T. We have also studied the low temperature magnetoresistance in the [100], [110], and [001] directions. The transverse magnetoresistance is well described by a power law for magnetic fields above 1 T with no saturation observed at high fields. We discuss our results in terms of the magnetic structure and the calculated electronic bandstructure of FeGe_2. We have also observed, for the first time in this compound, Shubnikov-de Haas oscillations in the transverse magnetoresistance with a frequency of 190 +- 10 T for a magnetic field along [001].Comment: 13 pages, RevTeX, 7 postscript figures, to appear in Journal of Physics: Condensed Matte

Polaron and bipolaron transport in a charge segregated state of doped strongly correlated 2D semiconductor

The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by the Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures

How to reduce the suspension thermal noise in LIGO without improving the Q's of the pendulum and violin modes

The suspension noise in interferometric gravitational wave detectors is caused by losses at the top and the bottom attachments of each suspension fiber. We use the Fluctuation-Dissipation theorem to argue that by careful positioning of the laser beam spot on the mirror face it is possible to reduce the contribution of the bottom attachment point to the suspension noise by several orders of magnitude. For example, for the initial and enhanced LIGO design parameters (i.e. mirror masses and sizes, and suspension fibers' lengths and diameters) we predict a reduction of $\sim 100$ in the "bottom" spectral density throughout the band $35-100\hbox{Hz}$ of serious thermal noise. We then propose a readout scheme which suppresses the suspension noise contribution of the top attachment point. The idea is to monitor an averaged horizontal displacement of the fiber of length $l$; this allows one to record the contribution of the top attachment point to the suspension noise, and later subtract it it from the interferometer readout. For enhanced LIGO this would allow a suppression factor about 100 in spectral density of suspension thermal noise.Comment: a few misprints corrected; submitted to Classical and Quantum Gravit

Charm Hadroproduction in kTk_T-Factorization Approach

We compare the theoretical status and the numerical predictions of two approaches for heavy quark production in the high energy hadron collisions, namely the conventional LO parton model with collinear approximation and $k_T$-factorization approach. The main assumptions used in the calculations are discussed. To extract the differences coming from the matrix elements we use very simple gluon structure function and fixed coupling. It is shown that the $k_T$-factorization approach calculated formally in LO and with Sudakov form factor accounts for many contributions related usually to NLO (and even NNLO) processes of the conventional parton modelComment: 17 pages, 8 figure

Three charged particles in the continuum. Astrophysical examples

We suggest a new adiabatic approach for description of three charged particles in the continuum. This approach is based on the Coulomb-Fourier transformation (CFT) of three body Hamiltonian, which allows to develop a scheme, alternative to Born-Oppenheimer one. The approach appears as an expansion of the kernels of corresponding integral transformations in terms of small mass-ratio parameter. To be specific, the results are presented for the system $ppe$ in the continuum. The wave function of a such system is compared with that one which is used for estimation of the rate for triple reaction $p+p+e\to d+\nu,$ which take place as a step of $pp$-cycle in the center of the Sun. The problem of microscopic screening for this particular reaction is discussed

Magnetic-field dependence of the critical currents in a periodic coplanar array of narrow superconducting strip

We calculate the magnetic-field dependence of the critical current due to both geometrical edge barriers and bulk pinning in a periodic coplanar array of narrow superconducting strips. We find that in zero or low applied magnetic fields the critical current can be considerably enhanced by the edge barriers, but in modest applied magnetic fields the critical current reduces to that due to bulk pinning alone.Comment: 23 pages, 7 figure