On Coherent States and q-Deformed Algebras

We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to provide a path integral formalism allowing to study a modified form of q-classical mechanics, to probe some geometrical consequences of the q-deformation and finally to construct Bargmann complex analytic realizations for some quantum algebras.Comment: Presented at the 'International Symposium on Coherent States' June 1993, USA 14 pages, plain LATEX, FTUV/93-37, IFIC/93-2

Can Feedback Traders Rock the Markets? A Logistic Tale of Persistence and Chaos

This paper introduces a nonlinear feedback trading model at high frequency. All price adjustment is endogenous, driven by asset return and volatility in the previous trading period. There is no stochastic uncertainty or asymmetric information. The dynamics of expected returns display stable or unstable behavior–including the possibility of turbulence and chaos–as a function of market liquidity (inverse price impact) and the concentration of investor beliefs, which is proportional to the intensity of positive feedback. The results highlight the complementary role of investor diversity and market liquidity in maintaining financial stability

Endogenous Market Turbulence

In this paper I study a nonlinear feedback trading model which can generate stable, unstable, turbulent or chaotic asset returns depending on market conditions. The dynamics are driven by the stochastic price impact of net order flow (inverse market liquidity). If price impact grows beyond exogenous threshold values, liquidity dries up and asset returns become turbulent. In the absence of fundamental factors, the occurrence of turbulence and chaos is entirely endogenous. The results highlight the critical role of maintaining stable market-making conditions for averting “liquidity black holes”

Gamma rays from active galactic nuclei

The general properties of Active Galactic Nuclei (AGN) and quasars are reviewed with emphasis on their continuum spectral emission. Two general classes of models for the continuum are outlined and critically reviewed in view of the impending GRO (Gamma Ray Observatory) launch and observations. The importance of GRO in distinguishing between these models and in general in furthering the understanding of AGN is discussed. The very broad terms the status of the current understanding of AGN are discussed

Quantized turbulence physics

We elaborate the physics of systems of unconstrained, reconnecting vortex filaments with dynamic finite cores of uniform ("quantized") circulation interacting via Biot-Savart and viscous forces. The phenomenology of this purely structured turbulent system includes an inertial range with Kolmogorov's k^–5/3 scaling for the energy spectrum, as well as Kolmogorov's linear in r scaling for the third order longitudinal structure function