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, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, 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

Thermospheric winds and temperatures above Mawson, Antarctica, observed with an all-sky imaging, Fabry-Perot spectrometer

A new all-sky imaging Fabry-Perot spectrometer has been installed at Mawson station (67°36' S, 62°52' E), Antarctica. This instrument is capable of recording independent spectra from many tens of locations across the sky simultaneously. Useful operation began in March 2007, with spectra recorded on a total of 186 nights. Initial analysis has focused on the large-scale daily and average behavior of winds and temperatures derived from observations of the 630.0 nm airglow line of atomic oxygen, originating from a broad layer centered around 240 km altitude, in the ionospheric F-region. <br><br> The 1993 Horizontal Wind Model (HWM93), NRLMSISE-00 atmospheric model, and the Coupled Thermosphere/Ionosphere Plasmasphere (CTIP) model were used for comparison. During the geomagnetically quiet period studied, observed winds and temperatures were generally well modelled, although temperatures were consistently higher than NRLMSISE-00 predicted, by up to 100 K. CTIP temperatures better matched our data, particularly later in the night, but predicted zonal winds which were offset from those observed by 70–180 ms<sup>−1</sup> westward. During periods of increased activity both winds and temperatures showed much greater variability over time-scales of less than an hour. For the active night presented here, a period of 45 min saw wind speeds decrease by around 180 ms<sup>−1</sup>, and temperatures increase by approximately 100 K. Active-period winds were poorly modelled by HWM93 and CTIP, although observed median temperatures were in better agreement with NRLMSISE-00 during such periods. <br><br> Average behavior was found to be generally consistent with previous studies of thermospheric winds above Mawson. The collected data set was representative of quiet geomagnetic and solar conditions. Geographic eastward winds in the afternoon/evening generally continued until around local midnight, when winds turned equatorward. Geographic meridional and zonal winds in the afternoon were approximately 50 ms<sup>−1</sup> weaker than expected from HWM93, as was the transition to equatorward flow around midnight. There was also a negligible geographic zonal component to the post-midnight wind where HWM93 predicted strong westward flow. Average temperatures between 19:00 and 04:00 local solar time were around 60 K higher than predicted by NRLMSISE-00

Phonon emission and arrival times of electrons from a single-electron source

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical-phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy

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 $^{40}$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

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

Oscillations in a maturation model of blood cell production.

We present a mathematical model of blood cell production which describes both the development of cells through the cell cycle, and the maturation of these cells as they differentiate to form the various mature blood cell types. The model differs from earlier similar ones by considering primitive stem cells as a separate population from the differentiating cells, and this formulation removes an apparent inconsistency in these earlier models. Three different controls are included in the model: proliferative control of stem cells, proliferative control of differentiating cells, and peripheral control of stem cell committal rate. It is shown that an increase in sensitivity of these controls can cause oscillations to occur through their interaction with time delays associated with proliferation and differentiation, respectively. We show that the characters of these oscillations are quite distinct and suggest that the model may explain an apparent superposition of fast and slow oscillations which can occur in cyclical neutropenia. © 2006 Society for Industrial and Applied Mathematics

Impact of localization on Dyson's circular ensemble

A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distribution towards a Poisson distribution with increasing localization.Comment: To be published in J. Phys.

Lagrangian versus Quantization

We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description.Comment: 8 pages, no figures; small corrections, references adde

Distribution of the Riemann zeros represented by the Fermi gas

The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.Comment: 7 page

Spectra of PT-symmetric Hamiltonians on Tobogganic Contours

A non-standard generalisation of the Bender potentials x^2(\ii x^\ve) is suggested. The spectra are obtained numerically and some of their particular properties are discussed.Comment: 9 page