Biennial Report 2005-2007 - Saha Institute of Nuclear Physics

130 Biennial Report 2005-07Using this property, we study the quench and ac dynamics of the model both numerically andanalytically, and develop a correspondence between the classical phase-space dynamics of a singlespin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, wecompare the behavior of the equal-time order-parameter correlation function both near to and awayfrom the quantum critical point in the presence of a quench or ac transverse field. We explicitlydemonstrate that a clear signature of the quantum critical point can be obtained by studying theac dynamics of the system even in the classical limit. We discuss possible realizations of our modelin experimental systems.A Das, K Sengupta, D Sen, BK ChakrabartiTCMP4.2.2.7 Analysis of a long-range random field quantum antiferromagnetic Ising modelWe introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transversefield, has infinite range antiferromagnetic interactions and random fields on each site followingan arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise toa many valley structure in the spin-configuration space. In addition, the antiferromagnetism alsoinduces a regular frustration even for the ground state. In this paper, we investigate analyticallythe critical phenomena in the model, having both randomness and frustration and we report someanalytical results for it.BK Chakrabarti, A Das, J-I Inoue†TCMP4.2.2.8 A fiber bundle model of traffic jamsWe apply the equal load-sharing fiber bundle model of fracture failure in composite materials tomodel the traffic failure in a system of parallel road network in a city. For some special distributionsof traffic handling capacities (thresholds) of the roads, the critical behavior of the jammingtransition can be studied analytically. This has been compared with that for the asymmetric simpleexclusion process in a single channel or road.BK ChakrabartiTCMP4.2.2.9 Master equation for a kinetic model of trading market and its analytic solutionWe analyze an ideal-gas-like model of a trading market with quenched random saving factors forits agents and show that the steady state income (m) distribution P(m) in the model has a powerlaw tail with Pareto index exactly equal to unity, confirming the earlier numerical studies on thismodel. The analysis starts with the development of a master equation for the time development ofP(m). Precise solutions are then obtained in some special cases.A. Chatterjee, BK Chakrabarti, RB Stinchcombe† TCMP