105 research outputs found
Theory of random matrices with strong level confinement: orthogonal polynomial approach
Strongly non-Gaussian ensembles of large random matrices possessing unitary
symmetry and logarithmic level repulsion are studied both in presence and
absence of hard edge in their energy spectra. Employing a theory of polynomials
orthogonal with respect to exponential weights we calculate with asymptotic
accuracy the two-point kernel over all distance scale, and show that in the
limit of large dimensions of random matrices the properly rescaled local
eigenvalue correlations are independent of level confinement while global
smoothed connected correlations depend on confinement potential only through
the endpoints of spectrum. We also obtain exact expressions for density of
levels, one- and two-point Green's functions, and prove that new universal
local relationship exists for suitably normalized and rescaled connected
two-point Green's function. Connection between structure of Szeg\"o function
entering strong polynomial asymptotics and mean-field equation is traced.Comment: 12 pages (latex), to appear in Physical Review
Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I
Classical Schur analysis is intimately connected to the theory of orthogonal
polynomials on the circle [Simon, 2005]. We investigate here the connection
between multipoint Schur analysis and orthogonal rational functions.
Specifically, we study the convergence of the Wall rational functions via the
development of a rational analogue to the Szeg\H o theory, in the case where
the interpolation points may accumulate on the unit circle. This leads us to
generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields
asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction,
Section 5 (Szeg\H o type asymptotics) is extende
Asymptotics of orthogonal polynomials for a weight with a jump on [â1,1]
We consider the orthogonal polynomials on [-1, 1] with respect to the weight
w(c)(x) = h(x)(1 - x)(alpha) (1+ x)beta Xi(c)(x), alpha, beta > -1,
where h is real analytic and strictly positive on [-1, 1] and Xi(c) is a step-like function: Xi(c)(x) = 1 for x is an element of [-1, 0) and Xi(c) (x) = c(2), c > 0, for x is an element of [0, 1]. We obtain strong uniform asymptotics of the monic orthogonal polynomials in C, as well as first terms of the asymptotic expansion of the main parameters (leading coefficients of the orthonormal polynomials and the recurrence coefficients) as n -> infinity. In particular, we prove for w(c) a conjecture of A. Magnus regarding the asymptotics of the recurrence coefficients. The main focus is on the local analysis at the origin. We study the asymptotics of the Christoffel-Darboux kernel in a neighborhood of the jump and show that the zeros of the orthogonal polynomials no longer exhibit clock behavior.
For the asymptotic analysis we use the steepest descent method of Deift and Zhou applied to the noncommutative Riemann-Hilbert problems characterizing the orthogonal polynomials. The local analysis at x = 0 is carried out in terms of confluent hypergeometric functions. Incidentally, we establish some properties of these functions that may have an independent interest.Junta de AndalucĂa-Spain- FQM-229 and P06- FQM-01735.Ministry of Science and Innovation of Spain - MTM2008-06689-C02-01FCT -SFRH/BD/29731/200
Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering
We report the first measurement of the parity-violating asymmetry A_PV in the
elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the
radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060
(stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of
the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides
the first electroweak observation of the neutron skin which is expected in a
heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur
A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
These notes are based on lectures delivered by the authors at a Langeoog
seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a
mixed audience of mathematicians and theoretical physicists. After a brief
outline of the basic physical concepts of equilibrium and nonequilibrium
states, the one-dimensional simple exclusion process is introduced as a
paradigmatic nonequilibrium interacting particle system. The stationary measure
on the ring is derived and the idea of the hydrodynamic limit is sketched. We
then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and
explain the associated universality conjecture for surface fluctuations in
growth models. This is followed by a detailed exposition of a seminal paper of
Johansson that relates the current fluctuations of the totally asymmetric
simple exclusion process (TASEP) to the Tracy-Widom distribution of random
matrix theory. The implications of this result are discussed within the
framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo
Design, Performance and Calibration of the CMS Forward Calorimeter Wedges
We report on the test beam results and calibration methods using charged particles of the CMS Forward Calorimeter (HF). The HF calorimeter covers a large pseudorapidity region (3\l |\eta| \le 5), and is essential for large number of physics channels with missing transverse energy. It is also expected to play a prominent role in the measurement of forward tagging jets in weak boson fusion channels. The HF calorimeter is based on steel absorber with embedded fused-silica-core optical fibers where Cherenkov radiation forms the basis of signal generation. Thus, the detector is essentially sensitive only to the electromagnetic shower core and is highly non-compensating (e/h \approx 5). This feature is also manifest in narrow and relatively short showers compared to similar calorimeters based on ionization. The choice of fused-silica optical fibers as active material is dictated by its exceptional radiation hardness. The electromagnetic energy resolution is dominated by photoelectron statistics and can be expressed in the customary form as a/\sqrt{E} + b. The stochastic term a is 198% and the constant term b is 9%. The hadronic energy resolution is largely determined by the fluctuations in the neutral pion production in showers, and when it is expressed as in the electromagnetic case, a = 280% and b = 11%
Design, Performance, and Calibration of CMS Hadron-Barrel Calorimeter Wedges
Extensive measurements have been made with pions, electrons and muons on four production wedges of the Compact Muon Solenoid (CMS) hadron barrel (HB) calorimeter in the H2 beam line at CERN with particle momenta varying from 20 to 300 GeV/c. Data were taken both with and without a prototype electromagnetic lead tungstate crystal calorimeter (EB) in front of the hadron calorimeter. The time structure of the events was measured with the full chain of preproduction front-end electronics running at 34 MHz. Moving-wire radioactive source data were also collected for all scintillator layers in the HB. These measurements set the absolute calibration of the HB prior to first pp collisions to approximately 4%
Design, Performance, and Calibration of the CMS Hadron-Outer Calorimeter
The CMS hadron calorimeter is a sampling calorimeter with brass absorber and plastic scintillator tiles with wavelength shifting fibres for carrying the light to the readout device. The barrel hadron calorimeter is complemented with an outer calorimeter to ensure high energy shower containment in the calorimeter. Fabrication, testing and calibration of the outer hadron calorimeter are carried out keeping in mind its importance in the energy measurement of jets in view of linearity and resolution. It will provide a net improvement in missing \et measurements at LHC energies. The outer hadron calorimeter will also be used for the muon trigger in coincidence with other muon chambers in CMS
- âŠ