1,463 research outputs found
Pieri's Formula for Generalized Schur Polynomials
Young's lattice, the lattice of all Young diagrams, has the
Robinson-Schensted-Knuth correspondence, the correspondence between certain
matrices and pairs of semi-standard Young tableaux with the same shape. Fomin
introduced generalized Schur operators to generalize the
Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur
operators are generalizations of semi-standard Young tableaux. We define a
generalization of Schur polynomials as expansion coefficients of generalized
Schur operators. We show that the commutating relation of generalized Schur
operators implies Pieri's formula to generalized Schur polynomials
Gate-voltage dependence of Kondo effect in a triangular quantum dot
We study the conductance through a triangular triple quantum dot, which are
connected to two noninteracting leads, using the numerical renormalization
group (NRG). It is found that the system shows a variety of Kondo effects
depending on the filling of the triangle. The SU(4) Kondo effect occurs at
half-filling, and a sharp conductance dip due to a phase lapse appears in the
gate-voltage dependence. Furthermore, when four electrons occupy the three
sites on average, a local S=1 moment, which is caused by the Nagaoka mechanism,
is induced along the triangle. The temperature dependence of the entropy and
spin susceptibility of the triangle shows that this moment is screened by the
conduction electrons via two separate stages at different temperatures. The
two-terminal and four-terminal conductances show a clear difference at the gate
voltages, where the SU(4) or the S=1 Kondo effects occurring.Comment: 4 pages, 4 figs: typos just below (4) are corrected, results are not
affecte
Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups
For the coinvariant rings of finite Coxeter groups of types other than H,
we show that a homogeneous element of degree one is a strong Lefschetz element
if and only if it is not fixed by any reflections. We also give the necessary
and sufficient condition for strong Lefschetz elements in the invariant
subrings of the coinvariant rings of Weyl groups.Comment: 18 page
Freely decaying turbulence in two-dimensional electrostatic gyrokinetics
In magnetized plasmas, a turbulent cascade occurs in phase space at scales
smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett.
103, 015003 (2009)]. When the turbulence is restricted to two spatial
dimensions perpendicular to the background magnetic field, two independent
cascades may take place simultaneously because of the presence of two
collisionless invariants. In the present work, freely decaying turbulence of
two-dimensional electrostatic gyrokinetics is investigated by means of
phenomenological theory and direct numerical simulations. A dual cascade
(forward and inverse cascades) is observed in velocity space as well as in
position space, which we diagnose by means of nonlinear transfer functions for
the collisionless invariants. We find that the turbulence tends to a
time-asymptotic state, dominated by a single scale that grows in time. A theory
of this asymptotic state is derived in the form of decay laws. Each case that
we study falls into one of three regimes (weakly collisional, marginal, and
strongly collisional), determined by a dimensionless number D*, a quantity
analogous to the Reynolds number. The marginal state is marked by a critical
number D* = D0 that is preserved in time. Turbulence initialized above this
value become increasingly inertial in time, evolving toward larger and larger
D*; turbulence initialized below D0 become more and more collisional, decaying
to progressively smaller D*.Comment: 12 pages, 12 figures; replaced to match published versio
Gyrokinetic Simulations of Solar Wind Turbulence from Ion to Electron Scales
The first three-dimensional, nonlinear gyrokinetic simulation of plasma
turbulence resolving scales from the ion to electron gyroradius with a
realistic mass ratio is presented, where all damping is provided by resolved
physical mechanisms. The resulting energy spectra are quantitatively consistent
with a magnetic power spectrum scaling of as observed in \emph{in
situ} spacecraft measurements of the "dissipation range" of solar wind
turbulence. Despite the strongly nonlinear nature of the turbulence, the linear
kinetic \Alfven wave mode quantitatively describes the polarization of the
turbulent fluctuations. The collisional ion heating is measured at
sub-ion-Larmor radius scales, which provides the first evidence of the ion
entropy cascade in an electromagnetic turbulence simulation.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence
Two-dimensional electrostatic turbulence in magnetized weakly-collisional
plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103,
015003 (2009)]. At scales smaller than the gyroradius, this cascade is
characterized by the dimensionless ratio D of the collision time to the eddy
turnover time measured at the scale of the thermal Larmor radius. When D >> 1,
a broad spectrum of fluctuations at sub-Larmor scales is found in both position
and velocity space. The distribution function develops structure as a function
of v_{perp}, the velocity coordinate perpendicular to the local magnetic field.
The cascade shows a local-scale nonlinear interaction in both position and
velocity spaces, and Kolmogorov's scaling theory can be extended into phase
space.Comment: 8 pages, 10 figures, Conference paper presented at 2009 Asia-Pacific
Plasma Theory Conference. Ver.2 includes corrected typos & updated reference
Exponents of 2-multiarrangements and multiplicity lattices
We introduce a concept of multiplicity lattices of 2-multiarrangements,
determine the combinatorics and geometry of that lattice, and give a criterion
and method to construct a basis for derivation modules effectively.Comment: 14 page
Error Reduction Methods for Integrated-path Differential-absorption Lidar Measurements
We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log"
Parametric instabilities in the LCGT arm cavity
We evaluated the parametric instabilities of LCGT (Japanese interferometric
gravitational wave detector project) arm cavity. The number of unstable modes
of LCGT is 10-times smaller than that of Advanced LIGO (U.S.A.). Since the
strength of the instabilities of LCGT depends on the mirror curvature more
weakly than that of Advanced LIGO, the requirement of the mirror curvature
accuracy is easier to be achieved. The difference in the parametric
instabilities between LCGT and Advanced LIGO is because of the thermal noise
reduction methods (LCGT, cooling sapphire mirrors; Advanced LIGO, fused silica
mirrors with larger laser beams), which are the main strategies of the
projects. Elastic Q reduction by the barrel surface (0.2 mm thickness
TaO) coating is effective to suppress instabilities in the LCGT arm
cavity. Therefore, the cryogenic interferometer is a smart solution for the
parametric instabilities in addition to thermal noise and thermal lensing.Comment: 6 pages,3 figures. Amaldi7 proceedings, J. Phys.: Conf. Ser.
(accepted
- …