Quantum phase transition and engineering in two-component BEC in optical lattices

In this paper we review recent progress in studying quantum phase transitions in one- and two-component Bose-Einstein condensates (BEC) in optical lattices. These phase transitions involve the emergence and disappearance of quantum coherence over whole optical lattice and of linear superposition of macroscopic quantum states. The latter may provide new means to engineer and to manipulate novel macroscopic quantum states and novel coherent atomic beams for quantum information processing, quantum computing etc.Comment: Format: LaTex2e. 7 pages, no figure. Talk at the Yang Symposium (in honor of C.N. Yang's 80th birthday), Beijing, China, June 2002. To appear in the Proceeding

Distributive Power Control Algorithm for Multicarrier Interference Network over Time-Varying Fading Channels - Tracking Performance Analysis and Optimization

Distributed power control over interference limited network has received an increasing intensity of interest over the past few years. Distributed solutions (like the iterative water-filling, gradient projection, etc.) have been intensively investigated under \emph{quasi-static} channels. However, as such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under \emph{time-varying} channels is in general unknown. In this paper, we shall investigate the distributed scaled gradient projection algorithm (DSGPA) in a $K$ pairs multicarrier interference network under a finite-state Markov channel (FSMC) model. We shall analyze the \emph{convergence property} as well as \emph{tracking performance} of the proposed DSGPA. Our analysis shows that the proposed DSGPA converges to a limit region rather than a single point under the FSMC model. We also show that the order of growth of the tracking errors is given by \mathcal{O}\(1 \big/ \bar{N}\), where $\bar{N}$ is the \emph{average sojourn time} of the FSMC. Based on the analysis, we shall derive the \emph{tracking error optimal scaling matrices} via Markov decision process modeling. We shall show that the tracking error optimal scaling matrices can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed DSGPA over three baseline schemes, such as the gradient projection algorithm with a constant stepsize.Comment: To Appear on the IEEE Transaction on Signal Processin

Extended Schmidt law holds for faint dwarf irregular galaxies

The extended Schmidt law (ESL) is a variant of the Schmidt law which relates the surface densities of gas and star formation, with the surface density of stellar mass added as an extra parameter. We empirically investigate for the first time whether low metallicity faint dwarf irregular galaxies (dIrrs) follow the ESL. Here we consider the `global' law where surface densities are averaged over the galactic discs. dIrrs are unique not only because they are at the lowest end of mass and star formation scales for galaxies, but also because they are metal-poor compared to the general population of galaxies. Our sample is drawn from the Faint Irregular Galaxy GMRT Survey (FIGGS) which is the largest survey of atomic hydrogen in such galaxies. The gas surface densities are determined using their atomic hydrogen content. The star formation rates are calculated using GALEX far ultraviolet fluxes after correcting for dust extinction, whereas the stellar surface densities are calculated using Spitzer 3.6 $\mu$m fluxes. All surface densities are calculated over stellar discs defined by the 3.6 $\mu$m images. We find dIrrs indeed follow the extended Schmidt law. The mean deviation of the FIGGS galaxies from the relation is 0.01 dex, with a scatter around the relation of less than half that seen in the original relation. In comparison, we also show that the FIGGS galaxies are much more deviant when compared to the `canonical' Kennicutt-Schmidt relation. Our results help strengthen the universality of the extended Schmidt law, especially for galaxies with low metallicities. We suggest that models of star formation in which feedback from previous generations of stars set the pressure in the ISM, are promising candidates for explaining the ESL. We also confirm that ESL is an independent relation and not a form of a relation between star formation efficiency and metallicity.Comment: Accepted for publication in Astronomy & Astrophysics. Figure 2 on Page 5 shows the main resul

Lower dimensional volumes and the Kastler-Kalau-Walze type theorem for Manifolds with Boundary

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}^{(2,2)}$ for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case

Distributive Network Utility Maximization (NUM) over Time-Varying Fading Channels

Distributed network utility maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the convergence behavior and tracking errors of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic scaling matrices (DSC) for solving distributive NUM problems under time-varying fading channels. We shall also study a specific application example, namely the multi-commodity flow control and multi-carrier power allocation problem in multi-hop ad hoc networks. Our analysis shows that the PDSGA converges to a limit region rather than a single point under the finite state Markov chain (FSMC) fading channels. We also show that the order of growth of the tracking errors is given by O(T/N), where T and N are the update interval and the average sojourn time of the FSMC, respectively. Based on this analysis, we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices, which can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes, such as the regular primal-dual gradient algorithm

Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We investigate the magnetic susceptibility $\chi(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $\alpha$ and cutoff length $\xi$. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of $\chi(T)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay ($\xi = \infty$) we find a crossover at $\alpha^*=1.066$ between a phase with a divergent low-temperature susceptibility $\chi(T\rightarrow 0)$ for $\alpha > \alpha^*$ to a phase with a vanishing $\chi(T\rightarrow 0)$ for $\alpha < \alpha^*$. For finite cutoff lengths $\xi$, this crossover occurs at a smaller $\alpha^*(\xi)$. Additionally we study the localization of spin excitations for $\xi = \infty$ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at $\alpha_c=\alpha^*$.Comment: 6 pages, 7 figure