Quantum anti-Zeno effect

Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated measurements on the quantum dynamics of the multilevel systems that exhibit the quantum localization of the classical chaos. The analysis is based on the wave function and Schroedinger equation, without introduction of the density matrix. We show how the quantum Zeno effect in simple few-level systems can be recovered and understood by formal modeling the measurement effect on the dynamics by randomizing the phases of the measured states. Further the similar analysis is extended to investigate of the dynamics of multilevel systems driven by an intense external force and affected by frequent measurement. We show that frequent measurements of such quantum systems results in the delocalization of the quantum suppression of the classical chaos. This result is the opposite of the quantum Zeno effect. The phenomenon of delocalization of the quantum suppression and restoration of the classical-like time evolution of these quasiclassical systems, owing to repetitive frequent measurements, can therefore be called the 'quantum anti-Zeno effect'. From this analysis we furthermore conclude that frequently or continuously observable quasiclassical systems evolve basically in a classical manner.Comment: 12 pages with 2 figure

Trading activity as driven Poisson process: comparison with empirical data

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal description of the trading activities with the same parameters applicable for all stocks.Comment: 9 pages, 5 figures, proceedings of APFA

Consentaneous agent-based and stochastic model of the financial markets

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.Comment: 17 pages, 6 figures, Gontis V, Kononovicius A (2014) Consentaneous Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7): e102201. doi: 10.1371/journal.pone.010220

Modelling financial markets by the multiplicative sequence of trades

We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law probability distribution of the trading activity. The model reproduces the spectral properties of trading activity and explains the mechanism of power-law distribution in real markets.Comment: 6 pages, 2 figure

Point Processes Modeling of Time Series Exhibiting Power-Law Statistics

We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.Comment: 4 pages, 2 figure

Point Process Models of 1/f Noise and Internet Traffic

We present a simple model reproducing the long-range autocorrelations and the power spectrum of the web traffic. The model assumes the traffic as Poisson flow of files with size distributed according to the power-law. In this model the long-range autocorrelations are independent of the network properties as well as of inter-packet time distribution.Comment: 6 pages, 2 figures, CNET2004 Proceedings AI