Covers of Point-Hyperplane Graphs

We construct a cover of the non-incident point-hyperplane graph of projective dimension 3 for fields of characteristic 2. If the cardinality of the field is larger than 2, we obtain an elementary construction of the non-split extension of SL_4 (F) by F^6.Comment: 10 pages, 3 figure

Parametric Evolution for a Deformed Cavity

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.Comment: 13 pages, 8 figures, improved introduction, to be published in Phys. Rev.

Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|\omega|<\omega_{cl}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $\Omega<\omega_{cl}$, and a relatively small response otherwise, independently of the driving amplitude $A$. We define a non-perturbative regime in the $(\Omega,A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>A_{prt}$, where $A_{prt}\propto\hbar$, the system may have a relatively strong response for $\Omega>\omega_{cl}$, and the shape of the response function becomes $A$ dependent.Comment: 4 pages, 2 figures, revised version with much better introductio

Optical, gravitational, and kinesthetic determinants of judged eye level

Subjects judged eye level, defined in three distinct ways relative to three distinct reference planes: a gravitational horizontal, giving the gravitationally referenced eye level (GREL); a visible surface, giving the surface-referenced eye level (SREL); and a plane fixed with respect to the head, giving the head-referenced eye level (HREL). The information available for these judgements was varied by having the subjects view an illuminated target that could be placed in a box which: (1) was pitched at various angles, (2) was illuminated or kept in darkness, (3) was moved to different positions along the subject's head-to-foot body axis, and (4) was viewed with the subjects upright or reclining. The results showed: (1) judgements of GREL made in the dark were 2.5 deg lower than in the light, with a significantly greater variability; (2) judged GREL was shifted approximately half of the way toward SREL when these two eye levels did not coincide; (3) judged SREL was shifted about 12 percent of the way toward HREL when these two eye levels did not coincide, (4) judged HREL was shifted about half way toward SREL when these two eye level did not coincide and when the subject was upright (when the subject was reclining, HREL was shifted approx. 90 percent toward SREL); (5) the variability of the judged HREL in the dark was nearly twice as great with the subject reclining than with the subject upright. These results indicate that gravity is an important source of information for judgement of eye level. In the absence of information concerning the direction of gravity, the ability to judge HREL is extremely poor. A visible environment does not seem to afford precise information as to judgements of direction, but it probably does afford significant information as to the stability of these judgements

Anomalous magnetic moment of an electron near a dispersive surface

Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a nondispersive dielectric and an undamped plasma, but the electron is described by the Dirac equation without matter-field quantization. Perturbation theory in the Dirac equation leads to a general formula for the magnetic-moment shift in terms of integrals over products of electromagnetic mode functions. In each of the models investigated, contour integration techniques over a complex wave vector can be used to derive a general formula featuring just integrals over transverse electric and transverse magnetic reflection coefficients of the surface. Analysis of the magnetic-moment shift for several classes of materials yields markedly different results from the previously considered simplistic “perfect-reflector” model, due to the inclusion of physically important features of the electromagnetic response of the surface such as evanescent field modes and dispersion in the material. For a general dispersive dielectric surface, the magnetic-moment shift of a nearby electron can exceed the previous prediction of the perfect-reflector model by several orders of magnitude

Enhancing efficiency of single, large-aperture antennas

Numerical analysis method provides means of describing energy distribution in focal plane of parabolic surface in terms of phase and wavelength. Two approaches for enhancing antenna efficiency include single, large reflector focused to feeding element, and array of smaller apertures whose individual outputs are summed

Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is found that a dimensionless velocity $v_{PR}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence (QCC). A perturbative regime and a non-perturbative semiclassical regime are distinguished.Comment: 4 pages, clear presentation of the main poin

Optical Dielectric Functions of III-V Semiconductors in Wurtzite Phase

Optical properties of semiconductors can exhibit strong polarization dependence due to crystalline anisotropy. A number of recent experiments have shown that the photoluminescence intensity in free standing nanowires is polarization dependent. One contribution to this effect is the anisotropy of the dielectric function due to the fact that most nanowires crystalize in the wurtzite form. While little is known experimentally about the band structures wurtzite phase III-V semiconductors, we have previously predicted the bulk band structure of nine III-V semiconductors in wurtzite phase.Here, we predict the frequency dependent dielectric functions for nine non-Nitride wurtzite phase III-V semiconductors (AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb). Their complex dielectric functions are calculated in the dipole approximation by evaluating the momentum matrix elements on a dense grid of special k-points using empirical pseudopotential wave functions. Corrections to the momentum matrix elements accounting for the missing core states are made using a scaling factor which is determined by using the optical sum rules on the calculated dielectric functions for the zincblende polytypes. The dielectric function is calculated for polarizations perpendicular and parallel to the c-axis of the crystal

Decays in Quantum Hierarchical Models

We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudo continuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudo continuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random several cases are identified. For a pseudo continuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudo continuum space. They last for a long time compared to the non-random case