Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as $l \to \infty$ or as $m \to \infty$. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit $l \to \infty$ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as $m \to \infty$ with both $k$ and $l$ fixed. Here we show that the ensemble is not ergodic, and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency towards picket-fence type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization.Comment: Minor corrections; figure 5 slightly modified (30 pages, 6 figs

A review of size and geometrical factors influencing resonant frequencies in metamaterials

Although metamaterials and so-called left-handed media have originated from theoretical considerations, it is only by their practical fabrication and the measurement of their properties that they have gained credibility and can fulfil the potential of their predicted properties. In this review we consider some of the more generally applicable fabrication methods and changes in geometry as they have progressed, exhibiting resonant frequencies ranging from radio waves to the visible optical region

Feasibility study and design concept for an orbiting ice-penetrating radar sounder to characterize in three-dimensions the Europan ice mantle down to (and including) any ice/ocean interface

This report presents a radar sounding model based on the range of current working hypotheses for the nature of Europa's icy shell.Institute for Geophysic

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

We consider $m$ spinless Fermions in $l > m$ degenerate single-particle levels interacting via a $k$-body random interaction with Gaussian probability distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body random ensembles). We address the cases of orthogonal and unitary symmetry. We derive a novel eigenvalue expansion for the second moment of the Hilbert-space matrix elements of these ensembles. Using properties of the expansion and the supersymmetry technique, we show that for $2k > m$, the average spectrum has the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson type. Using a generalization of the binary correlation approximation, we show that for $k << m << l$, the spectral fluctuations are Poissonian. This is consistent with the case $k = 1$ which can be solved explicitly. We construct limiting ensembles which are either fully integrable or fully chaotic and show that the $k$-body random ensembles lie between these two extremes. Combining all these results we find that the spectral correlations for the embedded ensembles gradually change from Wigner-Dyson for $2k > m$ to Poissonian for $k << m << l$.Comment: 44 pages, 3 postscript figures, revised version including a new proof of one of our main claim

Genetic variation in the zebrafish

Although zebrafish was introduced as a laboratory model organism several decades ago and now serves as a primary model for developmental biology, there is only limited data on its genetic variation. An establishment of a dense polymorphism map becomes a requirement for effective linkage analysis and cloning approaches in zebrafish. By comparing ESTs to whole-genome shotgun data, we predicted >50,000 high-quality candidate SNPs covering the zebrafish genome with average resolution of 41 kbp. We experimentally validated ∼65% of a randomly sampled subset by genotyping 16 samples from seven commonly used zebrafish strains. The analysis reveals very high nucleotide diversity between zebrafish isolates. Even with the limited number of samples that we genotyped, zebrafish isolates revealed considerable interstrain variation, ranging from 7% (inbred) to 37% (wild-derived) of polymorphic sites being heterozygous. The increased proportion of polymorphic over monomorphic sites results in five times more frequent observation of a three allelic variant compared with human or mouse. Phylogenetic analysis shows that comparisons between even the least divergent strains used in our analysis may provide one informative marker approximately every 500 nucleotides. Furthermore, the number of haplotypes per locus is relatively large, reflecting independent establishment of the different lines from wild isolates. Finally, our results suggest the presence of prominent C-to-U and A-to-I RNA editing events in zebrafish. Overall, the levels and organization of genetic variation between and within commonly used zebrafish strains are markedly different from other laboratory model organisms, which may affect experimental design and interpretation

Vibrations and Berry Phases of Charged Buckminsterfullerene

A simple model of electron-vibron interactions in buckminsterfullerene ions is solved semiclassically. Electronic degeneracies of C$_{60}$$^{n-}$ induce dynamical Jahn-Teller distortions, which are unimodal for $n\!\ne\!3$ and bimodal for $n\!=\!3$. The quantization of motion along the Jahn-Teller manifold leads to a symmetric-top rotator Hamiltonian. I find Molecular Aharonov-Bohm effects where electronic Berry phases determine the vibrational spectra, zero point fluctuations, and electrons' pair binding energies. The latter are relevant to superconductivity in alkali-fullerenes.Comment: Latex 11 pages. IIT-00

Recoil correction to the ground state energy of hydrogenlike atoms

The recoil correction to the ground state energy of hydrogenlike atoms is calculated to all orders in \alpha Z in the range Z = 1-110. The nuclear size corrections to the recoil effect are partially taken into account. In the case of hydrogen, the relativistic recoil correction beyond the Salpeter contribution and the nonrelativistic nuclear size correction to the recoil effect, amounts to -7.2(2) kHz. The total recoil correction to the ground state energy in hydrogenlike uranium (^{238}U^{91+}) constitutes 0.46 eV.Comment: 16 pages, 1 figure (eps), Latex, submitted to Phys.Rev.

Gravitation, electromagnetism and cosmological constant in purely affine gravity

The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous ($\Lambda$CDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell-$\Lambda$ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell-$\Lambda$CDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio

Shake-up Processes in a Low-Density Two-Dimensional Electron Gas: Spin-Dependent Transitions to Higher Hole Landau Levels

A theory of shake-up processes in photoabsorption of an interacting low-density two-dimensional electron gas (2DEG) in strong magnetic fields is presented. In these processes, an incident photon creates an electron-hole pair and, because of Coulomb interactions, simultaneously excites one particle to higher Landau levels (LL's). In this work, the spectra of correlated charged spin-singlet and spin-triplet electron-hole states in the first hole LL and optical transitions to these states (i.e., shake-ups to the first hole LL) are studied. Our results indicate, in particular, the presence of optically-active three-particle quasi-discrete states in the exciton continuum that may give rise to surprisingly sharp Fano resonances in strong magnetic fields. The relation between shake-ups in photoabsorption of the 2DEG and in the 2D hole gas (2DHG), and shake-ups of isolated negative X^- and positive X^+ trions are discussed.Comment: 8 pages, 8 figures. References updated, one figure added (Fig. 6). Accepted in Phys. Rev.