An effective method for the discrimination of motional anisotropy and chemical exchange

Analysis of the ratio of transverse and longitudinal relaxation rates (R2/R1) is an approach commonly used for estimation of overall correlation time and identification of chemical exchange in biological macromolecules. However, this analysis fails to distinguish between chemical exchange and motional anisotropy. We describe a simple method for identifying chemical exchange and motional anisotropy using the product, R1R2. In the slow tumbling regime, the R1R2 product results in a constant value that is independent of overall correlation time and motional anisotropy. This analysis provides a simple method for rapidly estimating and dissociating the effects of motional anisotropy and chemical exchange in NMR heteronuclear spin relaxation data. We demonstrate the utility of the method with 15N relaxation data collected on the proteins E. coli ribonuclease H and the trimeric E. coli membrane associated lipoprotein lpp.     

Smallβ expansion for infinite chain limit of one dimensional Hubbard model

The one dimensional Hubbard model can be solved exactly. In the limitN , the energy per particle remains finite and can be expressed as an integral. The small expansion in this limit is investigated. Several elementary derivations are presented as well as a simple formula which can be used to generate both small and large beta expansions.     

A simplified SO(6,2) model of SU(3)

A new realization is obtained of the representation of so(6,2) which has been shown recently by Flath and Biedenharn, and also by Bracken and MacGibbon, to define a model of SU(3). In contrast to the realization in terms of six pairs of boson operators used previously, which involved cubic expressions, the new realization involves only quadratic expressions in eight pairs of boson operators, and is manifestly hermitian. Properties of this new oscillator realization, and in particular its advantages over the old realization, are discussed briefly. It is deduced that the representation of so(6,2) is integrable to a unitary group representation.On leave from Department of Mathematics, University of Queensland, Australia     

The quantum group SU q (2), quasitriangularity,and application to theq-rotator model

The quantum group structure of SU _q (2) is described. The property of quasi triangularity and the Yang-Baxter equation are reviewed. A universalR-matrix for this algebra is written down. It is then shown in detail that this R-matrix satisfies the triangularity equations of Drinfeld and the Yang-Baxter equation given the algebraic SU _q (2) commutation relations. In physical terms, the group can be realized as theq-rotator. A specific physical application to diatomic molecules is presented.     

Interpolant polynomial technique applied to the PPP model. I. Asymptotics for excited states of cyclic polyenes in the finite cyclic Hubbard model

For theoretical reasons, and on account of the development of a new interpolation technique, it is useful and important to examine the asymptotic behavior of the solution to the one-dimensional Hubbard model. In this article, it is shown how perturbative expansions for the energy can be developed in the asymptotic region of the relevant coupling for all the relevant excited states of cyclic polyene rings. © 1996 John Wiley & Sons, Inc.     

Quantum phases for a generalized harmonic oscillator

An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.      

Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

The problem of studying the quantum Hall effect on manifolds with non constant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well. PACS numbers: 73.43.-f, 02.30.Jr.     

Hamiltonian for the spin quantum Hall effect solution and derivation based on an SU (2) gauge field

A Hamiltonian to describe a spin quantum Hall effect with two types of spin‐orbit coupling is introduced and the eigenfunctions and eigenvalues are obtained for it. It is shown that this Hamiltonian also results by gauging a kinetic energy Hamiltonian by an SU (2) gauge field. The Berry phase is obtained from the model wavefunction for the model and used to define a filling factor. This allows for the calculation of the spin Hall conductivity. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Determination of Lagrangians from Equations of Motion and Commutator Brackets

The question as to whether a given set of equations, which govern the dynamical evolution of a system, determine a Lagrangian is considered. This problem, which has come to be known as the inverse problem of the calculus of variations, is reviewed and theorems which contain systems of partial differential equations which determine a type of self-adjointness are developed. It is shown that, given a reasonable form for the classical correspondence, the usual quantum commutator brackets can be expressed in terms of classical quantities which satisfy a particular form of these equations.     

Intracavity Sum Frequency Generation Employing a Fiber Ring Resonator

Sum frequency generation using a fiber ring resonator was demonstrated. SFG power of over 40 μW was generated.Efficient SFG was produced for round-trip losses up to -20.5 dB, which is useful for practical applications.