A projection operator approach to the Bose-Hubbard model

We develop a projection operator formalism for studying both the zero temperature equilibrium phase diagram and the non-equilibrium dynamics of the Bose-Hubbard model. Our work, which constitutes an extension of Phys. Rev. Lett. {\bf 106}, 095702 (2011), shows that the method provides an accurate description of the equilibrium zero temperature phase diagram of the Bose-Hubbard model for several lattices in two- and three-dimensions (2D and 3D). We show that the accuracy of this method increases with the coordination number $z_0$ of the lattice and reaches to within 0.5% of quantum Monte Carlo data for lattices with $z_0=6$. We compute the excitation spectra of the bosons using this method in the Mott and the superfluid phases and compare our results with mean-field theory. We also show that the same method may be used to analyze the non-equilibrium dynamics of the model both in the Mott phase and near the superfluid-insulator quantum critical point where the hopping amplitude $J$ and the on-site interaction $U$ satisfy $z_0J/U \ll 1$. In particular, we study the non-equilibrium dynamics of the model both subsequent to a sudden quench of the hopping amplitude $J$ and during a ramp from $J_i$ to $J_f$ characterized by a ramp time $\tau$ and exponent $\alpha$: $J(t)=J_i +(J_f-J_i) (t/\tau)^{\alpha}$. We compute the wavefunction overlap $F$, the residual energy $Q$, the superfluid order parameter $\Delta(t)$, the equal-time order parameter correlation function $C(t)$, and the defect formation probability $P$ for the above-mentioned protocols and provide a comparison of our results to their mean-field counterparts. We find that $Q$, $F$, and $P$ do not exhibit the expected universal scaling. We explain this absence of universality and show that our results for linear ramps compare well with the recent experimental observations.Comment: v2; new references and new sections adde

New lower bounds for the independence number of sparse graphs and hypergraphs

We obtain new lower bounds for the independence number of $K_r$-free graphs and linear $k$-uniform hypergraphs in terms of the degree sequence. This answers some old questions raised by Caro and Tuza \cite{CT91}. Our proof technique is an extension of a method of Caro and Wei \cite{CA79, WE79}, and we also give a new short proof of the main result of \cite{CT91} using this approach. As byproducts, we also obtain some non-trivial identities involving binomial coefficients

Optically pumped submillimeter-waves and applications

Rapid development of optically pumped lasers has shown the potential to be used as a source for a high resolution spectrometer. In this connection, a compact, stable FIR laser was designed, fabricated, and assembled, integrating both the pump laser and the FIR cavity in the same mechanical structure for its improved (both thermal and mechanical) stability and mobility. Performance of the mixer structure which was designed and constructed for the evaluation of the Schottky diodes was found to be satisfactory. The feasibility of generating tunable sideband for molecular spectroscopy studies was demonstrated

Charmless Non-Leptonic B Decays and R-parity Violating Supersymmetry

We examine the charmless hadronic B decay modes in the context of R-parity violating (\rpv) supersymmetry. We try to explain the large branching ratio (compared to the Standard Model (SM) prediction) of the decay $B^{\pm}\to \eta' K^{\pm}$. There exist data for other observed $\eta^{(\prime)}$ modes and among these modes, the decay $B^{0}\to \eta K^{*0}$ is also found to be large compared to the SM prediction. We investigate all these modes and find that only two pairs of \rpv coupling can satisfy the requirements without affecting the other B\ra PP and B\ra VP decay modes barring the decay B\ra\phi K. From this analysis, we determine the preferred values of the \rpv couplings and the effective number of color $N_c$. We also calculate the CP asymmetry for the observed decay modes affected by these new couplings.Comment: 14 pages, 7 figures; revtex; version published in Phys. Lett.

Pion-induced Drell-Yan processes and the flavor-dependent EMC effect

Pion-induced Drell-Yan processes are proposed as a potential tool to measure the flavor dependence of the EMC effect, that is, the flavor-dependent modification of quark distributions in the nuclear medium. Existing pionic Drell-Yan data are compared with calculations using a recent model for nuclear quark distributions that incorporates flavor-dependent nuclear effects. While no firm conclusions can yet be drawn, we demonstrate that existing Drell-Yan data seem to imply a flavor dependence of the EMC effect. We highlight how pion-induced Drell-Yan experiments on nuclear targets can access important new aspects of the EMC effect, not probed in deep inelastic scattering, and will therefore provide very stringent constrains for models of nuclear quark distributions. Predictions for possible future pion-induced Drell-Yan experiments are also presented.Comment: 4 pages, 3 figure

