Quantized Transport in Two-Dimensional Spin-Ordered Structures

We study in detail the transport properties of a model of conducting electrons in the presence of double-exchange between localized spins arranged on a 2D Kagome lattice, as introduced by Ohgushi, Murakami, and Nagaosa (2000). The relationship between the canting angle of the spin texture $\theta$ and the Berry phase field flux per triangular plaquette $\phi$ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect (Haldane, 1988). The quantization of the transverse (Hall) conductivity $\sigma_{xy}$ is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity $\sigma_{xx}$ shows the existence of a metal-insulator transition as a function of the canting angle $\theta$ (or flux density $\phi$). This transition might be linked to that observable in the manganite compounds or in the pyrochlore ones, as the spin ordering changes from ferromagnetic to canted.Comment: 17 pages, 12 figure

On Atkin and Swinnerton-Dyer Congruence Relations (2)

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale

Effects of mismatched transmissions on two-mode squeezing and EPR correlations with a slow light medium

We theoretically discuss the preservation of squeezing and continuous variable entanglement of two mode squeezed light when the two modes are subjected to unequal transmission. One of the modes is transmitted through a slow light medium while the other is sent through an optical fiber of unit transmission. Balanced homodyne detection is used to check the presence of squeezing. It is found that loss of squeezing occurs when the mismatch in the transmission of the two modes is greater than 40% while near ideal squeezing is preserved when the transmissions are equal. We also discuss the effect of this loss on continuous variable entanglement using strong and weak EPR criteria and possible applications for this experimental scheme.Comment: 7 pages, 4 figure

Quantum phases of a Feshbach-resonant atomic Bose gas in one dimension

We study an atomic Bose gas with an s-wave Feshbach resonance in a one-dimensional optical lattice, with the densities of atoms and molecules incommensurate with the lattice. At zero temperature, most of the parameter region is occupied by a phase in which the superfluid fluctuations of atoms and molecules are the predominant ones, due to the phase fluctuations of atoms and molecules being locked by a Josephson coupling between them. When the density difference between atoms and molecules is commensurate with the lattice, two additional phases may exist: the two component Luttinger liquid where both the atomic and molecular sectors are gapless, and the inter-channel charge density wave where the relative density fluctuations between atoms and molecules are frozen at low energy.Comment: 4+epsilon pages, 3 figures; references adde

Characterizations of Pseudo-Codewords of LDPC Codes

An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so called fundamental cone in Euclidean space which is a function of a given parity check matrix of a code, rather than of the code itself. We give a number of properties of this fundamental cone derived from its connection to unramified covers of the graphical models on which the decoding algorithms operate. For the class of cycle codes, these developments naturally lead to a characterization of the fundamental polytope as the Newton polytope of the Hashimoto edge zeta function of the underlying graph.Comment: Submitted, August 200

Revised research about chaotic dynamics in Manko et al. spacetime

A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space and find chaos and unstable fixed points outside of stars with big mass-quadrupole moments. The calculations show that chaos can only occur when the stars have prolate deformation. Because real deformation of stars should be oblate, all orbits of test particles around the rotating neutron stars described by Manko et al. solutions are regular. The case of nonzero dipolar magnetic moment has also been taken into account in this study.Comment: 6 pages, 5 figure