5,093 research outputs found
Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach
We determine the asymptotic level spacing distribution for the Laguerre
Ensemble in a single scaled interval, , containing no levels,
E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the
Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by
both Edelman and Forrester, while for , the leading terms of
, found by Tracy and Widom, are reproduced without the use of the
Bessel kernel and the associated Painlev\'e transcendent. In the same
approximation, the next leading term, due to a ``finite temperature''
perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe
Action research in physical education: focusing beyond myself through cooperative learning
This paper reports on the pedagogical changes that I experienced as a teacher engaged in an action research project in which I designed and implemented an indirect, developmentally appropriate and childâcentred approach to my teaching. There have been repeated calls to expunge â or at least rationalise â the use of traditional, teacherâled practice in physical education. Yet despite the advocacy of many leading academics there is little evidence that such a change of approach is occurring. In my role as teacherâasâresearcher I sought to implement a new pedagogical approach, in the form of cooperative learning, and bring about a positive change in the form of enhanced pupil learning. Data collection included a reflective journal, postâteaching reflective analysis, pupil questionnaires, student interviews, document analysis, and nonâparticipant observations. The research team analysed the data using inductive analysis and constant comparison. Six themes emerged from the data: teaching and learning, reflections on cooperation, performance, time, teacher change, and social interaction. The paper argues that cooperative learning allowed me to place social and academic learning goals on an even footing, which in turn placed a focus on pupilsâ understanding and improvement of skills in athletics alongside their interpersonal development
Hot electron energy relaxation in lattice-matched InAlN/AlN/GaN heterostructures: The sum rules for electron-phonon interactions and hot-phonon effect
Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation and energy relaxation time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: with no hot phonons or screening the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for energy relaxation time with the two phonon models (within a 5% of deviation). However the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the power dissipation values obtained from the DC and 3DP models are in general different in the pure phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Registerâs scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the energy relaxation: their contribution is enhanced in the pure emission process but is dramatically reduced after including the HPE. Our calculation with both phonon models has obtained a great fall in energy relaxation time at low electron temperatures (Te < 750 K) and slow decrease at the high temperatures with the use of decreasing phonon lifetime with Te. The calculated temperature dependence of the relaxation time and the high-temperature relaxation time âŒ0.09 ps are in good agreement with experimental results
Momentum relaxation due to polar optical phonons in AlGaN/GaN heterostructures
Using the dielectric continuum (DC) model, momentum relaxation rates are calculated for electrons confined in quasi-two-dimensional (quasi-2D) channels of AlGaN/GaN heterostructures. Particular attention is paid to the effects of half-space and interface modes on the momentum relaxation. The total momentum relaxation rates are compared with those evaluated by the three-dimensional phonon (3DP) model, and also with the Callen results for bulk GaN. In heterostructures with a wide channel (effective channel width >100 Ă
), the DC and 3DP models yield very close momentum relaxation rates. Only for narrow-channel heterostructures do interface phonons become important in momentum relaxation processes, and an abrupt threshold occurs for emission of interface as well as half-space phonons. For a 30-Ă
GaN channel, for instance, the 3DP model is found to underestimate rates just below the bulk phonon energy by 70% and overestimate rates just above the bulk phonon energy by 40% compared to the DC model. Owing to the rapid decrease in the electron-phonon interaction with the phonon wave vector, negative momentum relaxation rates are predicted for interface phonon absorption in usual GaN channels. The total rates remain positive due to the dominant half-space phonon scattering. The quasi-2D rates can have substantially higher peak values than the three-dimensional rates near the phonon emission threshold. Analytical expressions for momentum relaxation rates are obtained in the extreme quantum limits (i.e., the threshold emission and the near subband-bottom absorption). All the results are well explained in terms of electron and phonon densities of states
Perturbations and Stability of Rotating Stars. 1: Completeness of Normal Modes
