Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.Comment: 4 pages, Plain Tex, no figure

Decoherence processes in a current biased dc SQUID

A current bias dc SQUID behaves as an anharmonic quantum oscillator controlled by a bias current and an applied magnetic flux. We consider here its two level limit consisting of the two lower energy states | 0 \right> and | 1 \right>. We have measured energy relaxation times and microwave absorption for different bias currents and fluxes in the low microwave power limit. Decoherence times are extracted. The low frequency flux and current noise have been measured independently by analyzing the probability of current switching from the superconducting to the finite voltage state, as a function of applied flux. The high frequency part of the current noise is derived from the electromagnetic environment of the circuit. The decoherence of this quantum circuit can be fully accounted by these current and flux noise sources.Comment: 4 pages, 4 figure

Galilean Lee Model of the Delta Function Potential

The scattering cross section associated with a two dimensional delta function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an appropriate Galilean covariant theory. The Lee model with a standard Yukawa interaction is shown to provide such a realization. The usual results for delta function scattering are then obtained in the case that a stable particle exists in the scattering channel provided that a certain limit is taken in the relevant parameter space. In the more general case in which no such limit is taken finite corrections to the cross section are obtained which (unlike the pure delta function case) depend on the coupling constant of the model.Comment: 7 pages, latex, no figure

Sub-ballistic behavior in quantum systems with L\'evy noise

We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a L\'evy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.Comment: 4 pages, 4 figure

Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

A theory of non-local linear drift wave transport

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.Comment: 22 pages, 2 figures. Manuscript submitted to Physics of Plasma

From laser cooling to aging: a unified Levy flight description

Intriguing phenomena such as subrecoil laser cooling of atoms, or aging phenomenon in glasses, have in common that the systems considered do not reach a steady-state during the experiments, although the experimental time scales are very large compared to the microscopic ones. We revisit some standard models describing these phenomena, and reformulate them in a unified framework in terms of lifetimes of the microscopic states of the system. A universal dynamical mechanism emerges, leading to a generic time-dependent distribution of lifetimes, independently of the physical situation considered.Comment: 8 pages, 2 figures; accepted for publication in American Journal of Physic

Analysis of aggregated tick returns: evidence for anomalous diffusion

In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time interval is important, it cannot alone explain the heavy tailed distribution of stock price changes. For this reason, we analyze intervals with a fixed number of trades in order to eliminate the influence of the trading frequency and investigate the relevance of other factors for the aggregate return. We show that in tick time the price follows a discrete diffusion process with a variable step width while the difference between the number of steps in positive and negative direction in an interval is Gaussian distributed. The step width is given by the return due to a single trade and is long-term correlated in tick time. Hence, its mean value can well characterize an interval of many trades and turns out to be an important determinant for large aggregate returns. We also present a statistical model reproducing the cumulative distribution of aggregate returns. For an accurate agreement with the empirical distribution, we also take into account asymmetries of the step widths in different directions together with crosscorrelations between these asymmetries and the mean step width as well as the signs of the steps.Comment: 9 pages, 10 figures, typos correcte

The Cooper Pair Pump as a Quantized Current Source

A new charge quantization in a phase-polarized Cooper Pair Pump (CPP) is proposed, based on the topological properties of its Hamiltonian ground state over a three-dimensional parameter space $\mathbb{P}$. The charge is quantized using a set of path in $\mathbb{P}$ covering the surface of a torus, and is a multiple of the integer Chern index $c_1$ of this surface. This quantization is asymptotic but the pumped charge converges rapidly to the quantized value with the increase in the path frequency. The topological nature of the current makes this CPP implementation an excellent candidate for a metrological current standard.Comment: 4 PRL page