The dynamics of traded value revisited

We conclude from an analysis of high resolution NYSE data that the distribution of the traded value $f_i$ (or volume) has a finite variance $\sigma_i$ for the very large majority of stocks $i$, and the distribution itself is non-universal across stocks. The Hurst exponent of the same time series displays a crossover from weakly to strongly correlated behavior around the time scale of 1 day. The persistence in the strongly correlated regime increases with the average trading activity \ev{f_i} as H_i=H_0+\gamma\log\ev{f_i}, which is another sign of non-universal behavior. The existence of such liquidity dependent correlations is consistent with the empirical observation that \sigma_i\propto\ev{f_i}^\alpha, where $\alpha$ is a non-trivial, time scale dependent exponent.Comment: 5 pages, 4 figures, to appear in Physica A (APFA5 2006), corrected a few errors in references and tex

Entanglement negativity in two-dimensional free lattice models

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case, we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.Comment: 11 pages, 6 figures, published versio

Scaling theory of temporal correlations and size dependent fluctuations in the traded value of stocks

Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average : sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The non-trivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provides information about the microscopic dynamics. We present a set of recently discovered stylized facts, and then show their connection to such behavior. The functional form alpha(dt) originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages, and also display stronger correlations of traded value.Comment: 8 pages, 7 figures, 1 table, accepted to Phys. Rev.

Volatility: A hidden Markov process in financial time series

Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are that (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model, (ii) the estimated volatility is related to trading volume by a power law of the form \ensuremath{\sigma}\ensuremath{\propto}{V}^{0.55}, and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns

Entanglement negativity in two-dimensional free lattice models

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case, we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found

Entanglement negativity bounds for fermionic Gaussian states

The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in theHilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators.We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature

Fluctuation scaling in complex systems: Taylor's law and beyond

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form "$fluctuations \approx const.\times average^\alpha$", where the exponent $\alpha$ is predominantly in the range $[1/2, 1]$. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names \emph{Taylor's law} or \emph{fluctuation scaling}. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic

Struktúrák dinamikája nagyszabadsági fokú rendszerekben (nagyenergiás és klasszikus makroszkopikus folyamatok) = Dynamics of structures in systems with large degrees of freedom (high energy and classical macroscopic processes)

A véges hőmérsékletű térelméletekben elért - Nature-ben is közölt - eredményünk szerint az ősrobbanás utáni kvark-hadronikus anyag átmenet folytonos, nem fázisátátalakulás. Rácstérelméleti módszerekkel megadtuk ezen átmenet karakterisztikus hőmérsékletét. Az integrálható térelméletek alkalmazhatók a kondenzált anyagok fizikájától a nyílt húrelméleten keresztül egészen a részecskefizikáig. Jelentős lépést tettünk a racionális konform térelméletek osztályozása felé. A statisztikus fizika területén külön figyelmet szenteltünk az egyensúlytól távoli jelenségek közül a frontoknak. A kémiai, biológia és mágneses frontok mozgását, alakváltozásait írtuk le és szabályozásukat dolgoztuk ki. A fizikai mennyiségek extrém értékeinek statisztikája az alkalmazások szempontjából is fontos új terület, melyen belül transzportjelenségek és 1/f típusú zaj ingadozásait jellemző mennyiségek maximumának eloszlását adtuk meg. A diszlokációrendszerek statisztikus fizikai vizsgálata segítségével több áttörést értünk el. A környezeti áramlások témakörében a Kármán Laboratórium aktív kutatóhellyé fejlődött. A frontoktól kezdve a ciklonképződésig számos kísérletet végeztünk. Kiemelendő, hogy egy forgókádbeli turbulenciában a hőmérséklet fluktuációinak statisztikája reprodukálja a földi meteorológiai állomások adataiét. A kísérletek a klímaváltozás vizsgálatában is ígéretesek. A pályázati időszakban 21 doktorandusz témavezetését láttuk el. | Our result - published also in Nature - on finite temperature field theories states that the quark-hadronic matter transition after the Big Bang happened continuously, not like a phase transition. We determined the characteristic crossover temperature using lattice field theoretical methods. Integrable field theories have applications from condensed matter physics to open string theory to particle physics. We made a major step towards the classification of rational conformal field theories. In statistical physics special attention has been payed to fronts, a phenomenon in far from equilibrium systems. We described and controlled motion and shapes of fronts in chemical, biological, and magnetic systems. Extreme statistics of physical quantities is a new area also important from the viewpoint of applications, where we determined the distribution of maxima in transport phenomena and in quantities characterizing fluctuations of 1/f-type noises. Several breakthroughs were achieved by means of statistical physical studies in dislocation systems. As to the topic of environmental flows, the von Karman Laboratory has become an active research unit where experiments ranging from fronts to cyclone-genesis have been carried out. As a highlight, in the turbulence from a rotating tank the statistics of temperature fluctuations reproduced that of data from meteorological stations. The experiments are promising for studies in climate change. In the grant period we supervised 21 PhD students