Activity Dependent Branching Ratios in Stocks, Solar X-ray Flux, and the Bak-Tang-Wiesenfeld Sandpile Model

We define an activity dependent branching ratio that allows comparison of different time series $X_{t}$. The branching ratio $b_x$ is defined as $b_x= E[\xi_x/x]$. The random variable $\xi_x$ is the value of the next signal given that the previous one is equal to $x$, so $\xi_x=\{X_{t+1}|X_t=x\}$. If $b_x>1$, the process is on average supercritical when the signal is equal to $x$, while if $b_x<1$, it is subcritical. For stock prices we find $b_x=1$ within statistical uncertainty, for all $x$, consistent with an ``efficient market hypothesis''. For stock volumes, solar X-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, $b_x$ is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power law behavior. For solar X-ray flux and the BTW model, there is a broad regime of activity where $b_x \simeq 1$, which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for $X_t$, and for $\xi_x$. For the BTW model the distribution of $\xi_x$ is Gaussian, for $x$ sufficiently larger than one, and its variance grows linearly with $x$. Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where $b_x$ is close to one disappears once bulk dissipation is introduced in the BTW model -- supporting our hypothesis that it is an indicator of criticality.Comment: 7 pages, 11 figure

Test of a Jastrow-type wavefunction for a trapped few-body system in one dimension

For a system with interacting quantum mechanical particles in a one-dimensional harmonic oscillator, a trial wavefunction with simple structure based on the solution of the corresponding two-particle system is suggested and tested numerically. With the inclusion of a scaling parameter for the distance between particles, at least for the very small systems tested here the ansatz gives a very good estimate of the ground state energy, with the error being of the order of ~1% of the gap to the first excited state

Signatures of Wigner Localization in Epitaxially Grown Nanowires

It was predicted by Wigner in 1934 that the electron gas will undergo a transition to a crystallized state when its density is very low. Whereas significant progress has been made towards the detection of electronic Wigner states, their clear and direct experimental verification still remains a challenge. Here we address signatures of Wigner molecule formation in the transport properties of InSb nanowire quantum dot systems, where a few electrons may form localized states depending on the size of the dot (i.e. the electron density). By a configuration interaction approach combined with an appropriate transport formalism, we are able to predict the transport properties of these systems, in excellent agreement with experimental data. We identify specific signatures of Wigner state formation, such as the strong suppression of the antiferromagnetic coupling, and are able to detect the onset of Wigner localization, both experimentally and theoretically, by studying different dot sizes.Comment: 4 pages, 4 figure

Decomposing the stock market intraday dynamics

The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the time period between November 1997 and September 1999, and makes use of both, the corresponding returns as well as volatility variations. One principal conclusion is that a bulk of the stock market dynamics is governed by the uncorrelated noise-like processes. There exists however a small number of components of coherent short term repeatable structures in fluctuations that may generate some memory effects seen in the standard autocorrelation function analysis. Laws that govern fluctuations associated with those various components are different, which indicates an extremely complex character of the financial fluctuations.Comment: 15 pages, 13 PostScript figure

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Scanning Tunneling Microscopy and Tunneling Luminescence of the Surface of GaN Films Grown by Vapor Phase Epitaxy

We report scanning tunneling microscopy (STM) images of surfaces of GaN films and the observation of luminescence from those films induced by highly spatially localized injection of electrons or holes using STM. This combination of scanning tunneling luminescence (STL) with STM for GaN surfaces and the ability to observe both morphology and luminescence in GaN is the first step to investigate possible correlations between surface morphology and optical properties.Comment: 12 pages, Revtex 3.0, submitted to Appl. Phys. Lett., three figures available from Jian Ma at [email protected]

Testing Consumer Rationality using Perfect Graphs and Oriented Discs

Given a consumer data-set, the axioms of revealed preference proffer a binary test for rational behaviour. A natural (non-binary) measure of the degree of rationality exhibited by the consumer is the minimum number of data points whose removal induces a rationalisable data-set.We study the computational complexity of the resultant consumer rationality problem in this paper. This problem is, in the worst case, equivalent (in terms of approximation) to the directed feedback vertex set problem. Our main result is to obtain an exact threshold on the number of commodities that separates easy cases and hard cases. Specifically, for two-commodity markets the consumer rationality problem is polynomial time solvable; we prove this via a reduction to the vertex cover problem on perfect graphs. For three-commodity markets, however, the problem is NP-complete; we prove thisusing a reduction from planar 3-SAT that is based upon oriented-disc drawings

Lineshape of the thermopower of quantum dots

Quantum dots are an important model system for thermoelectric phenomena, and may be used to enhance the thermal-to-electric energy conversion efficiency in functional materials. It is therefore important to obtain a detailed understanding of a quantum-dot's thermopower as a function of the Fermi energy. However, so far it has proven difficult to take effects of co-tunnelling into account in the interpretation of experimental data. Here we show that a single-electron tunnelling model, using knowledge of the dot's electrical conductance which in fact includes all-order co-tunneling effects, predicts the thermopower of quantum dots as a function of the relevant energy scales, in very good agreement with experiment.Comment: 10 pages, 5 figure

Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.Comment: 14 pages, 11 figures, 1 table, submitte