5,514 research outputs found
Effective Low Energy Theories and QCD Dirac Spectra
We analyze the smallest Dirac eigenvalues by formulating an effective theory
for the QCD Dirac spectrum. We find that in a domain where the kinetic term of
the effective theory can be ignored, the Dirac eigenvalues are distributed
according to a Random Matrix Theory with the global symmetries of the QCD
partition function. The kinetic term provides information on the slope of the
average spectral density of the Dirac operator. In the second half of this
lecture we interpret quenched QCD Dirac spectra at nonzero chemical potential
(with eigenvalues scattered in the complex plane) in terms of an effective low
energy theory.Comment: Invited talk at the 10th International Conference on Recent Progress
in Many-Body Theories (MBX), Seattle, September 1999, 13 pages, Latex, with 1
figure, uses ws-p9-75x6-50.cl
Direct solution of the hard pomeron problem for arbitrary conformal weight
A new method is applied to solve the Baxter equation for the one dimensional
system of noncompact spins. Dynamics of such an ensemble is equivalent to that
of a set of reggeized gluons exchanged in the high energy limit of QCD
amplitudes. The technique offers more insight into the old calculation of the
intercept of hard Pomeron, and provides new results in the odderon channel.Comment: Contribution to the ICHEP96 Conference, July 1996, Warsaw, Poland.
LaTeX, 4 pages, 3 epsf figures, includes modified stwol.sty file. Some
references were revise
Simple analytic potentials for linear ion traps
A simple analytical model was developed for the electric and ponderomotive (trapping) potentials in linear ion traps. This model was used to calculate the required voltage drive to a mercury trap, and the result compares well with experiments. The model gives a detailed picture of the geometric shape of the trapping potenital and allows an accurate calculation of the well depth. The simplicity of the model allowed an investigation of related, more exotic trap designs which may have advantages in light-collection efficiency
A hybrid approach to space power control
Conventional control systems have traditionally been utilized for space-based power designs. However, the use of expert systems is becoming important for NASA applications. Rocketdyne has been pursuing the development of expert systems to aid and enhance control designs of space-based power systems. The need for integrated expert systems is vital for the development of autonomous power systems
Solution of the Odderon Problem
The intercept of the odderon trajectory is derived, by finding the spectrum
of the second integral of motion of the three reggeon system in high energy
QCD. When combined with earlier solution of the appropriate Baxter equation,
this leads to the determination of the low lying states of that system. In
particular, the energy of the lowest state gives the intercept of the odderon
alpha_O(0)=1-0.2472 alpha_s N_c/pi.Comment: 11 pages, 2 Postscript figure
Unified description of Bjorken and Landau 1+1 hydrodynamics
We propose a generalization of the Bjorken in-out Ansatz for fluid
trajectories which, when applied to the (1+1) hydrodynamic equations, generates
a one-parameter family of analytic solutions interpolating between the
boost-invariant Bjorken picture and the non boost-invariant one by Landau. This
parameter characterises the proper-time scale when the fluid velocities
approach the in-out Ansatz. We discuss the resulting rapidity distribution of
entropy for various freeze-out conditions and compare it with the original
Bjorken and Landau results.Comment: 20 pages, 5 figure
Multiplication law and S transform for non-hermitian random matrices
We derive a multiplication law for free non-hermitian random matrices
allowing for an easy reconstruction of the two-dimensional eigenvalue
distribution of the product ensemble from the characteristics of the individual
ensembles. We define the corresponding non-hermitian S transform being a
natural generalization of the Voiculescu S transform. In addition we extend the
classical hermitian S transform approach to deal with the situation when the
random matrix ensemble factors have vanishing mean including the case when both
of them are centered. We use planar diagrammatic techniques to derive these
results.Comment: 25 pages + 11 figure
Summing free unitary random matrices
I use quaternion free probability calculus - an extension of free probability
to non-Hermitian matrices (which is introduced in a succinct but self-contained
way) - to derive in the large-size limit the mean densities of the eigenvalues
and singular values of sums of independent unitary random matrices, weighted by
complex numbers. In the case of CUE summands, I write them in terms of two
"master equations," which I then solve and numerically test in four specific
cases. I conjecture a finite-size extension of these results, exploiting the
complementary error function. I prove a central limit theorem, and its first
sub-leading correction, for independent identically-distributed zero-drift
unitary random matrices.Comment: 17 pages, 15 figure
Relaxation mechanisms of the persistent spin helix
We study the lifetime of the persistent spin helix in semiconductor quantum
wells with equal Rashba- and linear Dresselhaus spin-orbit interactions. In
order to address the temperature dependence of the relevant spin relaxation
mechanisms we derive and solve semiclassical spin diffusion equations taking
into account spin-dependent impurity scattering, cubic Dresselhaus spin-orbit
interactions and the effect of electron-electron interactions. For the
experimentally relevant regime we find that the lifetime of the persistent spin
helix is mainly determined by the interplay of cubic Dresselhaus spin-orbit
interaction and electron-electron interactions. We propose that even longer
lifetimes can be achieved by generating a spatially damped spin profile instead
of the persistent spin helix state.Comment: 12 pages, 2 figure
Spectrum of the Product of Independent Random Gaussian Matrices
We show that the eigenvalue density of a product X=X_1 X_2 ... X_M of M
independent NxN Gaussian random matrices in the large-N limit is rotationally
symmetric in the complex plane and is given by a simple expression
rho(z,\bar{z}) = 1/(M\pi\sigma^2} |z|^{-2+2/M} for |z|<\sigma, and is zero for
|z|> \sigma. The parameter \sigma corresponds to the radius of the circular
support and is related to the amplitude of the Gaussian fluctuations. This form
of the eigenvalue density is highly universal. It is identical for products of
Gaussian Hermitian, non-Hermitian, real or complex random matrices. It does not
change even if the matrices in the product are taken from different Gaussian
ensembles. We present a self-contained derivation of this result using a planar
diagrammatic technique for Gaussian matrices. We also give a numerical evidence
suggesting that this result applies also to matrices whose elements are
independent, centered random variables with a finite variance.Comment: 16 pages, 6 figures, minor changes, some references adde
- …