Annals of physics

Understanding the correlation between magnetic properties and nanostructure involves collaborative efforts between chemists, physicists, and materials scientists to study both fundamental properties and potential applications. This article introduces a classification of nanostructure morphology according to the mechanism responsible for the magnetic properties. The fundamental magnetic properties of interest and the theoretical frameworks developed to model these properties are summarized. Common chemical and physical techniques for the fabrication of magnetic nanostructures are surveyed, followed by some examples of recent investigations of magnetic systems with structure on the nanometer scale. The article concludes with a brief discussion of some promising experimental techniques in synthesis and measurements.

Magnetic Properties of Nanostructured Materials

The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

We review some electron transport experiments on few-electron, vertical quantum dot devices. The measurement of current versus source–drain voltage and gate voltage is used as a spectroscopic tool to investigate the energy characteristics of interacting electrons confined to a small region in a semiconducting material. Three energy scales are distinguished: the single-particle states, which are discrete due to the confinement involved; the direct Coulomb interaction between electron charges on the dot; and the exchange interaction between electrons with parallel spins. To disentangle these energies, a magnetic field is used to reorganize the occupation of electrons over the single-particle states and to induce changes in the spin states. We discuss the interactions between small numbers of electrons (between 1 and 20) using the simplest possible models. Nevertheless, these models consistently describe a large set of experiments. Some of the observations resemble similar phenomena in atomic physics, such as shell structure and periodic table characteristics, Hund’s rule, and spin singlet and triplet states. The experimental control, however, is much larger than for atoms: with one device all the artificial elements can be studied by adding electrons to the quantum dot when changing the gate voltage.

https://iopscience.iop.org/article/10.1088/0034-4885/64/6/201/pdf

Few-electron quantum dots

TOPICAL REVIEW: Nanomagnetics

We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that the mean realized variance of returns is a linear function of the number of days over which the returns are calculated. The slope is determined by the mean value of the variance (squared volatility) in the mean-reverting stochastic volatility models, such as Heston and multiplicative, independent of stochasticity. The distribution function of stock returns, which rescales with the increase of the number of days of return, is obtained from the steady-state variance distribution function using the product distribution with the normal distribution.

Distributions of historic market data – stock returns

We analyze correlations between squared volatility indices, VIX and VXO, and realized variances -- the known one, for the current month, and the predicted one, for the following month. We show that the ratio of the two is best fitted by a Beta Prime distribution, whose shape parameters depend strongly on which of the two months is used.

/pdf/implied-and-realized-volatility-a-study-of-the-ratio-2byooceytk.pdf

Implied and Realized Volatility: A Study of the Ratio Distribution

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger scales. We apply our results to a rectangle with incommensurate sides and show that they are in excellent agreement with the limiting cases established in the semiclassical theory of level rigidity.

Level Correlations in Integrable Systems

This article overviews several contemporary models that assume power law scaling is a plausible description of the skewed right tails that are typical of response time distributions. The properties and markers of these distribution functions have implications for cognitive and neurophysiological dynamics. The power law hypothesis suggests studies should collect larger samples, and that analyses may combine individual subjects' data into a single set for a distribution-function contrasts. Techniques for contrasting response time measurements are illustrated on data from a previously published study comparing the performance of children diagnosed with dyslexia and a group of age-matched controls in flanker, color naming, word naming, and arithmetic performance.

Modeling Response Time with Power Law Distributions.

On montre que la fonction de distribution du logarithme de la resistance pour la conduction par sauts a distance variable dans des filaments finis a une dimension, peut etre ajustee soit par une distribution gaussienne inverse, soit par une distribution log-normal. On explique egalement les fortes fluctuations, de filament a filament, de la variance des logarithmes de la resistance en termes de statistiques d'echantillonnage

R. A. Serota

Papers

Distributions of historic market data – stock returns

Implied and Realized Volatility: A Study of the Ratio Distribution

Level Correlations in Integrable Systems

Modeling Response Time with Power Law Distributions.

Resistance distribution function for fluctuating variable-range hopping conduction.