Biomedical subjects

H Rabitz

Publications and source records attributed to H Rabitz.

At least 19 recordsLinked to original sources

PubMed2000

Whither the future of controlling quantum phenomena?

This review puts into perspective the present state and prospects for controlling quantum phenomena in atoms and molecules. The topics considered include the nature of physical and chemical control objectives, the development of possible quantum control rules of thumb, the theoretical design of controls and their laboratory realization, quantum learning and feedback control in the laboratory, bulk media influences, and the ability to utilize coherent quantum manipulation as a means for extracting microscopic information. The preview of the field presented here suggests that important advances in the control of molecules and the capability of learning about molecular interactions may be reached through the application of emerging theoretical concepts and laboratory technologies.

Journal Article↗

PubMed2000

Optimal control of molecular motion: design, implementation, and inversion.

This paper reviews recent theoretical and experimental developments aimed at controlling molecular motion using tailored laser fields. Emphasis is given to seeking optimal designs for the laser controls and optimal implementation of the controls in the laboratory. Optimization on both counts provides a rigorous, flexible, and physically attractive means for obtaining the best possible control over molecular motion under any specified conditions. The theoretical design and laboratory implementation of control are best effected by a closed-loop process that draws on observations of the evolving molecular sample to steer it toward the desired target. Going beyond control, similar closed-loop laboratory learning concepts may lead to automated molecular monitors for inversion to systematically identify details of molecular Hamiltonians.

Chemistry, Physical↗

PubMed2000

Solving the bound-state Schrodinger equation by reproducing kernel interpolation

Based on reproducing kernel Hilbert space theory and radial basis approximation theory, a grid method is developed for numerically solving the N-dimensional bound-state Schrodinger equation. Central to the method is the construction of an appropriate bounded reproducing kernel (RK) Lambda(alpha)( ||r ||) from the linear operator -nabla(2)(r)+lambda(2) where nabla(2)(r) is the N-dimensional Laplacian, lambda>0 is a parameter related to the binding energy of the system under study, and the real number alpha>N. The proposed (Sobolev) RK Lambda(alpha)(r,r(')) is shown to be a positive-definite radial basis function, and it matches the asymptotic solutions of the bound-state Schrodinger equation. Numerical tests for the one-dimensional (1D) Morse potential and 2D Henon-Heiles potential reveal that the method can accurately and efficiently yield all the energy levels up to the dissociation limit. Comparisons are also made with the results based on the distributed Gaussian basis method in the 1D case as well as the distributed approximating functional method in both 1D and 2D cases.

Journal Article↗

PubMed2000

Solution of the quantum fluid dynamical equations with radial basis function interpolation

The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation psi = exp(R + iS)/[symbol: see text]. The technique rests on the QFD equations depending only on the form, not the magnitude, of the probability density rho = magnitude of psi 2 and on the structure of R = [symbol: see text]/2 ln rho generally being simpler and smoother than rho. The spatially smooth functions R and S are especially suitable for multivariate radial basis function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method rivals, in both efficiency and accuracy, the split-operator and Chebychev expansion methods. The results on a three-dimensional model system indicates that the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase for higher dimensional systems to provide a practical computational tool.

Journal Article↗

PubMed1998

Simulating energy flow in biomolecules: application to tuna cytochrome c.

By constructing a continuity equation of energy flow, one can utilize results from a molecular dynamics simulation to calculate the energy flux or flow in different parts of a biomolecule. Such calculations can yield useful insights into the pathways of energy flow in biomolecules. The method was first tested on a small system of a cluster of 13 argon atoms and then applied to the study of the pathways of energy flow after a tuna ferrocytochrome c molecule was oxidized. Initially, energy propagated faster along the direction perpendicular to the heme plane. This was due to an efficient through-bond mechanism, because the heme iron in cytochrome c was covalently bonded to a cysteine and a histidine. For the oxidation of cytochrome c, electrostatic interactions also facilitated a long-range through-space mechanism of energy flow. As a result, polar or charged groups that were further away from the oxidation site could receive energy earlier than nonpolar groups closer to the site. Another bridging mechanism facilitating efficient long-range responses to cytochrome c oxidation involved the coupling of far-off atoms with atoms that were nearer to, and interacted directly with, the oxidation site. The different characteristics of these energy transfer mechanisms defied a simple correlation between the time that the excess energy of the oxidation site first dissipated to an atom and the distance of the atom from the oxidation site. For tuna cytochrome c, all of the atoms of the protein had sensed the effects of the oxidation within approximately 40 fs. For the length scale of energy transfer considered in this study, the speed of the energy propagation in the protein was on the order of 10(5) m/s.

Animals↗

PubMed1996