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

Why is the condensed phase of DNA preferred at higher temperature? DNA compaction in the presence of a multivalent cation

Upon the addition of multivalent cations, a giant DNA chain exhibits a large discrete transition from an elongated coil into a folded compact state. We performed single-chain observation of long DNAs in the presence of a tetravalent cation (spermine), at various temperatures and monovalent salt concentrations. We confirmed that the compact state is preferred at higher temperatures and at lower monovalent salt concentrations. This result is interpreted in terms of an increase in the net translational entropy of small ions due to ionic exchange between higher and lower valence ions.Comment: 4pages,3figure

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

Has HERA reached a new QCD regime?

These notes are a summary of our efforts to answer the question in the title. Our answer is in the affirmative as: (i) HERA data indicate a large value of the gluon structure function; (ii) no contradictions with the asymptotic predictions of high density QCD have been observed; and (iii) the numerical estimates of our model give a natural description of the size of deviation from the routine DGLAP explanation. We discuss the alternative approaches and possible new experiments.Comment: 29 pages, 37 figures in eps file

Angular pattern of minijet transverse energy flow in hadron and nuclear collisions

The azimuthal asymmetry of minijet system produced at the early stage of nucleon-nucleon and nuclear collisions in a central rapidity window is studied. We show that in pp collisions the minijet transverse energy production in a central rapidity window is essentially unbalanced in azimuth due to asymmetric contributions in which only one minijet hits the acceptance window. We further study the angular pattern of transverse energy flow generated by semihard degrees of freedom at the early stage of high energy nuclear collisions and its dependence on the number of semihard collisions in the models both including and neglecting soft contributions to the inelastic cross section at RHIC and LHC energies as well as on the choice of the infrared cutoff.Comment: 25 LaTeX pages, 11 figures embedded with epsf; expanded versio

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

Speed Meter As a Quantum Nondemolition Measuring Device for Force

Quantum noise is an important issue for advanced LIGO. Although it is in principle possible to beat the Standard Quantum Limit (SQL), no practical recipe has been found yet. This paper dicusses quantum noise in the context of speedmeter-a devise monitoring the speed of the testmass. The scheme proposed to overcome SQL in this case might be more practical than the methods based on monitoring position of the testmass.Comment: 7 pages of RevTex, 1 postscript figur

Benchmarks for the Forward Observables at RHIC, the Tevatron-run II and the LHC

We present predictions on the total cross sections and on the ratio of the real part to the imaginary part of the elastic amplitude (rho parameter) for present and future pp and pbar p colliders, and on total cross sections for gamma p -> hadrons at cosmic-ray energies and for gamma gamma-> hadrons up to sqrt{s}=1 TeV. These predictions are based on an extensive study of possible analytic parametrisations invoking the biggest hadronic dataset available at t=0. The uncertainties on total cross sections, including the systematic errors due to contradictory data points from FNAL, can reach 1.9% at RHIC, 3.1% at the Tevatron, and 4.8% at the LHC, whereas those on the rho parameter are respectively 5.4%, 5.2%, and 5.4%.Comment: 11 pages, 2 figures, 4 tables, RevTeX

Enhanced tidal disruption rates from massive black hole binaries

"Hard" massive black hole (MBH) binaries embedded in steep stellar cusps can shrink via three-body slingshot interactions. We show that this process will inevitably be accompanied by a burst of stellar tidal disruptions, at a rate that can be several orders of magnitude larger than that appropriate for a single MBH. Our numerical scattering experiments reveal that: 1) a significant fraction of stars initially bound to the primary hole are scattered into its tidal disruption loss cone by gravitational interactions with the secondary hole, an enhancement effect that is more pronounced for very unequal-mass binaries; 2) about 25% (40%) of all strongly interacting stars are tidally disrupted by a MBH binary of mass ratio q=1/81 (q=1/243) and eccentricity 0.1; and 3) two mechanisms dominate the fueling of the tidal disruption loss cone, a Kozai non-resonant interaction that causes the secular evolution of the stellar angular momentum in the field of the binary, and the effect of close encounters with the secondary hole that change the stellar orbital parameters in a chaotic way. For a hard MBH binary of 10^7 solar masses and mass ratio 0.01, embedded in an isothermal stellar cusp of velocity dispersion sigma*=100 km/s, the tidal disruption rate can be as large as 1/yr. This is 4 orders of magnitude higher than estimated for a single MBH fed by two-body relaxation. When applied to the case of a putative intermediate-mass black hole inspiraling onto Sgr A*, our results predict tidal disruption rates ~0.05-0.1/yr.Comment: 5 pages, 3 figures, accepted for publication in the Astrophysical Journal Letter