17,450 research outputs found

### Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of
a symmetric Kac-Moody algebra. There is a geometric realization of this object
using Nakajima's quiver varieties, but in many particular cases it can also be
realized by elementary combinatorial methods. Here we propose a framework for
extracting combinatorial realizations from the geometric picture: We construct
certain torus actions on the quiver varieties and use Morse theory to index the
irreducible components by connected components of the subvariety of torus fixed
points. We then discuss the case of affine sl(n). There the fixed point
components are just points, and are naturally indexed by multi-partitions.
There is some choice in our construction, leading to a family of combinatorial
models for each highest weight crystal. Applying this construction to the
crystal of the fundamental representation recovers a family of combinatorial
realizations recently constructed by Fayers. This gives a more conceptual proof
of Fayers' result as well as a generalization to higher level. We also discuss
a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some
references; v3: many small correction

### Geometric and combinatorial realizations of crystal graphs

For irreducible integrable highest weight modules of the finite and affine
Lie algebras of type A and D, we define an isomorphism between the geometric
realization of the crystal graphs in terms of irreducible components of
Nakajima quiver varieties and the combinatorial realizations in terms of Young
tableaux and Young walls. For affine type A, we extend the Young wall
construction to arbitrary level, describing a combinatorial realization of the
crystals in terms of new objects which we call Young pyramids.Comment: 34 pages, 17 figures; v2: minor typos corrected; v3: corrections to
section 8; v4: minor typos correcte

### Thermodynamic Construction of an One-Step Replica-Symmetry-Breaking Solution in Finite Connectivity Spin Glasses

An one-step replica-symmetry-breaking solution for finite connectivity
spin-glass models with K body interaction is constructed at finite temperature
using the replica method and thermodynamic constraints. In the absence of
external fields, this construction provides a general extension of replica
symmetric solution at finite replica number to one-step
replica-symmetry-breaking solution. It is found that this result is formally
equivalent to that of the one-step replica-symmetry-breaking cavity method. To
confirm the validity of the obtained solution, Monte Carlo simulations are
performed for K = 2 and 3. The thermodynamic quantities of the Monte Carlo
results extrapolated to a large-size limit are consistent with those estimated
by our solution for K = 2 at all simulated temperatures and for K = 3 except
near the transition temperature.Comment: 11pages, 19 figures. Added content and references. Accepted to Phys.
Rev.

### Analyses of multiplicity distributions by means of the Modified Negative Binomial Distribution and its KNO scaling function

We analyze various data of multiplicity distributions by means of the
Modified Negative Binomial Distribution (MNBD) and its KNO scaling function,
since this MNBD explains the oscillating behavior of the cumulant moment
observed in e^+e^- annihilations, h-h collisions and e-p collisions. In the
present analyses, we find that the MNBD(discrete distributions) describes the
data of charged particles in e^+e^- annihilations much better than the Negative
Binomial Distribution (NBD). To investigate stochastic property of the MNBD, we
derive the KNO scaling function from the discrete distribution by using a
straightforward method and the Poisson transform. It is a new KNO function
expressed by the Laguerre polynomials. In analyses of the data by using the KNO
scaling function, we find that the MNBD describes the data better than the
gamma function.Thus, it can be said that the MNBD is one of useful formulas as
well as NBD.Comment: 12 pages, latex, 3 figure

### High-Energy Spin Dynamics in La$_{1.69}$Sr$_{0.31}$NiO$_4$

We have mapped out the spin dynamics in a stripe-ordered nickelate,
La$_{2-x}$Sr$_{x}$NiO$_{4}$ with $x \simeq 0.31$, using inelastic neutron
scattering. We observe spin-wave excitations up to 80 meV emerging from the
incommensurate magnetic peaks with an almost isotropic spin-velocity: $\hbar
c_s\sim 0.32$ eV \AA, very similar to the velocity in the undoped, insulating
parent compound, La$_{2}$NiO$_{4}$. We also discuss the similarities and
differences of the inferred spin-excitation spectrum with those reported in
superconducting high-$T_c$ cuprates.Comment: 4 figure

### Inverted Hybrid Inflation as a solution to gravitino problems in Gravity Mediation

It was recently found that the decay of inflaton and the SUSY breaking field
produces many gravitinos in the gravity mediation scenario. These discoveries
led to an exclusion of many inflation models such as chaotic, (smooth) hybrid,
topological and new inflation models. Under these circumstances we searched for
a successful inflation model and found that the ``inverted'' hybrid inflation
models can solve the gravitino overproduction problem by their distinctive
shape of the potential. Furthermore, we found that this inflation model
simultaneously can explain the observed baryon asymmetry through the
non-thermal leptogenesis and is consistent with the WMAP results, that is,
$n_s=0.951^{+0.015}_{-0.019}$ and the negligible tensor to scalar ratio.Comment: 23 pages, 2 figures in

### Spin-squeezed Ground States in the Bilayer Quantum Hall Ferromagnet

A "squeezed-vacuum" state considered in quantum optics is shown to be
realized in the ground-state wavefunction for the bilayer quantum Hall system
at the total Landau level filling of $\nu=1/m$ (m: odd integer). This is
derived in the boson approximation, where a particle-hole pair creation across
the symmetric-antisymmetric gap, $\Delta_{SAS}$, is regarded as a boson. In
terms of the pseudospin describing the layers, the state is a spin-squeezed
state, where the degree of squeezing is controlled by the layer separation and
$\Delta_{SAS}$. An exciton condensation, which amounts to a rotated
spin-squeezed state, has a higher energy due to the degraded SU(2) symmetry for
$\Delta_{SAS} \neq 0$.Comment: 4 pages, revtex, one figure, to appear in PRB Rapid Communicatio

### A Systematic Study of X-Ray Flares from Low-Mass Young Stellar Objects in the Rho Ophiuchi Star-Forming Region with Chandra

We report on the results of a systematic study of X-ray flares from low-mass
young stellar objects, using Chandra observations of the main region of the Rho
Oph. From 195 X-ray sources, including class I-III sources and some young brown
dwarfs, we detected a total of 71 X-ray flares. Most of the flares have the
typical profile of solar and stellar flares, fast rise and slow decay. We
derived the time-averaged temperature (kT), luminosity (L_X), rise and decay
timescales (tau_r and tau_d) of the flares, finding that (1) class I-II sources
tend to have a high kT, (2) the distribution of L_X during flares is nearly the
same for all classes, and (3) positive and negative log-linear correlations are
found between tau_r and tau_d, and kT and tau_r. In order to explain these
relations, we used the framework of magnetic reconnection model to formulate
the observational parameters as a function of the half-length of the
reconnected magnetic loop (L) and magnetic field strength (B). The estimated L
is comparable to the typical stellar radius of these objects (10^{10-11} cm),
which indicates that the observed flares are triggered by solar-type loops,
rather than larger ones (10^{12} cm) connecting the star with its inner
accretion disk. The higher kT observed for class I sources may be explained by
a higher magnetic field strength (about 500 G) than for class II-III sources
(200-300 G).Comment: 33 pages, 7 figures, accepted for publication in PASJ, the complete
version of tables are available at
ftp://ftp-cr.scphys.kyoto-u.ac.jp/pub/crmember/kensuke/PASJ_RhoOph/KI_all.tar
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