arXiv subjects

Bikas K Chakrabarti

Publications and source records attributed to Bikas K Chakrabarti.

At least 19 recordsLinked to original sources

arXiv2026

Relations Among Different Inequality Measures in Complex Systems: From Kinetic Exchange to Earthquake Models

We present a numerical study of several inequality measures across two kinetic wealth exchange models with extreme inequality features (namely the Banerjee model, and the Chakraborti or Yard Sale model) and two earthquake simulating models (namely the Chakrabarti Stinchcombe two fractal overlap model and the nonlinear dynamical Burridge Knopoff model). For each model we compute numerically the Lorenz function for the respective models wealth, overlap magnitude or avalanche distributions. We then estimate the variations of Gini (g), Pietra (p) and Kolkata (k) indices in these models with systematic variations of saving propensity (for the two wealth exchange models), with systematic variations of generation or block numbers (for the two earthquake simulating models). We find that for appropriate values of the respective model parameters, the inequality indices g and k in corresponding the distributions (of wealth or avalanche) show quantitatively similar behavior, namely g equal to k nearly equal to 0.86, which was identified earlier to correspond to the precursor point of criticality in self organized critical models (k equal to 0.80 corresponds to that for Pareto 80/20 law). The values of p/(2k-1) in all these (wealth exchange and earthquake) models remain a little above unity, as was predicted theoretically. These observations for the inequality indices g, k and p across the socio economic and geophysical models indicate the presence of unifying subtle features in the statistics of such disparate dynamical systems.

physics.soc-ph↗

arXiv2023

Quantum Annealing in Sherrington-Kirkpatrick Spin Glass in Presence of Time-Dependent Longitudinal Field

Motivated by the recent development of quantum technology using quantum annealing technique and the recent works on the static properties of the Sherrington-Kirkpatrick (SK) spin glass model, we study quantum annealing of the spin glass model by tuning both transverse and longitudinal fields. We numerically solve the time-dependent Schrödinger equation of the total Hamiltonian when both the fields are made time-dependent and eventually vanish at the same time. We have computed the time-evolution of the probability of finding the system in one of two degenerate ground states of the classical spin glass. At the end of annealing, using the configuration averaged probability, we have shown a clear advantage while the longitudinal field is annealed rather than keeping it constant throughout the process of quantum annealing. We further investigate the order parameter distribution of a quantum SK spin glass in presence of a small longitudinal field and find, from our exact diaginalization results for small system sizes, evidence for quantum tunneling induced disappearance of the classical Almeida-Thouless phase boundary separating the replica symmetry broken (nonergodic) and replica symmetric (ergodic) spin glass phase (reported already in $2022$). We believe that this longitudinal field induced ergodicity in quantum SK model to be responsible for the observed enhancement of quantum annealing (reported earlier for smaller systems by us in $2014$).

cond-mat.stat-mech↗

arXiv2022

Quantum Annealing and Computation

We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to demonstrate the quantum advantage in the search for the ground state(s) through annealing. Quantum annealing as a physical (analog) process to search for the optimal solutions of computationally hard problems are also discussed.

cond-mat.stat-mech↗

arXiv2022

Stochastic Learning in Kolkata Paise Restaurant Problem: Classical \& Quantum Strategies

We will review the results for stochastic learning strategies, both classical (one-shot and iterative) and quantum (one-shot only), for optimizing the available many-choice resources among a large number of competing agents, developed over the last decade in the context of the Kolkata Paise Restaurant Problem. Apart from a few rigorous and approximate analytical results, both for classical and quantum strategies, most of the interesting results on the phase transition behavior (obtained so far for the classical model) using classical Monte Carlo simulations. All these, including the applications to computer science (job or resource allotments in Internet-of-Things), transport engineering (on-line vehicle hire problems), operation research (optimizing efforts for delegated search problem, efficient solution of Travelling Salesman problem), etc will be discussed.

physics.soc-ph↗

arXiv2021

Development of Econophysics: A biased account and perspective from Kolkata

We present here a somewhat personalized account of the emergence of econophysics as an attractive research topic in physical as well as social sciences. After a rather detailed story telling about our endeavors from Kolkata, we give a brief description of the main research achievements in a simple and non-technical language. We also present briefly, in technical language, a piece of our recent research result. We conclude our paper with a brief perspective.

physics.soc-ph↗

arXiv2021

Limiting Value of the Kolkata Index for Social Inequality and a Possible Social Constant

Based on some analytic structural properties of the Gini and Kolkata indices for social inequality, as obtained from a generic form of the Lorenz function, we make a conjecture that the limiting (effective saturation) value of the above-mentioned indices is about 0.865. This, together with some more new observations on the citation statistics of individual authors (including Nobel laureates), suggests that about $14\%$ of people or papers or social conflicts tend to earn or attract or cause about $86\%$ of wealth or citations or deaths respectively in very competitive situations in markets, universities or wars. This is a modified form of the (more than a) century old $80-20$ law of Pareto in economy (not visible today because of various welfare and other strategies) and gives an universal value ($0.86$) of social (inequality) constant or number.

physics.soc-ph↗

arXiv2020

Econophysics Through Computation

We introduce here very briefly, through some selective choices of problems and through the sample computer simulation programs (following the request of the editor for this invited review in the Journal of Physics Through Computation), the newly developed field of econophysics. Though related attempts could be traced much earlier (see the Appendix), the formal researches in econophysics started in 1995. We hope, the readers (students \& researchers) can start themselves to enjoy the excitement, through the sample computer programs given, and eventually can undertake researches in the frontier problems, through the indicated survey literature provided.

physics.soc-ph↗

arXiv2019

On the Question of Ergodicity in Quantum Spin Glass Phase and its role in Quantum Annealing

We first review, following our earlier studies, the critical behavior of the quantum Sherrington-Kirkpatrick (SK) model at finite as well as at zero temperatures. Through the analysis of the Binder cumulant we determined the entire phase diagram of the model and from the scaling analysis of the numerical data we obtained the correlation length exponent. For both the critical Binder cumulant and the correlation length exponent, we observed a crossover from classical- to quantum-fluctuation-dominated values at a finite temperature. We studied the behavior of the order parameter distribution of the model in the glass phase (at finite and zero temperatures). Along with a classical-fluctuation-dominated nonergodic region (where the replica symmetry is broken), we also found a quantum-fluctuation-dominated low-temperature ergodic region in the spin glass phase. In this quantum-fluctuation-dominated region, the order parameter distribution has a narrow peak around its most probable value, eventually becoming a delta function in the infinite-system-size limit (indicating replica symmetry restoration or ergodicity in the system). We also found that the annealing time (to reach a very low energy level of the classical SK model) becomes practically system-size-independent when the annealing paths pass through this ergodic region. In contrast, when such paths pass through the nonergodic region, the convergence time grows rapidly with the system size. We present a new study of the autocorrelation of the spins in both ergodic and nonergodic regions. We found a significant increase in the relaxation time (and also a change in the relaxation behavior) in the classical-fluctuation-dominated (nonergodic) region compared with that in the quantum-fluctuation-dominated (ergodic) region of the spin glass phase.

cond-mat.stat-mech↗

arXiv2018

Possible Ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

We explore the behavior of order parameter distribution of quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamil- tonian at finite temperatures and that at zero temperature obtained using exact diagonalization method. Our numerical results indicate the existence of low but finite temperature quantum fluc- tuation dominated ergodic region along with the classical fluctuation dominated high temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has non-vanishing value every- where in thermodynamic limit, indicating nonergodicity. We also show, that the average annealing time for convergence (to a low energy level of the model; within a small error range) becomes system size independent for annealing down through the (quantum fluctuation dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite size scaling type behavior for the extent of the ergodic region is also addressed.

cond-mat.stat-mech↗

arXiv2016

Socio-economic inequality and prospects of institutional Econophysics

Socio-economic inequality is measured using various indices. The Gini ($g$) index, giving the overall inequality is the most commonly used, while the recently introduced Kolkata ($k$) index gives a measure of $1-k$ fraction of population who possess top $k$ fraction of wealth in the society. This article reviews the character of such inequalities, as seen from a variety of data sources, the apparent relationship between the two indices, and what toy models tell us. These socio-economic inequalities are also investigated in the context of man-made social conflicts or wars, as well as in natural disasters. Finally, we forward a proposal for an international institution with sufficient fund for visitors, where natural and social scientists from various institutions of the world can come to discuss, debate and formulate further developments.

q-fin.GN↗

arXiv2016

Socio-economic inequality: Relationship between Gini and Kolkata indices

Socio-economic inequality is characterized from data using various indices. The Gini ($g$) index, giving the overall inequality is the most common one, while the recently introduced Kolkata ($k$) index gives a measure of $1-k$ fraction of population who possess top $k$ fraction of wealth in the society. Here, we show the relationship between the two indices, using both empirical data and analytical estimates. The significance of their relationship has been discussed.

physics.soc-ph↗

arXiv2016

Fat tailed distributions for deaths in conflicts and disasters

We study the statistics of human deaths from wars, conflicts, similar man-made conflicts as well as natural disasters. The probability distribution of number of people killed in natural disasters as well as man made situations show power law decay for the largest sizes, with similar exponent values. Comparisons with natural disasters, when event sizes are measured in terms of physical quantities (e.g., energy released in earthquake, volume of rainfall, land area affected in forest fires, etc.) also show striking resemblances. The universal patterns in their statistics suggest that some subtle similarities in their mechanisms and dynamics might be responsible.

physics.soc-ph↗

arXiv2015

Universality of citation distributions for academic institutions and journals

Citations measure the importance of a publication, and may serve as a proxy for its popularity and quality of its contents. Here we study the distributions of citations to publications from individual academic institutions for a single year. The average number of citations have large variations between different institutions across the world, but the probability distributions of citations for individual institutions can be rescaled to a common form by scaling the citations by the average number of citations for that institution. We find this feature seem to be universal for a broad selection of institutions irrespective of the average number of citations per article. A similar analysis for citations to publications in a particular journal in a single year reveals similar results. We find high absolute inequality for both these sets, Gini coefficients being around $0.66$ and $0.58$ for institutions and journals respectively. We also find that the top $25$% of the articles hold about $75$% of the total citations for institutions and the top $29$% of the articles hold about $71$% of the total citations for journals.

physics.soc-ph↗

arXiv2015

Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model

We study the critical behavior of Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their `classical' to `quantum' values at a finite temperature (unlike the cases of pure systems where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.

cond-mat.stat-mech↗

arXiv2014

Zipf's law in city size from a resource utilization model

We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, it gives rise to a Zipf law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness. A variant of the model is also introduced where the fitness can be treated as an ability to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, while the distribution of the number of customers still follows the Zipf law, implying the robustness of the model. Our model serves as a paradigm for the emergence of Zipf law in city size distribution.

physics.soc-ph↗

arXiv2010

Statistics of the Kolkata Paise Restaurant Problem

We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent tries get to dinner in the best restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents and assume that each follow the same probabilistic or stochastic strategy dependent on the information of the past successes in the game. We show that some 'naive' strategies lead to much better utilization of the services than some relatively 'smarter' strategies. We also show that the service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not; with probability decreasing inversely in the past crowd size). The numerical results for utilization fraction of the services in some limiting cases are analytically examined.

physics.soc-ph↗

arXiv2007

A Brief History of Economics: An Outsider's Account

A dangerously brief history of the developments of the main ideas in economics, as observed by a physicist, is given. This was published in 'Econophysics of Stock and Other Markets', Eds. A. Chatterjee, B. K. Chakrabarti, New Economic Windows Series, Springer, Milan, 2006, pp~219-224.

q-fin.GN↗

arXiv2006

Ideal-gas like market models with savings: quenched and annealed cases

We analyze the ideal gas like models of markets and review the different cases where a `savings' factor changes the nature and shape of the distribution of wealth. These models can produce similar distribution of wealth as observed across varied economies. We present a more realistic model where the saving factor can vary over time (annealed savings) and yet produces Pareto distribution of wealth in certain cases. We discuss the relevance of such models in the context of wealth distribution, and address some recent issues in the context of these models.

physics.soc-ph↗