On a conjecture of Widom

We prove a conjecture of H.Widom stated in [W] (math/0108008) about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large Toeplitz determinants. As a byproduct we obtain a new proof of A.Okounkov's formula for the (determinantal) correlation functions of the Schur measures on partitions.Comment: 9 page

Coherent current transport in wide ballistic Josephson junctions

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.Comment: 4 pages, 4 figure

HYDRO + JETS (HYDJET++) event generator for Pb+Pb collisions at LHC

The Monte Carlo event generator HYDJET++ is one of the few generators, designed for the calculations of heavy-ion collisions at ultrarelativistic energies, which combine treatment of soft hydro-like processes with the description of jets traversing the hot and dense partonic medium. The model is employed to study the azimuthal anisotropy phenomena, dihadron angular correlations and event-by-event (EbyE) fluctuations of the anisotropic flow in Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV. The interplay of soft and hard processes describes the violation of the mass hierarchy of meson and baryon elliptic and triangular flows at p_T > 2 GeV/c, the fall-off of the flow harmonics at intermediate transverse momenta, and the worsening of the number-of-constituent-quark (NCQ) scaling of elliptic/triangular flow at LHC compared to RHIC energies. The cross-talk of v_2 and v_3 leads to emergence of higher order harmonics in the model and to appearance of the ridge structure in dihadron angular correlations in a broad pseudorapidity range. HYDJET++ possesses also the dynamical EbyE fluctuations of the anisotropic flow. The model results agree well with the experimental data.Comment: 8 pages, 6 figures, contribution to Proceedings of the Winter Workshop on Nuclear Dynamics 201

Vicious Walkers and Hook Young Tableaux

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure

Increasing subsequences and the hard-to-soft edge transition in matrix ensembles

Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free involutions. It is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively. The gap probabilities can be written as a sum over correlations for certain determinantal point processes. From these expressions a proof can be given that the limiting form of Pr(L(t) \le l) in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively, thereby reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page

Interaction-induced oscillations of the tunneling density of states in a non-quantizing magnetic field

We study tunneling into interacting disordered two-dimensional electron gas in a non-quantizing magnetic field, which does not cause the standard de Haas-- van Alphen oscillations. Interaction induces a new type of oscillations in the tunneling density of states with the characteristic period of cyclotron quantum.Comment: 4 pages, 1 .eps figure, submitted to Phys. Rev. Let

Higher harmonics of azimuthal anisotropy in relativistic heavy ion collisions in HYDJET++ model

The LHC data on azimuthal anisotropy harmonics from PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted in the framework of the HYDJET++ model. The cross-talk of elliptic $v_2$ and triangular $v_3$ flow in the model generates both even and odd harmonics of higher order. Comparison with the experimental data shows that this mechanism is able to reproduce the $p_{\rm T}$ and centrality dependencies of quadrangular flow $v_4$, and also the basic trends for pentagonal $v_5$ and hexagonal $v_6$ flows.Comment: 12 pages including 13 figures as EPS-files; prepared using LaTeX package for publication in the European Physical Journal

Spatial distribution of low-energy plasma around 2 comet 67P/CG from Rosetta measurements

International audienceWe use measurements from the Rosetta plasma consortium (RPC) Langmuir probe (LAP) and mutual impedance probe (MIP) to study the spatial distribution of low-energy plasma in the near-nucleus coma of comet 67P/Churyumov-Gerasimenko. The spatial distribution is highly structured with the highest density in the summer hemisphere and above the region connecting the two main lobes of the comet, i.e. the neck region. There is a clear correlation with the neutral density and the plasma to neutral density ratio is found to be ∼1-2·10 −6 , at a cometocentric distance of 10 km and at 3.1 AU from the sun. A clear 6.2 h modulation of the plasma is seen as the neck is exposed twice per rotation. The electron density of the collisonless plasma within 260 km from the nucleus falls of with radial distance as ∼1/r. The spatial structure indicates that local ionization of neutral gas is the dominant source of low-energy plasma around the comet