51,276 research outputs found
Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain
Recently a new integral equation describing the thermodynamics of the 1D
Heisenberg model was discovered by Takahashi. Using the integral equation we
have succeeded in obtaining the high temperature expansion of the specific heat
and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than
those obtained so far by the standard methods such as the linked-cluster
algorithm. Our results will be useful to examine various approximation methods
to extrapolate the high temperature expansion to the low temperature region.Comment: 5 pages, 4 figures, 2 table
Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe
When a gravitational wave (GW) from a distant source propagates through the
universe, its amplitude and phase change due to gravitational lensing by the
inhomogeneous mass distribution. We derive the amplitude and phase
fluctuations, and calculate these variances in the limit of a weak
gravitational field of density perturbation. If the scale of the perturbation
is smaller than the Fresnel scale ( is the
GW frequency), the GW is not magnified due to the diffraction effect. The rms
amplitude fluctuation is for Hz, but it is reduced less
than 5% for a very low frequency of Hz. The rms phase
fluctuation in the chirp signal is radian at LISA frequency band
( Hz). Measurements of these fluctuations will provide
information about the matter power spectrum on the Fresnel scale pc.Comment: 6 pages, 6 figures, refferences added, accepted for publication in
Ap
Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has
proved successful for treating the structure and thermodynamics of a variety of
non-uniform liquids. By reformulating LMF in terms of one-body direct
correlation functions we recast the theory in the framework of classical
Density Functional Theory (DFT). We show that the general LMF equation for the
effective reference potential phi_R follows directly from the standard
mean-field DFT treatment of attractive interatomic forces. Using an accurate
(Fundamental Measures) DFT for the non-uniform hard-sphere reference fluid we
determine phi_R for a hard-core Yukawa liquid adsorbed at a planar hard wall.
In the approach to bulk liquid-gas coexistence we find the effective potentials
exhibit rich structure that can include damped oscillations at large distances
from the wall as well as the repulsive hump near the wall required to generate
the low density 'gas' layer characteristic of complete drying. We argue that it
would be difficult to obtain the same level of detail from other (non DFT
based) implementations of LMF. LMF emphasizes the importance of making an
intelligent division of the interatomic pair potential of the full system into
a reference part and a remainder that can be treated in mean-field
approximation. We investigate different divisions for an exactly solvable one-
dimensional model where the pair potential has a hard-core plus a linear
attractive tail. Results for the structure factor and the equation of state of
the uniform fluid show that including a significant portion of the attraction
in the reference system can be much more accurate than treating the full
attractive tail in mean-field approximation. We discuss further aspects of the
relationship between LMF and DFT.Comment: 35 pages, 10 Fig
Entanglement Scaling in the One-Dimensional Hubbard Model at Criticality
We derive exact expressions for the local entanglement entropy E in the
ground state of the one-dimensional Hubbard model at a quantum phase transition
driven by a change in magnetic field h or chemical potential u. The leading
divergences of dE/dh and dE/du are shown to be directly related to those of the
zero-temperature spin and charge susceptibilities. Logarithmic corrections to
scaling signal a change in the number of local states accessible to the system
as it undergoes the transition.Comment: 4+ pages, 2 figures. Fig. 2 and minor typos correcte
Test of Chemical freeze-out at RHIC
We present the results of a systematic test applying statistical thermal
model fits in a consistent way for different particle ratios, and different
system sizes using the various particle yields measured in the STAR experiment.
Comparison between central and peripheral Au+Au and Cu+Cu collisions with data
from p+p collisions provides an interesting tool to verify the dependence with
the system size. We also present a study of the rapidity dependence of the
thermal fit parameters using available data from RHIC in the forward rapidity
regions and also using different parameterization for the rapidity distribution
of different particles.Comment: SQM2008 conference proceeding
Analytical Tachyonic Lump Solutions in Open Superstring Field Theory
We construct a classical solution in the GSO(-) sector in the framework of a
Wess-Zumino-Witten-like open superstring field theory on a non-BPS D-brane. We
use an su(2) supercurrent, which is obtained by compactifying a direction to a
circle with the critical radius, in order to get analytical tachyonic lump
solutions to the equation of motion. By investigating the action expanded
around a solution we find that it represents a deformation from a non-BPS
D-brane to a D-brane-anti-D-brane system at the critical value of a parameter
which is contained in classical solutions. Although such a process was
discussed in terms of boundary conformal field theory before, our study is
based on open superstring field theory including interaction terms.Comment: 17 pages, references adde
Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the
sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer
matrix. These TBA equations are identical to the ones from the string
hypothesis. Next we derive a new family of nonlinear integral equations (NLIE).
In particular, a subset of these NLIE forms a system of NLIE which contains
only a finite number of unknown functions. For r=1, this subset of NLIE reduces
to Takahashi's NLIE for the XXX spin chain. A relation between the traditional
TBA equations and our new NLIE is clarified. Based on our new NLIE, we also
calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge
Monte Carlo Simulations of Globular Cluster Evolution - II. Mass Spectra, Stellar Evolution and Lifetimes in the Galaxy
We study the dynamical evolution of globular clusters using our new 2-D Monte
Carlo code, and we calculate the lifetimes of clusters in the Galactic
environment. We include the effects of a mass spectrum, mass loss in the
Galactic tidal field, and stellar evolution. We consider initial King models
containing N = 10^5 - 3x10^5 stars, and follow the evolution up to core
collapse, or disruption, whichever occurs first. We find that the lifetimes of
our models are significantly longer than those obtained using 1-D Fokker-Planck
(F-P) methods. We also find that our results are in very good agreement with
recent 2-D F-P calculations, for a wide range of initial conditions. Our
results show that the direct mass loss due to stellar evolution can
significantly accelerate the mass loss through the tidal boundary, causing most
clusters with a low initial central concentration (Wo <~ 3) to disrupt quickly
in the Galactic tidal field. Only clusters born with high initial central
concentrations (Wo >~ 7) or steep initial mass functions are likely to survive
to the present and undergo core collapse. We also study the orbital
characteristics of escaping stars, and find that the velocity distribution of
escaping stars in collapsing clusters looks significantly different from the
distribution in disrupting clusters. We calculate the lifetime of a cluster on
an eccentric orbit in the Galaxy, such that it fills its Roche lobe only at
perigalacticon. We find that such an orbit can extend the lifetime by at most a
factor of a few compared to a circular orbit in which the cluster fills its
Roche lobe at all times.Comment: 32 pages, including 10 figures, to appear in ApJ, minor corrections
onl
Integrable Magnetic Model of Two Chains Coupled by Four-Body Interactions
An exact solution for an XXZ chain with four-body interactions is obtained
and its phase diagram is determined. The model can be reduced to two chains
coupled by four-body interactions, and it is shown that the ground state of the
two-chain model is magnetized in part. Furthermore, a twisted four-body
correlation function of the anti-ferromagnetic Heisenberg chain is obtained.Comment: 7 pages, LaTeX, to be published in J. Phys. Soc. Jpn., rederived the
mode
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