3,016 research outputs found
Pfaffian Expressions for Random Matrix Correlation Functions
It is well known that Pfaffian formulas for eigenvalue correlations are
useful in the analysis of real and quaternion random matrices. Moreover the
parametric correlations in the crossover to complex random matrices are
evaluated in the forms of Pfaffians. In this article, we review the
formulations and applications of Pfaffian formulas. For that purpose, we first
present the general Pfaffian expressions in terms of the corresponding skew
orthogonal polynomials. Then we clarify the relation to Eynard and Mehta's
determinant formula for hermitian matrix models and explain how the evaluation
is simplified in the cases related to the classical orthogonal polynomials.
Applications of Pfaffian formulas to random matrix theory and other fields are
also mentioned.Comment: 28 page
Spectra of massive QCD dirac operators from random matrix theory: All three chiral symmetry breaking patterns
The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index β = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for β = 4
Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem
We consider random hermitian matrices made of complex blocks. The symmetries
of these matrices force them to have pairs of opposite real eigenvalues, so
that the average density of eigenvalues must vanish at the origin. These
densities are studied for finite matrices in the Gaussian ensemble.
In the large limit the density of eigenvalues is given by a semi-circle
law. However, near the origin there is a region of size in which
this density rises from zero to the semi-circle, going through an oscillatory
behavior. This cross-over is calculated explicitly by various techniques. We
then show to first order in the non-Gaussian character of the probability
distribution that this oscillatory behavior is universal, i.e. independent of
the probability distribution. We conjecture that this universality holds to all
orders. We then extend our consideration to the more complicated block matrices
which arise from lattices of matrices considered in our previous work. Finally,
we study the case of random real symmetric matrices made of blocks. By using a
remarkable identity we are able to determine the oscillatory behavior in this
case also. The universal oscillations studied here may be applicable to the
problem of a particle propagating on a lattice with random magnetic flux.Comment: 47 pages, regular LateX, no figure
Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction
We study a chaotic quantum transport in the presence of a weak spin-orbit
interaction. Our theory covers the whole symmetry crossover regime between
time-reversal invariant systems with and without a spin-orbit interaction. This
situation is experimentally realizable when the spin-orbit interaction is
controlled in a conductor by applying an electric field. We utilize a
semiclassical approach which has recently been developed. In this approach, the
non-Abelian nature of the spin diffusion along a classical trajectory plays a
crucial role. New analytical expressions with one crossover parameter are
semiclassically derived for the average conductance, conductance variance and
shot noise. Moreover numerical results on a random matrix model describing the
crossover from the GOE (Gaussian Orthogonal Ensemble) to the GSE (Gaussian
Symplectic Ensemble) are compared with the semiclassical expressions.Comment: 13 pages, 7 figure
Eigenvalue statistics of the real Ginibre ensemble
The real Ginibre ensemble consists of random matrices formed
from i.i.d. standard Gaussian entries. By using the method of skew orthogonal
polynomials, the general -point correlations for the real eigenvalues, and
for the complex eigenvalues, are given as Pfaffians with explicit
entries. A computationally tractable formula for the cumulative probability
density of the largest real eigenvalue is presented. This is relevant to May's
stability analysis of biological webs.Comment: 4 pages, to appear PR
Potentially Large One-loop Corrections to WIMP Annihilation
We compute one-loop corrections to the annihilation of non--relativistic
particles due to the exchange of a (gauge or Higgs) boson with
mass in the initial state. In the limit this leads to
the "Sommerfeld enhancement" of the annihilation cross section. However, here
we are interested in the case \mu \lsim m_\chi, where the one--loop
corrections are well--behaved, but can still be sizable. We find simple and
accurate expressions for annihilation from both and wave initial
states; they differ from each other if . In order to apply our
results to the calculation of the relic density of Weakly Interacting Massive
Particles (WIMPs), we describe how to compute the thermal average of the
corrected cross sections. We apply this formalism to scalar and Dirac fermion
singlet WIMPs, and show that the corrections are always very small in the
former case, but can be very large in the latter. Moreover, in the context of
the Minimal Supersymmetric Standard Model, these corrections can decrease the
relic density of neutralinos by more than 1%, if the lightest neutralino is a
strongly mixed state.Comment: 25 pages, 8 figures. Added an appendix showing that the approximation
works well in a scalar toy model. To be published in PRD
Direct observation of localization in the minority-spin-band electrons of magnetite below the Verwey temperature
Two-dimensional spin-uncompensated momentum density distributions, s, were reconstructed in magnetite at 12K and 300K from
several measured directional magnetic Compton profiles. Mechanical de-twinning
was used to overcome severe twinning in the single crystal sample below the
Verwey transition. The reconstructed in the first
Brillouin zone changes from being negative at 300 K to positive at 12 K. This
result provides the first clear evidence that electrons with low momenta in the
minority spin bands in magnetite are localized below the Verwey transition
temperature.Comment: 13 pages, 4 figures, accepted in Physical Review
Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
We introduce a random two-matrix model interpolating between a chiral
Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without
symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE)
and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n
limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit)
this theory is in one to one correspondence to the partition function of Wilson
chiral perturbation theory in the epsilon regime, such as the related two
matrix-model previously introduced in refs. [20,21]. For a generic number of
flavours and rectangular block matrices in the chGUE part we derive an
eigenvalue representation for the partition function displaying a Pfaffian
structure. In the quenched case with nu=0,1 we derive all spectral correlations
functions in our model for finite-n, given in terms of skew-orthogonal
polynomials. The latter are expressed as Gaussian integrals over standard
Laguerre polynomials. In the weakly non-chiral microscopic limit this yields
all corresponding quenched eigenvalue correlation functions of the Hermitian
Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio
Is there any evidence that ionised outflows quench star formation in type 1 quasars at z<1?
The aim of this paper is to test the basic model of negative AGN feedback.
According to this model, once the central black hole accretes at the Eddington
limit and reaches a certain critical mass, AGN driven outflows blow out gas,
suppressing star formation in the host galaxy and self-regulating black hole
growth. We consider a sample of 224 quasars selected from the SDSS at z<1
observed in the infrared band by Herschel. We evaluate the star formation rate
in relation to several outflow signatures traced by the [OIII]4959,5007 and
[OII]3726,3729 emission lines in about half of the sample with high quality
spectra. Most of the quasars show asymmetric and broad wings in [OIII], which
we interpret as outflow signatures. We separate the quasars in two groups,
``weakly'' and ``strongly'' outflowing, using three different criteria. When we
compare the mean star formation rate in five redshift bins in the two groups,
we find that the SFRs are comparable or slightly larger in the strongly
outflowing quasars. We estimate the stellar mass from SED fitting and the
quasars are distributed along the star formation main sequence, although with a
large scatter. The scatter from this relation is uncorrelated with respect to
the kinematic properties of the outflow. Moreover, for quasars dominated in the
infrared by starburst or by AGN emission, we do not find any correlation
between the star formation rate and the velocity of the outflow, a trend
previously reported in the literature for pure starburst galaxies. We conclude
that the basic AGN negative feedback scenario seems not to agree with our
results. Although we use a large sample of quasars, we did not find any
evidence that the star formation rate is suppressed in the presence of AGN
driven outflows on large scale. A possibility is that feedback is effective
over much longer timescales than those of single episodes of quasar activity.Comment: 18 pages, new version that implements the suggestions of the referee
and matches the AA published versio
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