90 research outputs found
Rigidity and Normal Modes in Random Matrix Spectra
We consider the Gaussian ensembles of random matrices and describe the normal
modes of the eigenvalue spectrum, i.e., the correlated fluctuations of
eigenvalues about their most probable values. The associated normal mode
spectrum is linear, and for large matrices, the normal modes are found to be
Chebyshev polynomials of the second kind. We contrast this with the behaviour
of a sequence of uncorrelated levels, which has a quadratic normal mode
spectrum. The difference in the rigidity of random matrix spectra and sequences
of uncorrelated levels can be attributed to this difference in the normal mode
spectra. We illustrate this by calculating the number variance in the two
cases.Comment: 12 pages, 1 LaTeX fil
Asymptotics for the Fredholm Determinant of the Sine Kernel on a Union of Intervals
In the bulk scaling limit of the Gaussian Unitary Ensemble of Hermitian
matrices the probability that an interval of length contains no eigenvalues
is the Fredholm determinant of the sine kernel over
this interval. A formal asymptotic expansion for the determinant as tends
to infinity was obtained by Dyson. In this paper we replace a single interval
of length by where is a union of intervals and present a proof
of the asymptotics up to second order. The logarithmic derivative with respect
to of the determinant equals a constant (expressible in terms of
hyperelliptic integrals) times , plus a bounded oscillatory function of
(zero of , periodic if , and in general expressible in terms of the
solution of a Jacobi inversion problem), plus . Also determined are the
asymptotics of the trace of the resolvent operator, which is the ratio in the
same model of the probability that the set contains exactly one eigenvalue to
the probability that it contains none. The proofs use ideas from orthogonal
polynomial theory.Comment: 24 page
Solution of coupled vertex and propagator Dyson-Schwinger equations in the scalar Munczek-Nemirovsky model
In a scalar model, we exactly solve the vertex and
propagator Dyson-Schwinger equations under the assumption of a spatially
constant (Munczek-Nemirovsky) propagator for the field. Various
truncation schemes are also considered.Comment: 7 pages,4 figures, minor changes, reference added for published
versio
An Algebraic Spin and Statistics Theorem
A spin-statistics theorem and a PCT theorem are obtained in the context of
the superselection sectors in Quantum Field Theory on a 4-dimensional
space-time. Our main assumption is the requirement that the modular groups of
the von Neumann algebras of local observables associated with wedge regions act
geometrically as pure Lorentz transformations. Such a property, satisfied by
the local algebras generated by Wightman fields because of the
Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.Comment: 15 pages, plain TeX, an error in the statement of a theorem has been
corrected, to appear in Commun. Math. Phy
Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem
In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at
random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the
key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a
GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined
Persistence in a Stationary Time-series
We study the persistence in a class of continuous stochastic processes that
are stationary only under integer shifts of time. We show that under certain
conditions, the persistence of such a continuous process reduces to the
persistence of a corresponding discrete sequence obtained from the measurement
of the process only at integer times. We then construct a specific sequence for
which the persistence can be computed even though the sequence is
non-Markovian. We show that this may be considered as a limiting case of
persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte
NN Core Interactions and Differential Cross Sections from One Gluon Exchange
We derive nonstrange baryon-baryon scattering amplitudes in the
nonrelativistic quark model using the ``quark Born diagram" formalism. This
approach describes the scattering as a single interaction, here the
one-gluon-exchange (OGE) spin-spin term followed by constituent interchange,
with external nonrelativistic baryon wavefunctions attached to the scattering
diagrams to incorporate higher-twist wavefunction effects. The short-range
repulsive core in the NN interaction has previously been attributed to this
spin-spin interaction in the literature; we find that these perturbative
constituent-interchange diagrams do indeed predict repulsive interactions in
all I,S channels of the nucleon-nucleon system, and we compare our results for
the equivalent short-range potentials to the core potentials found by other
authors using nonperturbative methods. We also apply our perturbative
techniques to the N and systems: Some
channels are found to have attractive core potentials and may accommodate
``molecular" bound states near threshold. Finally we use our Born formalism to
calculate the NN differential cross section, which we compare with experimental
results for unpolarised proton-proton elastic scattering. We find that several
familiar features of the experimental differential cross section are reproduced
by our Born-order result.Comment: 27 pages, figures available from the authors, revtex, CEBAF-TH-93-04,
MIT-CTP-2187, ORNL-CCIP-93-0
Impact of sympathetic nervous system activity on post-exercise flow-mediated dilatation in humans
Transient reduction in vascular function following systemic large muscle group exercise has previously been reported in humans. The mechanisms responsible are currently unknown. We hypothesised that sympathetic nervous system activation, induced by cycle ergometer exercise, would contribute to post-exercise reductions in flow-mediated dilatation (FMD). Ten healthy male subjects (28 ± 5 years) undertook two 30 min sessions of cycle exercise at 75% HRmax. Prior to exercise, individuals ingested either a placebo or an α1-adrenoreceptor blocker (prazosin; 0.05 mg kg−1). Central haemodynamics, brachial artery shear rate (SR) and blood flow profiles were assessed throughout each exercise bout and in response to brachial artery FMD, measured prior to, immediately after and 60 min after exercise. Cycle exercise increased both mean and antegrade SR (P < 0.001) with retrograde SR also elevated under both conditions (P < 0.001). Pre-exercise FMD was similar on both occasions, and was significantly reduced (27%) immediately following exercise in the placebo condition (t-test, P = 0.03). In contrast, FMD increased (37%) immediately following exercise in the prazosin condition (t-test, P = 0.004, interaction effect P = 0.01). Post-exercise FMD remained different between conditions after correction for baseline diameters preceding cuff deflation and also post-deflation SR. No differences in FMD or other variables were evident 60 min following recovery. Our results indicate that sympathetic vasoconstriction competes with endothelium-dependent dilator activity to determine post-exercise arterial function. These findings have implications for understanding the chronic impacts of interventions, such as exercise training, which affect both sympathetic activity and arterial shear stress
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