4,237 research outputs found

    Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

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    We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, (0,s)(0,s), containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the α=0\alpha=0 Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for α≠0\alpha\neq 0, the leading terms of E2(0,s)E_{2}(0,s), found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

    Wigner-Dyson Statistics from the Replica Method

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    We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non--trivial saddle points, which break replica symmetry, must be included in the calculation in order to reproduce correctly the exact results for the correlation functions at large distance.Comment: 13 pages, added reference

    Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

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    We establish a correspondence between the evolution of the distribution of eigenvalues of a N×NN\times N matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.Comment: 10 pages, revte

    Fluctuation properties of strength functions associated with giant resonances

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    We performed fluctuation analysis by means of the local scaling dimension for the strength function of the isoscalar (IS) and the isovector (IV) giant quadrupole resonances (GQR) in 40^{40}Ca, where the strength functions are obtained by the shell model calculation within up to the 2p2h configurations. It is found that at small energy scale, fluctuation of the strength function almost obeys the Gaussian orthogonal ensemble (GOE) random matrix theory limit. On the other hand, we found a deviation from the GOE limit at the intermediate energy scale about 1.7MeV for the IS and at 0.9MeV for the IV. The results imply that different types of fluctuations coexist at different energy scales. Detailed analysis strongly suggests that GOE fluctuation at small energy scale is due to the complicated nature of 2p2h states and that fluctuation at the intermediate energy scale is associated with the spreading width of the Tamm-Dancoff 1p1h states.Comment: 14 pages including 13figure

    Complex temperatures zeroes of partition function in spin-glass models

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    An approximate method is proposed for investigating complex-temperature properties of real-dimensional spin-glass models. The method uses the complex-temperature data of the ferromagnetic model on the same lattice. The universality line in the complex-temperature space is obtained.Comment: latex, corrected some misprint

    Infrared Search for Young Stars in HI High-velocity Clouds

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    We have searched the IRAS Point Source Catalog and HIRES maps for young stellar objects (YSOs) in the direction of five \HI high-velocity clouds (HVCs). In agreement with optical searches in the halo, no evidence was found for extensive star-forming activity inside the high-latitude HVCs. Specifically, we have found no signs of star formation or YSOs in the direction of the A IV cloud or in the very-high-velocity clouds HVC~110-7-465 and HVC~114-10-440. We have identified only one young star in the direction of the M~I.1 cloud, which shows almost perfect alignment with a knot of \HI emission. Because of the small number of early-type stars observed in the halo, the probability for such a positional coincidence is low; thus, this young star appears to be physically associated with the M~I.1 cloud. We have also identified a good YSO candidate in the \HI shell-like structure observed in the core region of the low-latitude cloud complex H (HVC~131+1-200). This region could be a supernova remnant with several other YSO candidates formed along the shock front produced by the explosion. In agreement with recent theoretical estimates, these results point to a low but significant star-formation rate in intermediate and high Galactic latitude HVCs. For M~I.1 in particular, we estimate that the efficiency of the star-formation process is M(YSO)/M(\HI)\ga 10^{-4}-10^{-3} by mass. Such efficiency is sufficient to account for (a) the existence of the few young blue stars whose ages imply that they were born in the Galactic halo, and (b) the nonprimordial metallicities inferred for some HVCs if their metal content proves to be low.Comment: 9 pages, 4 JPEG figures. PostScript figures available from author

    Distribution of the Riemann zeros represented by the Fermi gas

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    The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.Comment: 7 page

    Renormalized energy concentration in random matrices

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    We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of [SS1,SS3]. Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β\beta-sine processes on the real line (beta=1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the beta=2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.Comment: last version, to appear in Communications in Mathematical Physic

    Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors

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    We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point correlation function, which exhibits a new kind of universal behavior characteristic of disordered conductors. Systems with orthogonal and symplectic symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of Oxford), to appear in Phys. Rev. B (Rapid Communication
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