Flow Representation of the Bose-Hubbard Hamiltonian : General Case

In this paper the explicit flow representation to the Bose-Hubbard Hamiltonian is given in the general case. This representation may be useful in creating cat states for the system of atoms trapped in the optical ring.Comment: Latex ; 8 pages ; 1 figure ; minor change

Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime

In this paper we generalize the Jaynes--Cummings Hamiltonian by making use of some operators based on Lie algebras su(1,1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (quant--ph/0202081) under the rotating--wave approximation. In the first half we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1,1) and su(2). In the latter half we carry out a detailed examination of Frasca (quant--ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in Quantum Computation. Lastly we make a brief comment on application to Holonomic Quantum Computation.Comment: Latex file, 24 pages. I added a new section (Quantum Computation), so this paper became self-contained in a certain sens

Asymptotic form of two-point correlation function of the XXZ spin chain

Correlation functions of the XXZ spin chain in the critical regime is studied at zero-temperature. They are exactly represented in the Fredholm determinant form and are related with an operator-valued Riemann-Hilbert problem. Analyzing this problem we prove that a two-point correlation function consisting of sufficiently separated spin operators is expressed by power-functions of the distance between those operators.Comment: 9 pages, LaTeX2e (+ amssymb, amsthm); Proof of Lemma 1 is revise

CGC predictions for p+Pb collisions at the LHC

We present predictions for total multiplicities and single inclusive particle production in proton-lead collisions at the LHC. The main dynamical input in our calculations is the use of solutions of the running coupling BK equation tested in e+p data. We use a Monte-Carlo treatment of the nuclear geometry and either $k_t$-factorization or the hybrid formalisms to describe particle production in the central and forward rapidity regions, respectively.Comment: 17 pages, 13 figures; v1: draft of predictions submitted in time for the upcoming p+Pb test run at the LHC; a more polished version will follow soon. v2: text and discussion cleaned up. v3: added spectra at 5 TeV (pp and p+Pb mb), final version as submitted to Nucl Phys

Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices

Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment

Low-cost directionally-solidified turbine blades, volume 1

A low cost process of manufacturing high stress rupture strength directionally-solidified high pressure turbine blades was successfully developed for the TFE731-3 Turbofan Engine. The basic processing parameters were established using MAR-M 247 and employing the exothermic directional-solidification process in trial castings of turbine blades. Nickel-based alloys were evaluated as directionally-solidified cast blades. A new turbine blade, disk, and associated components were then designed using previously determined material properties. Engine tests were run and the results were analyzed and compared to the originally established goals. The results showed that the stress rupture strength of exothermically heated, directionally-solidified MAR-M 247 turbine blades exceeded program objectives and that the performance and cost reduction goals were achieved

Cavity QED and Quantum Computation in the Weak Coupling Regime

In this paper we consider a model of quantum computation based on n atoms of laser-cooled and trapped linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schr{\" o}dinger equation of the model in the case of n=2 and construct the controlled NOT gate by making use of a resonance condition and rotating wave approximation associated to it. Our method is not heuristic but completely mathematical, and the significant feature is a consistent use of Rabi oscillations. We also present an idea of the construction of three controlled NOT gates in the case of n=3 which gives the controlled-controlled NOT gate.Comment: Latex file, 22 pages, revised version. To appear in Journal of Optics B : Quantum and Semiclassical Optic

Comment on "Estimate of the vibrational frequencies of spherical virus particles"

This comment corrects some errors which appeared in the calculation of an elastic sphere eigenenergies. As a result, the symmetry of the mode having the lowest frequency is changed. Also a direction for calculating the damping of these modes for embedded elastic spheres is given.Comment: comment L. H. Ford Phys. Rev. E 67 (2003) 05192

Quintessence, scalar-tensor theories and non-Newtonian gravity

We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement the scenario of a ``decaying cosmological constant,'' which offers a reasonable understanding of why the observed upper bound of the cosmological constant is smaller than the theoretically natural value by as much as 120 orders of magnitude. In this context, the scalar field can be a candidate of quintessence in a broader sense. We find, however, a serious drawback in the prototype Brans-Dicke model with $\Lambda$ added; a static universe in the physical conformal frame which is chosen to have constant particle masses. We propose a remedy by modifying the matter coupling of the scalar field taking advantage of scale invariance and its breakdown through quantum anomaly. By combining this with a conjecture on another cosmological constant problem coming from the vacuum energy of matter fields, we expect a possible link between quintessence and non-Newtonian gravity featuring violation of Weak Equivalence Principle and intermediate force range, likely within the experimental constraints. A new prediction is also offered on the time-variability of the gravitational constant.Comment: 12 pages LaTex including 1 eps figur