Biennial Report 2005-2007 - Saha Institute of Nuclear Physics

Condensed Matter Physics 1294.2.2.3 Ideal-gas like market models with savings: quenched and annealed casesWe analyze the ideal-gas-like models of markets and review the different cases where a savingsfactor changes the nature and shape of the distribution of wealth. These models can producesimilar distribution of wealth as observed across varied economies. We present a more realisticmodel where the saving factor can vary over time (annealed savings) and yet produce Paretodistribution of wealth in certain cases. We discuss the relevance of such models in the context ofwealth distribution, and address some recent issues in the context of these models.A Chatterjee, BK ChakrabartiTCMP4.2.2.4 A common origin of the power law distributions in models of market andearthquakeWe show here that the Pareto power law distribution observed in an ideal gas-like trading marketmodel (with random saving propensity of its agents) and the Gutenberg-Richter like distributionfor the overlap measure between two Cantor sets (as one moves uniformly over the other in adynamical model of earthquakes) have a common origin. The identification of this common genericorigin helps in developing generalized views and understanding of such diverse phenomena.P Bhattacharyya, A Chatterjee, BK ChakrabartiTCMP4.2.2.5 Kinetic market models with single commodity having price fluctuationsWe study here numerically the behavior of an ideal gas like model of markets having only one nonconsumablecommodity. We investigate the behavior of the steady-state distributions of money,commodity and total wealth, as the dynamics of trading or exchange of money and commodityproceeds, with local (in time) fluctuations in the price of the commodity. These distributions arestudied in markets with agents having uniform and random saving factors. The self-organizing featuresin money distribution are similar to the cases without any commodity (or with consumablecommodities), while the commodity distribution shows an exponential decay. The wealth distributionshows interesting behavior: gamma like distribution for uniform saving propensity and has thesame power-law tail, as that of the money distribution, for a market with agents having randomsaving propensity.A Chatterjee, BK ChakrabartiTCMP4.2.2.6 Infinite-range Ising ferromagnet in time-dependent transverse field: dynamicsnear quantum critical pointWe study an infinite-range ferromagnetic Ising model in the presence of a transverse magnetic field,which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of thetransverse field. In the thermodynamic limit, the low-temperature properties of this model aredominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian.