217,589 research outputs found
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
Effective Hamiltonian and low-lying energy clustering patterns of four-sublattice antiferromagnets
We study the low-lying energy clustering patterns of quantum antiferromagnets
with p sublattices (in particular p=4). We treat each sublattice as a large
spin, and using second-order degenerate perturbation theory, we derive the
effective (biquadratic) Hamiltonian coupling the p large spins. In order to
compare with exact diagonalizations, the Hamiltonian is explicitly written for
a finite-size lattice, and it contains information on energies of excited
states as well as the ground state. The result is applied to the
face-centered-cubic Type I antiferromagnet of spin 1/2, including
second-neighbor interactions. A 32-site system is exactly diagonalized, and the
energy spectrum of the low-lying singlets follows the analytically predicted
clustering pattern.Comment: 17 pages, 4 table
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