Exact quantum phase model for mesoscopic Josephson junctions

Starting from the two-mode Bose-Hubbard model, we derive an exact version of the standard Mathieu equation governing the wave function of a Josephson junction. For a finite number of particles N, we find an additional cos 2 phi term in the potential. We also find that the inner product in this representation is nonlocal in phi. Our model exhibits phenomena, such as pi oscillations, which are not found in the standard phase model, but have been predicted from Gross-Pitaevskii mean-field theory.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Theory of a mode-locked atom laser with toroidal geometry

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to (h) over bar /2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

Multiple bifurcations in atom optics

We report the observation of multiple bifurcations in a nonlinear Hamiltionian system: laser-cooled atoms in a standing wave with single-frequency intensity modulation. We provide clear evidence of the occurrence of bifurcations by analyzing the atomic momentum distributions.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Subspace wavepacket evolution with Newton polynomials

Time-dependent wavepacket evolution techniques demand the action of the propagator, exp(-iHt/(h)over-bar), on a suitable initial wavepacket. When a complex absorbing potential is added to the Hamiltonian for combating unwanted reflection effects, polynomial expansions of the propagator are selected on their ability to cope with non-Hermiticity. An efficient subspace implementation of the Newton polynomial expansion scheme that requires fewer dense matrix-vector multiplications than its grid-based counterpart has been devised. Performance improvements are illustrated with some benchmark one and two-dimensional examples. (C) 2001 Elsevier Science B.V. All rights reserved.

Prediction of many new exons and introns in Plasmodium falciparum chromosome 2

The current prediction or genes in the Plasmodium falciparum genome database relies upon a limited number of specially developed computer algorithms. We have re-annotated the sequence of chromosome 2 of P. falciparum by a computer-assisted manual analysis. which is described here. Of 161 newly predicted introns, we have experimentally confirmed 98. We regard 110 introns from the previously published analyses as probable, we delete 3, change 26 and add 135. We recognise 214 genes in chromosome 2. We have predicted introns in 121 genes. The increased complexity or gene structure on chromosome 2 is likely to be mirrored by the entire genome. (C) 2001 Elsevier Science B.V. All rights reserved.

Recent advances in processing and characterization of periodic mesoporous MCM-41 silicate molecular sieves

The discovery of periodic mesoporous MCM-41 and related molecular sieves has attracted significant attention from a fundamental as well as applied perspective. They possess well-defined cylindrical/hexagonal mesopores with a simple geometry, tailored pore size, and reproducible surface properties. Hence, there is an ever-growing scientific interest in the challenges posed by their processing and characterization and by the refinement of various sorption models. Further, MCM-41-based materials are currently under intense investigation with respect to their utility as adsorbents, catalysts, supports, ion-exchangers, and molecular hosts. In this article, we provide a critical review of the developments in these areas with particular emphasis on adsorption characteristics, progress in controlling the pore sizes, and a comparison of pore size distributions using traditional and newer models. The model proposed by the authors for adsorption isotherms and criticalities in capillary condensation and hysteresis is found to explain unusual adsorption behavior in these materials while providing a convenient characterization tool.

Quantum slow motion

We investigate the center-of-mass motion of cold atoms in a standing amplitude modulated laser field. We use a simple model to explain the momentum distribution of the atoms after any distinct number of modulation cycles. The atoms starting near a classical phase-space resonance move slower than we would expect classically. We explain this by showing that for a wave packet on the classical resonances we can replace the complicated dynamics in the quantum Liouville equation in phase space by its classical dynamics with a modified potential.

Measurement of qubits

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

Universal state inversion and concurrence in arbitrary dimensions

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters's concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT Superoperator.

Aluminophosphate-based mesoporous molecular sieves: Synthesis and characterization of TAPOs

Mesoporous Ti-substituted aluminophosphates (AlPOs) with a hexagonal, cubic and lamellar pore structure, characteristic of MCM-41, MCM-48, and MCM-50, respectively, were synthesized. The stability of these mesophases upon template removal was studied. The pore structures, surface properties, and local atom environments of Al, P, and Ti of the hexagonal and cubic Ti-containing mesoporous products were extensively characterized using X-ray diffraction, magic angle spinning nuclear magnetic resonance, AAS, XPS, ultraviolet–visible, and adsorption of nitrogen and water vapor techniques while the lamellar mesophase was not further characterized due to its very poor thermal stability. Ti-containing mesoporous AlPO materials show a reasonable thermal stability upon template removal, a hydrophilic surface property, and high porosity showing application potentials in catalytic oxidation of hydrocarbons.

Vitamin B12 and hepatitis C: Molecular biology and human pathology

Cobalamins are stored in high concentrations in the human liver and thus are available to participate in the regulation of hepatotropic virus functions. We show that cyanocobalamin (vitamin B12) inhibited the H(IV internal ribosome entry site (IRES)-dependent translation of a reporter gene in vitro in a dose-dependent manner without significantly affecting the cap-dependent mechanism. Vitamin B12 failed to inhibit translation by IRES elements from encephalomyocarditis virus (EMCV) or classical swine fever virus (CSFV), We also demonstrate a relationship between the total cobalamin concentration in human sera and HCV viral load (a measure of viral replication in the host), The mean viral load was two orders of magnitude greater when the serum cobalamin concentration was above 200 pM (P < 0.003), suggesting that the total cobalamin concentration in an HCV-infected liver is biologically significant in HCV replication.