Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component "magnetic flux" describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely the difference between the two components of the "magnetic flux." A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained "moth," a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing "magnetic fluxes" penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to non-relativistic theory.Comment: A version with higher resolution figures is available at http://physics.gmu.edu/~isatija/NALFinal.pd

Phantom thermodynamics

This paper deals with the thermodynamic properties of a phantom field in a flat Friedmann-Robertson-Walker universe. General expressions for the temperature and entropy of a general dark-energy field with equation of state $p=\omega\rho$ are derived from which we have deduced that, whereas the temperature of a cosmic phantom fluid ($\omega<-1$) is definite negative, its entropy is always positive. We interpret that result in terms of the intrinsic quantum nature of the phantom field and apply it to (i) attain a consistent explanation for some recent results concerning the evolution of black holes which,induced by accreting phantom energy, gradually loss their mass to finally vanish exactly at the big rip, and (ii) introduce the concept of cosmological information and its relation with life and the anthropic principle. Some quantum statistical-thermodynamic properties of the quantum quantum field are also considered that include a generalized Wien law and the prediction of some novel phenomena such as the stimulated absorption of phantom energy and the anti-laser effect.Comment: 19 pages, LaTex, 2 figures, accepted for publication in Nuclear Physics