Comparative Analysis of Non-thermal Emissions and Study of Electron Transport in a Solar Flare

We study the non-thermal emissions in a solar flare occurring on 2003 May 29 by using RHESSI hard X-ray (HXR) and Nobeyama microwave observations. This flare shows several typical behaviors of the HXR and microwave emissions: time delay of microwave peaks relative to HXR peaks, loop-top microwave and footpoint HXR sources, and a harder electron energy distribution inferred from the microwave spectrum than from the HXR spectrum. In addition, we found that the time profile of the spectral index of the higher-energy (\gsim 100 keV) HXRs is similar to that of the microwaves, and is delayed from that of the lower-energy (\lsim 100 keV) HXRs. We interpret these observations in terms of an electron transport model called {\TPP}. We numerically solved the spatially-homogeneous {\FP} equation to determine electron evolution in energy and pitch-angle space. By comparing the behaviors of the HXR and microwave emissions predicted by the model with the observations, we discuss the pitch-angle distribution of the electrons injected into the flare site. We found that the observed spectral variations can qualitatively be explained if the injected electrons have a pitch-angle distribution concentrated perpendicular to the magnetic field lines rather than isotropic distribution.Comment: 32 pages, 12 figures, accepted for publication in The Astronomical Journa

Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details

In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of Quantum Mechanics. This epoch-making paper is generally regarded as being difficult to follow, perhaps partly because Heisenberg provided few clues as to how he arrived at the results which he reported. Here we give details of calculations of the type which, we suggest, Heisenberg may have performed. We take as a specific example one of the anharmonic oscillator problems considered by Heisenberg, and use our reconstruction of his approach to solve it up to second order in perturbation theory. We emphasize that the results are precisely those obtained in standard quantum mechanics, and suggest that some discussion of the approach - based on the direct computation of transition amplitudes - could usefully be included in undergraduate courses in quantum mechanics.Comment: 24 pages, no figures, Latex, submitted to Am. J. Phy

Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.Comment: 9 pages, Latex, 6 PostScript figures in uuencoded compressed tar file are appende

Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published

Energy-level statistics at the metal-insulator transition in anisotropic systems

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e. weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition using energy-level statistics. The values of the critical disorder $W_c$ are consistent with results of previous studies, including the transfer-matrix method and multifractal analysis of the wave functions. $W_c$ decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent $\nu=1.45\pm0.2$. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. The critical level statistics which is independent of the system size at the transition changes from its isotropic form towards the Poisson statistics with increasing anisotropy.Comment: 22 pages, including 8 figures, revtex few typos corrected, added journal referenc

Gold as an inflation hedge?

This paper attempts to reconcile an apparent contradiction between short-run and long-run movements in the price of gold. The theoretical model suggests a set of conditions under which the price of gold rises over time at the general rate of inflation and hence be an effective hedge against inflation. The model also demonstrates that short-run changes in the gold lease rate, the real interest rate, convenience yield, default risk, the covariance of gold returns with other assets and the dollar/world exchange rate can disturb this equilibrium relationship and generate short-run price volatility. Using monthly gold price data (1976-1999), and cointegration regression techniques, an empirical analysis confirms the central hypotheses of the theoretical model

Localization Transition in Multilayered Disordered Systems

The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation expansion, we estimate the mean free paths in the main directions and verify by scaling of the conductance that the states remain extended for any finite $p$, despite the interlayer disorder. In the presence of additional diagonal disorder ($W > 0$) we obtain an Anderson transition with critical disorder $W_c$ and localization length exponent $\nu$ independently of the direction. The critical conductance distribution $P_{c}(g)$ varies, however, for the parallel and the perpendicular directions. The results are discussed in connection to disordered anisotropic materials.Comment: 10 pages, Revtex file, 8 postscript files, minor change

Kondo effect in two-dimensional disordered electron systems

We investigate the Kondo effect in two-dimensional disordered electron systems using a finite-temperature quantum Monte Carlo method. Depending on the position of a magnetic impurity, the local moment is screened or unscreened by the spin of the conduction electron. On the basis of the results, we show that the distribution of the Kondo temperature becomes wide and the weight at $T_K=0$ becomes large as randomness increases. The average susceptibility shows a weak power-law or logarithmic divergence at low temperature, indicating a non-Fermi-liquid behavior.Comment: 2 pages, 2 figures, to be published in supplement of J. Phys. Soc. Japan, Proceedings of Localisation 2002, (Tokyo, Japan, 2002