64 research outputs found
Stochastic B\"acklund transformations
How does one introduce randomness into a classical dynamical system in order
to produce something which is related to the `corresponding' quantum system? We
consider this question from a probabilistic point of view, in the context of
some integrable Hamiltonian systems
Moments of vicious walkers and M\"obius graph expansions
A system of Brownian motions in one-dimension all started from the origin and
conditioned never to collide with each other in a given finite time-interval
is studied. The spatial distribution of such vicious walkers can be
described by using the repulsive eigenvalue-statistics of random Hermitian
matrices and it was shown that the present vicious walker model exhibits a
transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian
orthogonal ensemble (GOE) statistics as the time is going on from 0 to .
In the present paper, we characterize this GUE-to-GOE transition by presenting
the graphical expansion formula for the moments of positions of vicious
walkers. In the GUE limit , only the ribbon graphs contribute and the
problem is reduced to the classification of orientable surfaces by genus.
Following the time evolution of the vicious walkers, however, the graphs with
twisted ribbons, called M\"obius graphs, increase their contribution to our
expansion formula, and we have to deal with the topology of non-orientable
surfaces. Application of the recent exact result of dynamical correlation
functions yields closed expressions for the coefficients in the M\"obius
expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function
and references added. v.3: minor additions and corrections made for
publication in Phys.Rev.
The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach
We readdress the problem of finding a simultaneous description of the pion
form factor data in e+e- annihilations and in tau decays. For this purpose, we
work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify
the vector meson mass term by including the pion and kaon loop contributions.
This leads us to define the physical rho, omega and phi fields as linear
combinations of their ideal partners, with coefficients being meromorphic
functions of s, the square of the 4--momentum flowing into the vector meson
lines. This allows us to define a dynamical, i.e. s-dependent, vector meson
mixing scheme. The model is overconstrained by extending the framework in order
to include the description of all meson radiative (V P gamma and P gamma gamma
couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking
(omega/ phi --> pi+ pi-) decay modes. The model provides a simultaneous,
consistent and good description of the e+e- and tau dipion spectra. The
expression for pion form factor in the latter case is derived from those in the
former case by switching off the isospin breaking effects specific to e+e- and
switching on those for tau decays. Besides, the model also provides a good
account of all decay modes of the form V P gamma, Pgamma gamma as well as the
isospin breaking decay modes. It leads us to propose new reference values for
the rho^0 --> e+ e- and omega --> pi+ pi- partial widths which are part of our
description of the pion form factor. Other topics (phi --> K anti K, the rho
meson mass and width parameters) are briefly discussed. Therefore, we confirm
the 3.3 sigma discrepancy between the theoretical estimate of a_mu based on
e+e- and its direct BNL measurement.Comment: 71 pages, 8 figures. Accepted by EPJ C. Version 3: correct minor
typos, minor changes spread out into the text. Extension of Sections 12.2 and
12.3.5 and introduction of the new Appendix
Weak reaction freeze-out constraints on primordial magnetic fields
We explore constraints on the strength of the primordial magnetic field based
upon the weak reaction freeze-out in the early universe. We find that limits on
the strength of the magnetic field found in other works are recovered simply by
examining the temperature at which the rate of weak reactions drops below the
rate of universal expansion ( H). The temperature for which the
ratio at freeze-out leads to acceptable helium production implies limits
on the magnetic field. This simplifies the application of magnetic fields to
other cosmological variants of the standard big-bang. As an illustration we
also consider effects of neutrino degeneracy on the allowed limits to the
primordial magnetic field.Comment: Submitted to Phys. Rev. D., 6 pages, 2 figure
Airy processes and variational problems
We review the Airy processes; their formulation and how they are conjectured
to govern the large time, large distance spatial fluctuations of one
dimensional random growth models. We also describe formulas which express the
probabilities that they lie below a given curve as Fredholm determinants of
certain boundary value operators, and the several applications of these
formulas to variational problems involving Airy processes that arise in
physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI
Proceedings: Topics in percolative and disordered systems
Endpoint distribution of directed polymers in 1+1 dimensions
We give an explicit formula for the joint density of the max and argmax of
the Airy process minus a parabola. The argmax has a universal distribution
which governs the rescaled endpoint for large time or temperature of directed
polymers in 1+1 dimensions.Comment: Expanded introductio
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies
It has been assumed until very recently that all long-range correlations are
screened in three-dimensional melts of linear homopolymers on distances beyond
the correlation length characterizing the decay of the density
fluctuations. Summarizing simulation results obtained by means of a variant of
the bond-fluctuation model with finite monomer excluded volume interactions and
topology violating local and global Monte Carlo moves, we show that due to an
interplay of the chain connectivity and the incompressibility constraint, both
static and dynamical correlations arise on distances . These
correlations are scale-free and, surprisingly, do not depend explicitly on the
compressibility of the solution. Both monodisperse and (essentially)
Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure
The Size Evolution of Passive Galaxies: Observations From the Wide-Field Camera 3 Early Release Science Program
We present the size evolution of passively evolving galaxies at z approximately 2 identified in Wide-Field Camera 3 imaging from the Early Release Science program. Our sample was constructed using an analog to the passive BzK galaxy selection criterion, which isolates galaxies with little or no ongoing star formation at z greater than approximately 1.5. We identify 30 galaxies in approximately 40 arcmin(sup 2) to H less than 25 mag. By fitting the 10-band Hubble Space Telescope photometry from 0.22 micrometers less than approximately lambda (sub obs) 1.6 micrometers with stellar population synthesis models, we simultaneously determine photometric redshift, stellar mass, and a bevy of other population parameters. Based on the six galaxies with published spectroscopic redshifts, we estimate a typical redshift uncertainty of approximately 0.033(1+z).We determine effective radii from Sersic profile fits to the H-band image using an empirical point-spread function. By supplementing our data with published samples, we propose a mass-dependent size evolution model for passively evolving galaxies, where the most massive galaxies (M(sub ) approximately 10(sup 11) solar mass) undergo the strongest evolution from z approximately 2 to the present. Parameterizing the size evolution as (1 + z)(sup - alpha), we find a tentative scaling of alpha approximately equals (0.6 plus or minus 0.7) + (0.9 plus or minus 0.4) log(M(sub )/10(sup 9 solar mass), where the relatively large uncertainties reflect the poor sampling in stellar mass due to the low numbers of highredshift systems. We discuss the implications of this result for the redshift evolution of the M(sub )-R(sub e) relation for red galaxies
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