Signature of strong atom-cavity interaction on critical coupling

We study a critically coupled cavity doped with resonant atoms with metamaterial slabs as mirrors. We show how resonant atom-cavity interaction can lead to a splitting of the critical coupling dip. The results are explained in terms of the frequency and lifetime splitting of the coupled system.Comment: 8 pages, 5 figure

Instability, Intermittency and Multiscaling in Discrete Growth Models of Kinetic Roughening

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Depending on the details of the model, the instability found in the discretized version may or may not be present in the truly continuum growth equation, indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts. This instability can be controlled either by the introduction of higher-order nonlinear terms with appropriate coefficients or by restricting the growth of pillars (or grooves) by other means. A number of such ``controlled instability'' models are studied by simulation. For appropriate choice of the parameters used for controlling the instability, these models exhibit intermittent behavior, characterized by multiexponent scaling of height fluctuations, over the time interval during which the instability is active. The behavior found in this regime is very similar to the ``turbulent'' behavior observed in recent simulations of several one- and two-dimensional atomistic models of epitaxial growth. [pacs{61.50.Cj, 68.55.Bd, 05.70.Ln, 64.60.Ht}]Comment: 47 pages + 26 postscript figures, submitted to Phys. Rev.

5G Millimeter Wave Cellular System Capacity with Fully Digital Beamforming

Due to heavy reliance of millimeter-wave (mmWave) wireless systems on directional links, Beamforming (BF) with high-dimensional arrays is essential for cellular systems in these frequencies. How to perform the array processing in a power efficient manner is a fundamental challenge. Analog and hybrid BF require fewer analog-to-digital converters (ADCs), but can only communicate in a small number of directions at a time,limiting directional search, spatial multiplexing and control signaling. Digital BF enables flexible spatial processing, but must be operated at a low quantization resolution to stay within reasonable power levels. This paper presents a simple additive white Gaussian noise (AWGN) model to assess the effect of low resolution quantization of cellular system capacity. Simulations with this model reveal that at moderate resolutions (3-4 bits per ADC), there is negligible loss in downlink cellular capacity from quantization. In essence, the low-resolution ADCs limit the high SNR, where cellular systems typically do not operate. The findings suggest that low-resolution fully digital BF architectures can be power efficient, offer greatly enhanced control plane functionality and comparable data plane performance to analog BF.Comment: To appear in the Proceedings of the 51st Asilomar Conference on Signals, Systems, and Computers, 201

Modern Aerocapture Guidance to Enable Reduced-Lift Vehicles at Neptune

Aerocapture is covered extensively in the literature as means of achieving orbital insertion with dramatic mass-saving results compared to fully-propulsive systems. One of the primary obstacles facing aerocapture is the inherent uncertainty associated with passing through a planets upper atmosphere. In-flight dispersions due to delivery errors, environment variables, and aerodynamic performance impose a large flight envelope. System studies for aerocapture often select high lift-to-drag ratios to compensate for these uncertainties. However, modern predictor-corrector guidance strategies have shown promise in recent years to provide robust control schemes in-situ. These algorithms do not rely on a pre-calculated reference trajectory and instead employ a numerical optimizer to continuously solve nonlinear equations of motion each guidance cycle. Numerical predictor-corrector strategies may provide considerable accuracy over heritage guidance schemes. The goal of this study is reproduce a landmark study of Neptune aerocapture and apply modern guidance to illustrate relative performance improvements and cost-saving potential. Capture constraints based on the theoretical corridor width are considered. Results indicate that heritage vehicles with moderate lift-to-drag ratios, lower than previous studies have indicated, may prove viable for aerocapture at Neptune

The Large Magellanic Cloud: A power spectral analysis of Spitzer images

We present a power spectral analysis of Spitzer images of the Large Magellanic Cloud. The power spectra of the FIR emission show two different power laws. At larger scales (kpc) the slope is ~ -1.6, while at smaller ones (tens to few hundreds of parsecs) the slope is steeper, with a value ~ -2.9. The break occurs at a scale around 100-200 pc. We interpret this break as the scale height of the dust disk of the LMC. We perform high resolution simulations with and without stellar feedback. Our AMR hydrodynamic simulations of model galaxies using the LMC mass and rotation curve, confirm that they have similar two-component power-laws for projected density and that the break does indeed occur at the disk thickness. Power spectral analysis of velocities betrays a single power law for in-plane components. The vertical component of the velocity shows a flat behavior for large structures and a power law similar to the in-plane velocities at small scales. The motions are highly anisotropic at large scales, with in-plane velocities being much more important than vertical ones. In contrast, at small scales, the motions become more isotropic.Comment: 8 pages, 4 figures, talk presented at "Galaxies and their Masks", celebrating Ken Freeman's 70-th birthday, Sossusvlei, Namibia, April 2010. To be published by Springer, New York, editors D.L. Block, K.C. Freeman, & I. Puerar