Studies of complex systems in condensed matter physics and economics

Abstract

This dissertation reports the study of complex systems from two very different fields. The dissertation is divided into two parts. The

first part involves study of angular magnetoresistance in quasi-one-dimensional organic conductors and graphene bilayers (chapter 2 and 3). The second part is devoted to the modeling and empirical study of personal income distribution (chapter 4 and 5).

First, we study the effect of crystal superstructures, produced by orientational ordering of the ReO₄ and ClO₄ anions in the quasi-one-dimensional organic conductors (TMTSF)₂ReO₄ and

(TMTSF)₂ClO₄, on the angular magnetoresistance oscillations (AMRO) observed in these materials. Folding of the Brillouin zone due to anion ordering generates effective tunneling amplitudes between distant chains. These amplitudes cause multiple peaks in interlayer conductivity for the magnetic field orientations along the rational crystallographic directions (the Lebed magic angles). Different wave vectors of the anion ordering in (TMTSF)₂ReO₄ and

(TMTSF)₂ClO₄ result in the odd and even Lebed angles, as observed experimentally. When a strong magnetic field is applied parallel to the layers and perpendicular the chains and exceeds a certain threshold, the interlayer tunneling between different branches

of the folded electron spectrum becomes possible, and interlayer conductivity should increase sharply. This effect can be utilized to probe the anion ordering gaps in (TMTSF)₂ClO₄ and

(TMTSF)₄ReO₄. An application of this effect to

kappa-(ET)₂Cu(NCS)₂ is also briefly discussed. Next, we study AMRO in graphene bilayers. We calculate the interlayer

conductivity and investigate the effects of a parallel magnetic field on the low energy bands of graphene bilayer.

Next, we analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the

exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the

log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability

density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution. We also analyze data on individual income from

Internal Revenue Service and University of Maryland. Finally, we discuss a model which captures the two-class structure of income

distribution in the USA.