Kinetic models of immediate exchange

We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or uni-directional movements of wealth. Such dynamics produces wealth distributions that describe more faithfully real data at small values of wealth. Secondly, a general probabilistic trading criterion is introduced, so that two economic units can decide independently whether to trade or not depending on their profit. It is found that the type of the equilibrium wealth distribution is the same for a large class of trading criteria formulated in a symmetrical way with respect to the two interacting units. This establishes unexpected links between and provides a microscopic foundations of various kinetic exchange models in which the existence of a saving propensity is postulated. We also study the generalized heterogeneous version of the model in which units use different trading criteria and show that suitable sets of diversified parameter values with a moderate level of heterogeneity can reproduce realistic wealth distributions with a Pareto power law.Comment: 10 pages, 7 figure

Classical and quantum Brownian motion in an electromagnetic field

The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and Caldeira-Leggett framework for the quantum problem. We study the time evolution in configuration space of the probability distribution of an initial pure state represented by an asymmetrical Gaussian wave function and show that it can be described as the superposition of (a) the classical motion of the center of mass, (b) a rotation around the mean position, and (c) a spreading processes along the principal axes.Comment: Presented at FQMT15-Frontiers of Quantum and Mesoscopic Thermodynamics, July 27-August 1, 2015, Prague, Czech Republi

Stability of charge inversion, Thomson problem and application to electrophoresis

We analyse charge inversion in colloidal systems at zero temperature using stability concepts, and connect this to the classical Thomson problem of arranging electrons on sphere. We show that for a finite microion charge, the globally stable, lowest energy state of the complex formed by the colloid and the oppositely charged microions is always overcharged. This effect disappears in the continuous limit. Additionally, a layer of at least twice as many microions as required for charge neutrality is always locally stable. In an applied external electric field the stability of the microion cloud is reduced. Finally, this approach is applied to a system of two colloids at low but finite temperature

Econophysics: empirical facts

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words "Economics" and "Physics", this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes. We give a brief introduction in the first part and begin with discussing interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics in the second part. Then the third part is dedicated to empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged "stylized facts" describing the distribution of the returns of financial assets: fat-tails, volatility clustering, etc. Then we show that some of these properties are directly linked to the way "time" is taken into account, and present some new remarks on this account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrations in this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Contributions to the study of correlations of assets such as random matrix theory and graph theory are finally presented in this part. The fourth part of our review deals with models in Econophysics through the point of view of agent-based modeling. Using previous work originally presented in the fields of behavioural finance and market microstructure theory, econophysicists have developed agent-based models of orderdriven markets that are extensively reviewed here. We then turn to models of wealth distribution where an agent-based approach also prevails: kinetic theory models, and continue with game theory models and review the now classic minority games. We end this review by providing an outlook on possible directions of research.