It is noted that linear adiabatic perturbations of a differentially rotating, axisymmetric, perfect fluid stellar model have normal modes described by a quadratic problem. The paper studies the problem and the associated time evolution equation. It is shown that in the Hilbert space H-prime, whose norm is square-integration weighted by A, the operators (A to the -1st power)(B) and (A to the -1st power)(C) are anti-selfadjoint and selfadjoint, respectively, when restricted to vectors belonging to a particular but arbitrary axial harmonic. Bounds are found on the spectrum of normal modes and it is shown that any initial data in the domain of C leads to a solution whose growth rate is limited by the spectrum and which can be expressed in a certain weak sense as a linear superposition of the normal modes
Wigner-Dyson Statistics from the Replica Method
We compute the correlation functions of the eigenvalues in the Gaussian
unitary ensemble using the fermionic replica method. We show that non--trivial
saddle points, which break replica symmetry, must be included in the
calculation in order to reproduce correctly the exact results for the
correlation functions at large distance.Comment: 13 pages, added reference
Kepler and the Kuiper Belt
The proposed field-of-view of the Kepler mission is at an ecliptic latitude
of ~55 degrees, where the surface density of scattered Kuiper Belt Objects
(KBOs) is a few percent that in the ecliptic plane. The rate of occultations of
Kepler target stars by scattered KBOs with radii r>10km is ~10^-6 to 10^-4 per
star per year, where the uncertainty reflects the current ignorance of the
thickness of the scattered KBO disk and the faint-end slope of their magnitude
distribution. These occultation events will last only ~0.1% of the planned
t_exp=15 minute integration time, and thus will appear as single data points
that deviate by tiny amounts. However, given the target photometric accuracy of
Kepler, these deviations will nevertheless be highly significant, with typical
signal-to-noise ratios of ~10. I estimate that 1-20 of the 10^5 main-sequence
stars in Kepler's field-of-view will exhibit detectable occultations during its
four-year mission. For unresolved events, the signal-to-noise of individual
occultations scales as t_exp^{-1/2}, and the minimum detectable radius could be
decreased by an order of magnitude to ~1 km by searching the individual
3-second readouts for occultations. I propose a number of methods by which
occultation events may be differentiated from systematic effects. Kepler should
measure or significantly constrain the frequency of highly-inclined, ~10
km-sized KBOs.Comment: 5 pages, 1 figure. No changes. Accepted to ApJ, to appear in the
August 1, 2004 issue (v610
Fluctuation properties of strength functions associated with giant resonances
We performed fluctuation analysis by means of the local scaling dimension for
the strength function of the isoscalar (IS) and the isovector (IV) giant
quadrupole resonances (GQR) in Ca, where the strength functions are
obtained by the shell model calculation within up to the 2p2h configurations.
It is found that at small energy scale, fluctuation of the strength function
almost obeys the Gaussian orthogonal ensemble (GOE) random matrix theory limit.
On the other hand, we found a deviation from the GOE limit at the intermediate
energy scale about 1.7MeV for the IS and at 0.9MeV for the IV. The results
imply that different types of fluctuations coexist at different energy scales.
Detailed analysis strongly suggests that GOE fluctuation at small energy scale
is due to the complicated nature of 2p2h states and that fluctuation at the
intermediate energy scale is associated with the spreading width of the
Tamm-Dancoff 1p1h states.Comment: 14 pages including 13figure
Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
Hamiltonian light-front field theory can be used to solve for hadron states
in QCD. To this end, a method has been developed for systematic renormalization
of Hamiltonian light-front field theories, with the hope of applying the method
to QCD. It assumed massless particles, so its immediate application to QCD is
limited to gluon states or states where quark masses can be neglected. This
paper builds on the previous work by including particle masses
non-perturbatively, which is necessary for a full treatment of QCD. We show
that several subtle new issues are encountered when including masses
non-perturbatively. The method with masses is algebraically and conceptually
more difficult; however, we focus on how the methods differ. We demonstrate the
method using massive phi^3 theory in 5+1 dimensions, which has important
similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra
disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final
published versio
Final state interaction phase in B decays
From an estimate of the meson-meson inelastic scatterin at 5 GeV it is
concluded that a typical strong phase in B decays to two mesons is of order of
20 degrees. For a particular final state an estimate of the phase depends on
whether that state is more or less probable as a final state compared to those
states to which it is connected by the strong interaction S matrix.Comment: 10 pages in RevTex with 1 eps figur
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