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Bikas K. Chakrabarti

Publications and source records attributed to Bikas K. Chakrabarti.

At least 91 records · Page 5Linked to original sources
arXiv2009

Fractal Models of Earthquake Dynamics

Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of two such models of earthquake dynamics with main focus on a relatively new model namely The Two Fractal Overlap Model.

physics.geo-ph↗
arXiv2009

Kolkata Paise Restaurant Problem in Some Uniform Learning Strategy Limits

We study the dynamics of some uniform learning strategy limits or a probabilistic version of the "Kolkata Paise Restaurant" problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent can get dinner in the best possible ranked restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning to be uniform among the agents and assume that each follow the same probabilistic strategy dependent on the information of the past successes in the game. The numerical results for utilization of the restaurants in some limiting cases are analytically examined.

cs.GT↗
arXiv2009

The Kolkata Paise Restaurant Problem and Resource Utilization

We study the dynamics of the "Kolkata Paise Restaurant problem". The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.

physics.soc-ph↗
arXiv2008

A Novel Quantum Transition in a Fully Frustrated Transverse Ising Antiferromagnet

We consider a long-range Ising antiferromagnet (LRIAF) put in a transverse field. Applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in Trotter time direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We also discuss the phase diagram for the Sherrington-Kirkpatrick (SK) model with the same LRIAF bias, also in presence of a transverse field. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the antiferromagnet. This glass order eventually gets destroyed as the thermal or quantum fluctuations increased beyond their threshold values and the transition to para phase occurs. Indications of this novel phase transition are discussed. Because of the presence of full frustration, this surrogate property of the LRIAF for incubation of stable spin glass phase in it (induced by addition of a small disorder) should enable eventually the study of classical and quantum spin glass phases by using some perturbation theory with respect to the disorder.

cond-mat.stat-mech↗
arXiv2008

Queue-length Variations In A Two-Restaurant Problem

This paper attempts to find out numerically the distribution of the queue-length ratio in the context of a model of preferential attachment. Here we consider two restaurants only and a large number of customers (agents) who come to these restaurants. Each day the same number of agents sequentially arrives and decides which restaurant to enter. If all the agents literally follow the crowd then there is no difference between this model and the famous `Pólya's Urn' model. But as agents alter their strategies different kind of dynamics of the model is seen. It is seen from numerical results that the existence of a distribution of the fixed points is quite robust and it is also seen that in some cases the variations in the ratio of the queue-lengths follow a power-law.

cs.GT↗
arXiv2008

Classical and quantum breakdown in disordered materials

We have discussed the classical failure of the fuse system, the dielectric breakdown and the quantum breakdown in the Anderson insulators. We have discussed how the extreme value statistics and the resulting Gumbel distribution arises in breakdown and failure processes, especially when the disorder concentration is low. At high concentration of disorder near the percolation threshold, we have discussed how the cross-over might take place from extreme value to percolation statistics. We have discussed the system size dependence that arises at the distribution of the failure current at low disordered regime. Finally, the extension of Zener breakdown phenomenon for band insulators to the disordered-induced Anderson insulators has been discussed.

cond-mat.stat-mech↗
arXiv2008

Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo

Here we discuss the annealing behavior of an infinite-range $\pm J$ Ising spin glass in presence of a transverse field using a zero-temperature quantum Monte Carlo. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particularly, when the transverse field is low, much more efficiently.

quant-ph↗
arXiv2008

Quantum Annealing and Analog Quantum Computation

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.

quant-ph↗
arXiv2007

Two Fractal Overlap Time Series: Earthquakes and Market Crashes

We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.

physics.soc-ph↗
arXiv2007

Kinetic Exchange Models for Income and Wealth Distributions

Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium. However, it also deviates in the low income and more significantly for the high income ranges. Application of physics models provides illuminating ideas and understanding, complementing the observations.

q-fin.GN↗
arXiv2007

Kolkata Restaurant Problem as a generalised El Farol Bar Problem

Generalisation of the El Farol bar problem to that of many bars here leads to the Kolkata restaurant problem, where the decision to go to any restaurant or not is much simpler (depending on the previous experience of course, as in the El Farol bar problem). This generalised problem can be exactly analysed in some limiting cases discussed here. The fluctuation in the restaurant service can be shown to have precisely an inverse cubic behavior, as widely seen in the stock market fluctuations.

physics.soc-ph↗
arXiv2007

Economic Inequality: Is it Natural?

Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating significantly for high income groups. Application of physics models seem to provide illuminating ideas and understanding, complimenting the observations.

physics.soc-ph↗
arXiv2006

Kolmogorov Dispersion for Turbulence in Porous Media: A Conjecture

We will utilise the self-avoiding walk (SAW) mapping of the vortex line conformations in turbulence to get the Kolmogorov scale dependence of energy dispersion from SAW statistics, and the knowledge of the disordered fractal geometries on the SAW statistics. These will give us the Kolmogorov energy dispersion exponent value for turbulence in porous media in terms of the size exponent for polymers in the same. We argue that the exponent value will be somewhat less than 5/3 for turbulence in porous media.

cond-mat.stat-mech↗
arXiv2006

Kinetic market models with single commodity having price fluctuations

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. 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 commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: Gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.

physics.soc-ph↗
arXiv2006

Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point

We 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 the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, we compare the behavior of the equal-time order parameter correlation function both near to and away from the quantum critical point in the presence of a quench or AC transverse field. We explicitly demonstrate that a clear signature of the quantum critical point can be obtained by studying the AC dynamics of the system even in the classical limit. We discuss possible realizations of our model in experimental systems.

cond-mat.stat-mech↗
arXiv2006

Statistical Physics of Fracture and Earthquake

This chapter introduces the fracture nucleation process, their (extreme) statistics in disordered solids, in fiber bundle models, and in the two fractal overlap models of earthquake.

cond-mat.stat-mech↗
arXiv2006

Tranverse Ising Model, Glass and Quantum Annealing

We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Next we introduce Suzuki-Trotter formalism to show the correspondence between $d$-dimensional quantum system with a $(d+1)$-dimensional classical system. We then discuss transverse Ising spin glass models, namely S-K model, E-A model, and the $\pm J$ model with Ising spin in transverse field. We briefly discuss the mean field, exact diagonalization, and quantum Monte Carlo results for their phase diagrams. Next we discuss the question of replica symmetry restoration in quantum spin glasses (due to tunnelling possibility through the barriers). Then we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses. We have also breifly discussed the possibility of Quantum Annealing in context of kinetically constrained systems. Mean-field calculation for BCS superconductivity, Real-space RG calculation for one dimensional transverse Ising system, scattering amplitude calculation for tunneling through asymmetric barrier (useful for quantum kinetically constrained system) are given in the appendices.

cond-mat.dis-nn↗