Spin-dependent electron dynamics and recombination in GaAs(1-x)N(x) alloys at room temperature

We report on both experimental and theoretical study of conduction-electron spin polarization dynamics achieved by pulsed optical pumping at room temperature in GaAs(1-x)N(x) alloys with a small nitrogen content (x = 2.1, 2.7, 3.4%). It is found that the photoluminescence circular polarization determined by the mean spin of free electrons reaches 40-45% and this giant value persists within 2 ns. Simultaneously, the total free-electron spin decays rapidly with the characteristic time ~150 ps. The results are explained by spin-dependent capture of free conduction electrons on deep paramagnetic centers resulting in dynamical polarization of bound electrons. We have developed a nonlinear theory of spin dynamics in the coupled system of spin-polarized free and localized carriers which describes the experimental dependencies, in particular, electron spin quantum beats observed in a transverse magnetic field.Comment: 5 pages, 4 figures, Submitted to JETP Letter

Rough paths in idealized financial markets

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is positive and right-continuous. The qualification "typical" means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.Comment: 21 pages, this version adds (in Appendix C) a reference to new results in the foundations of game-theoretic probability based on Hardin and Taylor's work on hat puzzle

Influence of Co3+^{3+} spin-state on optical properties of LaCoO3_3 and HoCoO3_3

Optical properties of the isoelectronic compounds LaCoO$_3$ and HoCoO$_3$ has been experimentally and theoretically investigated. We've measured the real $\epsilon_1(\omega)$ and imaginary $\epsilon_2(\omega)$ parts of the dielectric function, reflectance $R(\omega)$ and optical conductivity at room temperature. The shift of the most pronounced spectral features to the high energy region on 0.3 eV associated with larger distortions due to the smaller rare earth ionic radii in HoCoO$_3$ in comparison with LaCoO$_3$ was observed. Also there was found an enhancement of absorption intensity in the range 1.3-2.3 eV in all kinds of spectra in HoCoO$_3$, which can be attributed basing on the results of LDA+U calculations to the different spin-states of Co$^{3+}$ ion in these compounds. The shift of the onset of the absorption from less than 0.1 eV in LaCoO$_3$ to 0.7 eV in HoCoO$_3$ and an absorption intensity enhancement in a narrow spectral range 1.2-2.6 eV in HoCoO$_3$ are clearly seen from the calculated convolution of partial densities of states obtained in the LDA+U approach. Such changes are assumed to be induced by the different Co$^{3+}$ spin-state in these compounds at room temperature.Comment: 10 pages, 3 figure

The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent ``Meissner'' phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert $W$-functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.Comment: 22 pages, 23 figures. Accepted for publication on Phys. Rev.

The filtering equations revisited

The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the change-of--probability-measure method originally introduced by Kallianpur and Striebel to derive the filtering equations and the Bayes-like formula that bears their names. More recent work, however, has generally preferred other methods. In this paper, we reconsider the change-of-measure approach to the derivation of the filtering equations and show that many of the technical conditions present in previous work can be relaxed. The filtering equations are established for general Markov signal processes that can be described by a martingale-problem formulation. Two specific applications are treated

How to quantify deterministic and random influences on the statistics of the foreign exchange market

It is shown that prize changes of the US dollar - German Mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore we show that from the empirical data the Kramers-Moyal coefficients can be estimated. Finally, we present an explicite Fokker-Planck equation which models very precisely the empirical probabilitiy distributions.Comment: 3 figure

Magnetic excitations in the geometric frustrated multiferroic CuCrO2_2

In this paper detailed neutron scattering measurements of the magnetic excitation spectrum of CuCrO$_2$ in the ordered state below $T_{\rm{N1}}=24.2$ K are presented. The spectra are analyzed using a model Hamiltonian which includes intralayer-exchange up to the next-next-nearest neighbor and interlayer-exchange. We obtain a definite parameter set and show that exchange interaction terms beyond the next-nearest neighbor are important to describe the inelastic excitation spectrum. The magnetic ground state structure generated with our parameter set is in agreement with the structure proposed for CuCrO$_2$ from the results of single crystal diffraction experiments previously published. We argue that the role of the interlayer exchange is crucial to understand the incommensurability of the magnetic structure as well as the spin-charge coupling mechanism

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon