Sudhakar Yarlagadda

An analytic treatment of the Gibbs-Pareto behavior in wealth distribution

We develop a general framework, based on Boltzmann transport theory, to analyze the distribution of wealth in societies. Within this framework we derive the distribution function of wealth by using a two-party trading model for the poor people, while for the rich people a new model is proposed, where interaction with wealthy entities (huge reservoir) is relevant. At equilibrium, the interaction with wealthy entities gives a power-law (Pareto-like) behavior in the wealth distribution, while the two-party interaction gives a Boltzmann–Gibbs distribution.

Analytic Treatment of a Trading Market Model

We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process. The exchange involves random re-distribution among the two players of a fixed fraction of their total money. We obtain a simple integral nonlinear equation for the money distribution. We find that the zero savings and finite savings cases belong to different universality classes. While the zero savings case can be solved analytically, the finite savings solution is obtained by numerically solving the integral equation. We find remarkable agreement with results obtained by other researchers using sophisticated numerical techniques.

Phase diagram of the one-dimensional Hubbard-Holstein model at quarter filling

We derive an effective Hamiltonian for the one-dimensional Hubbard-Holstein model, valid in a regime of both strong electron-electron (e-e) and electron-phonon (e-ph) interactions and in the non-adiabatic limit (

Many-polaron effects in the Holstein model

t/\omega_0 \leq 1

Light scattering theory from dispersions of nonspherical Rayleigh particles

), by using a non-perturbative approach. We obtain the phase diagram at quarter-filling by employing a modified Lanczos method and studying various density-density correlations. The spin-spin AF (antiferromagnetic) interactions and nearest-neighbor repulsion, resulting from the e-e and the e-ph interactions respectively, are the dominant terms (compared to hopping) and compete to determine the various correlated phases. As e-e interaction

Colossal magnetoresistance using the small polaron picture with finite bandwidth effects

(U/t)

Polaron dynamics and decoherence in an interacting two-spin system coupled to an optical-phonon environment

is increased, the system transits from an AF cluster to a correlated singlet phase through a discontinuous transition at all strong e-ph couplings

Correlated singlet phase in the one-dimensional Hubbard-Holstein model

2 \leq g \leq 3

Study of cooperative breathing-mode in molecular chains

considered. At higher values of

Jahn-Teller polarons and their superconductivity in a molecular conductor

U/t