Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions

While there are well established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power $\alpha$, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing $\alpha$. At $\alpha_c$ the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many body localization transition in disordered antiferromagnetic spin chains with long range interactions.Comment: 6 pages, 4 figures, references adde

Search for Second and Third Generation Leptoquarks at CDF

We report the results of a search for second and third generation leptoquarks using 88 ${pb}^{-1}$ of data recorded by the Collider Detector at Fermilab. Color triplet technipions, which play the role of scalar leptoquarks, are investigated due to their potential production in decays of strongly coupled color octet technirhos. Events with a signature of two heavy flavor jets and missing energy may indicate the decay of a second (third) generation leptoquark to a charm (bottom) quark and a neutrino. As the data is found to be consistent with Standard Model expectations, mass limits are determined.Comment: Talk given at DPF2000, Columbus (OH), 9-12 Aug 2000. 3 pages, 4 figures. Submitted to Int.J.Mod.Phys.

New nonlinear structures in a degenerate one-dimensional electron gas

The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both analytical and numerical results demonstrate the formation of stable, breather-like modes, provided certain conditions are meet. For large amplitude of the initial density perturbation, a catastrophic collapse of the plasma density is predicted, even in the presence of the quantum statistical pressure and quantum diffraction dispersive effects. The results are useful for the understanding of the properties of general nonlinear structures in dense plasmas

Dynamics of weakly coupled random antiferromagnetic quantum spin chains

We study the low-energy collective excitations and dynamical response functions of weakly coupled random antiferromagnetic spin-1/2 chains. The interchain coupling leads to Neel order at low temperatures. We use the real-space renormalization group technique to tackle the intrachain couplings and treat the interchain couplings within the Random Phase Approximation (RPA). We show that the system supports collective spin wave excitations, and calculate the spin wave velocity and spectra weight within RPA. Comparisons will be made with inelastic neutron scattering experiments quasi-one-dimensional disordered spin systems such as doped CuGeO$_3$Comment: 4 page

Comment on "A note on the construction of the Ermakov-Lewis invariant"

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new

Mixed normal conditional heteroskedasticity

Both unconditional mixed-normal distributions and GARCH models with fat-tailed conditional distributions have been employed for modeling financial return data. We consider a mixed-normal distribution coupled with a GARCH-type structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. An empirical application to NASDAQ-index data indicates the appropriateness of the model class and illustrates that the approach can generate a plausible disaggregation of the conditional variance process, in which the components' volatility dynamics have a clearly distinct behavior that is, for example, compatible with the well-known leverage effect. Klassifikation: C22, C51, G1

Asymmetric multivariate normal mixture GARCH

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out–of–sample Value–at–Risk measures

Multivariate normal mixture GARCH

We present a multivariate generalization of the mixed normal GARCH model proposed in Haas, Mittnik, and Paolella (2004a). Issues of parametrization and estimation are discussed. We derive conditions for covariance stationarity and the existence of the fourth moment, and provide expressions for the dynamic correlation structure of the process. These results are also applicable to the single-component multivariate GARCH(p, q) model and simplify the results existing in the literature. In an application to stock returns, we show that the disaggregation of the conditional (co)variance process generated by our model provides substantial intuition, and we highlight a number of findings with potential significance for portfolio selection and further financial applications, such as regime-dependent correlation structures and leverage effects. Klassifikation: C32, C51, G10, G11Die vorliegende Arbeit ist einer multivariaten Verallgemeinerung des sog. Normal Mixture GARCH Modells gewidmet, dessen univariate Variante von Haas, Mittnik und Paolella (2004a, siehe auch CFS Working Paper 2002/10) vorgeschlagen wurde. Dieses Modell unterscheidet sich von traditionellen GARCH-Ansätzen insbesondere dadurch, dass es eine Abhängigkeit der Risikoentwicklung von - typischerweise unbeobachtbaren - Marktzuständen explizit in Rechnung stellt. Dies wird durch die Beobachtung motiviert, dass das weit verbreitete GARCH Modell in seiner Standardvariante auch dann keine adäquate Beschreibung der Risikodynamik leistet, wenn die Normalverteilung durch flexiblere bedingte Verteilungen ersetzt wird. Zustandsabhängige Volatilitätsprozesse können etwa durch die variierende Dominanz heterogener Marktteilnehmer oder durch wechselnde Marktstimmungen ökonomisch zu erklären sein. Anwendungen des Normal Mixture GARCH Modells auf zahlreiche Aktien- und Wechselkurszeitreihen (siehe z.B. Alexander und Lazar, 2004, 2005; und Haas, Mittnik und Paolella, 2004a,b) haben gezeigt, dass es sich zur Modellierung und Prognose des Volatilitätsprozesses der Renditen solcher Aktiva hervorragend eignet. Indes beschränken sich diese Analysen bisher auf die Untersuchung univariater Zeitreihen. Zahlreiche Probleme der Finanzwirtschaft erfordern jedoch zwingend eine multivariate Modellierung, mithin also eine Beschreibung der Abhängigkeitsstruktur zwischen den Renditen verschiedener Wertpapiere. Insbesondere für solche Analysen erweist sich der Mischungsansatz aber als besonders vielversprechend. So spielen etwa im Portfoliomanagement die Korrelationen zwischen einzelnen Wertpapierrenditen eine herausragende Rolle. Die Stärke der Korrelationen ist von entscheidender Bedeutung dafür, in welchem Ausmaß das Risiko eines effizienten Portfolios durch Diversifikation reduziert werden kann. Nun gibt es empirische Hinweise darauf, dass die Korrelationen etwa zwischen Aktien in Perioden, die durch starke Marktschwankungen und tendenziell fallende Kurse charakterisiert sind, stärker sind als in ruhigeren Perioden. Das bedeutet, dass die Vorteile der Diversifikation in genau jenen Perioden geringer sind, in denen ihr Nutzen am größten wäre. Modelle, die die Existenz unterschiedlicher Marktregime nicht berücksichtigen, werden daher dazu tendieren, die Korrelationen in den adversen Marktzuständen zu unterschätzen. Dies kann zu erheblichen Fehleinschätzungen des tatsächlichen Risikos während solcher Perioden führen. Diese und weitere Implikationen des Mischungsansatzes im Kontext multivariater GARCH Modelle werden in der vorliegenden Arbeit diskutiert, und ihre Relevanz wird anhand einer empirischen Anwendung dokumentiert. Erörtert werden ferner Fragen der Parametrisierung und Schätzung des Modells, und einige relevante theoretische Eigenschaften werden hergeleitet

Low Momentum Classical Mechanics with Effective Quantum Potentials

A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a smoothed potential both of them constructed from the classical potential. The exact solution of the approximated theory in one spatial dimension is found. The concept of effective transmission and reflection coefficients for effective quantum potentials is proposed and discussed in comparison with an analogous quantum statistical mixture problem. The results are applied to the case of a square barrier.Comment: 4 figure

Testing conformal mapping with kitchen aluminum foil

We report an experimental verification of conformal mapping with kitchen aluminum foil. This experiment can be reproduced in any laboratory by undergraduate students and it is therefore an ideal experiment to introduce the concept of conformal mapping. The original problem was the distribution of the electric potential in a very long plate. The correct theoretical prediction was recently derived by A. Czarnecki (Can. J. Phys. 92, 1297 (2014))