1,897 research outputs found
Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to a many body quantum boson system with
attractive interactions. Performing the summation over the entire spectrum of
excited states the problem is reduced to the Fredholm determinant with the Airy
kernel which is known to yield the Tracy-Widom distributionComment: 5 page
Heat Capacity of ^3He in Aerogel
The heat capacity of pure ^3He in low density aerogel is measured at 22.5
bar. The superfluid response is simultaneously monitored with a torsional
oscillator. A slightly rounded heat capacity peak, 65 mu K in width, is
observed at the ^3He-aerogel superfluid transition, T_{ca}. Subtracting the
bulk ^3He contribution, the heat capacity shows a Fermi-liquid form above
T_{ca}. The heat capacity attributed to superfluid within the aerogel can be
fit with a rounded BCS form, and accounts for 0.30 of the non-bulk fluid in the
aerogel, indicating a substantial reduction in the superfluid order parameter
consistent with earlier superfluid density measurements.Comment: 4 pages, 5 figure
From interacting particle systems to random matrices
In this contribution we consider stochastic growth models in the
Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large
time distribution and processes and their dependence on the class on initial
condition. This means that the scaling exponents do not uniquely determine the
large time surface statistics, but one has to further divide into subclasses.
Some of the fluctuation laws were first discovered in random matrix models.
Moreover, the limit process for curved limit shape turned out to show up in a
dynamical version of hermitian random matrices, but this analogy does not
extend to the case of symmetric matrices. Therefore the connections between
growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor
corrections in scaling of section 2.
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to the -particle quantum boson system with
attractive interactions. We find the full set of eigenfunctions and eigenvalues
of this many-body system and perform the summation over the entire spectrum of
excited states. It is shown that in the thermodynamic limit the problem is
reduced to the Fredholm determinant with the Airy kernel yielding the universal
Tracy-Widom distribution, which is known to describe the statistical properties
of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page
Discovery of a Variable Star Population in NGC 2808
We have applied the image subtraction method to images of the peculiar,
bimodal-horizontal branch globular cluster NGC 2808, taken over a total of six
nights over a range of five months. As a result, we have found, for the first
time, a sizeable population of variable stars in the crowded inner regions of
the cluster, thus raising the known RR Lyrae population in the cluster to a
total of 18 stars. In addition, an eclipsing binary and two other variables
with periods longer than 1 day were also found. Periods, positions and
(differential) light curves are provided for all the detected variables. The
Oosterhoff classification of NGC 2808, which has recently been associated with
a previously unknown dwarf galaxy in Canis Major, is briefly discussed.Comment: 8 pages, 4 figures. A&A, in pres
NGC 300: an extremely faint, outer stellar disk observed to 10 scale lengths
We have used the Gemini Multi-object Spectrograph (GMOS) on the Gemini South
8m telescope in exceptional conditions (0.6" FWHM seeing) to observe the outer
stellar disk of the Sculptor group galaxy NGC 300 at two locations. At our
point source detection threshold of r' = 27.0 (3-sigma) mag, we trace the
stellar disk out to a radius of 24', or 2.2 R_25 where R_25 is the 25
mag/arcsec**2 isophotal radius. This corresponds to about 10 scale lengths in
this low-luminosity spiral (M_B = -18.6), or about 14.4 kpc at a cepheid
distance of 2.0 +/- 0.07 Mpc. The background galaxy counts are derived in the
outermost field, and these are within 10% of the mean survey counts from both
Hubble Deep Fields. The luminosity profile is well described by a nucleus plus
a simple exponential profile out to 10 optical scale lengths. We reach an
effective surface brightness of 30.5 mag/arcsec**2 (2-sigma) at 55%
completeness which doubles the known radial extent of the optical disk. These
levels are exceedingly faint in the sense that the equivalent surface
brightness in B or V is about 32 mag/arcsec**2. We find no evidence for
truncation of the stellar disk. Only star counts can be used to reliably trace
the disk to such faint levels, since surface photometry is ultimately limited
by nonstellar sources of radiation. In the Appendix, we derive the expected
surface brightness of one such source: dust scattering of starlight in the
outer disk.Comment: ApJ accepted -- 30 pages, 13 figures -- see
ftp://www.aao.gov.au/pub/local/jbh/astro-ph/N300 for full resolution figures
and preprin
A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation
We estimate the variance of the value function for a random optimal control
problem. The value function is the solution of a Hamilton-Jacobi
equation with random Hamiltonian
in dimension . It is known that homogenization occurs as , but little is known about the statistical fluctuations of .
Our main result shows that the variance of the solution is bounded
by . The proof relies on a modified Poincar\'e
inequality of Talagrand
Extremal statistics of curved growing interfaces in 1+1 dimensions
We study the joint probability distribution function (pdf) of the maximum M
of the height and its position X_M of a curved growing interface belonging to
the universality class described by the Kardar-Parisi-Zhang equation in 1+1
dimensions. We obtain exact results for the closely related problem of p
non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M)
where \tau_M is there the time at which the maximal height M is reached. Our
analytical results, in the limit p \to \infty, become exact for the interface
problem in the growth regime. We show that our results, for moderate values of
p \sim 10 describe accurately our numerical data of a prototype of these
systems, the polynuclear growth model in droplet geometry. We also discuss
applications of our results to the ground state configuration of the directed
polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics
Letters. New results added for non-intersecting excursion
M75, a Globular Cluster with a Trimodal Horizontal Branch. I. Color-Magnitude Diagram
Deep UBVI photometry for a large field covering the distant globular cluster
M75 (NGC 6864) is presented. We confirm a previous suggestion (Catelan et al.
1998a) that M75 possesses a bimodal horizontal branch (HB) bearing striking
resemblance to the well-known case of NGC 1851. In addition, we detect a third,
smaller grouping of stars on the M75 blue tail, separated from the bulk of the
blue HB stars by a gap spanning about 0.5 mag in V. Such a group of stars may
correspond to the upper part of a very extended, though thinly populated, blue
tail. Thus M75 appears to have a trimodal HB. The presence of the "Grundahl
jump" is verified using the broadband U filter. We explore the color-magnitude
diagram of M75 with the purpose of deriving the cluster's fundamental
parameters, and find a metallicity of [Fe/H] = -1.03 +/- 0.17 dex and -1.24 +/-
0.21 dex in the Carretta & Gratton (1997) and Zinn & West (1984) scales,
respectively. We discuss earlier suggestions that the cluster has an
anomalously low ratio of bright red giants to HB stars. A differential age
analysis with respect to NGC 1851 suggests that the two clusters are
essentially coeval.Comment: 19 pages, 15 figures, emulateapj5/apjfonts style. Astronomical
Journal, in press. This version contains some very low-resolution figures,
due to the size constraints of astro-ph. We strongly encourage the interested
reader to download instead the preprint with full-resolution figures, which
can be found at http://www.astro.puc.cl/~mcatelan
A multi-layer extension of the stochastic heat equation
Motivated by recent developments on solvable directed polymer models, we
define a 'multi-layer' extension of the stochastic heat equation involving
non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio
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