Study of the Wealth Inequality in the Minority Game

To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG). We gauge the wealth inequality of players in the MG by a well-known measure in economics known as the modified Gini index. From our numerical results, we conclude that the wealth inequality in the MG is very severe near the point of maximum cooperation among players, where the diversity of the strategy space is approximately equal to the number of strategies at play. In other words, the optimal cooperation between players comes hand in hand with severe wealth inequality. We also show that our numerical results in the asymmetric phase of the MG can be reproduced semi-analytically using a replica method.Comment: 9 pages in revtex 4 style with 3 figures; minor revision with a change of title; to appear in PR

Wigner crystal and bubble phases in graphene in the quantum Hall regime

Graphene, a single free-standing sheet of graphite with honeycomb lattice structure, is a semimetal with carriers that have linear dispersion. A consequence of this dispersion is the absence of Wigner crystallization in graphene, since the kinetic and potential energies both scale identically with the density of carriers. We study the ground state of graphene in the presence of a strong magnetic field focusing on states with broken translational symmetry. Our mean-field calculations show that at integer fillings a uniform state is preferred, whereas at non-integer filling factors Wigner crystal states (with broken translational symmetry) have lower energy. We obtain the phase diagram of the system. We find that it is qualitatively similar to that of quantum Hall systems in semiconductor heterostructures. Our analysis predicts that non-uniform states, including Wigner crystal state, will occur in graphene in the presence of a magnetic field and will lead to anisotropic transport in high Landau levels.Comment: New references added; 9 pages, 9 figures, (paper with high-resolution images is available at http://www.physics.iupui.edu/yogesh/graphene.pdf

Phase Diffusion in Single-Walled Carbon Nanotube Josephson Transistors

We investigate electronic transport in Josephson junctions formed by single-walled carbon nanotubes coupled to superconducting electrodes. We observe enhanced zero-bias conductance (up to 10e^2/h) and pronounced sub-harmonic gap structures in differential conductance, which arise from the multiple Andreev reflections at superconductor/nanotube interfaces. The voltage-current characteristics of these junctions display abrupt switching from the supercurrent branch to resistive branch, with a gate-tunable switching current ranging from 50 pA to 2.3 nA. The finite resistance observed on the supercurrent branch and the magnitude of the switching current are in good agreement with calculation based on the model of classical phase diffusion

Set-theoretical reflection equation: Classification of reflection maps

The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for constructing reflection maps and we obtain a classification of solutions associated to all the families of quadrirational Yang-Baxter maps that have been classified recently