Stereocontrol of attosecond time-scale electron dynamics in ABCU using ultrafast laser pulses: a computational study

The attosecond time-scale electronic dynamics induced by an ultrashort laser pulse is computed using a multi configuration time dependent approach in ABCU (C(10)H(19)N), a medium size polyatomic molecule with a rigid cage geometry. The coupling between the electronic states induced by the strong pulse is included in the many electron Hamiltonian used to compute the electron dynamics. We show that it is possible to implement control of the electron density stereodynamics in this medium size molecule by varying the characteristics of the laser pulse, for example by polarizing the electric field either along the N-C axis of the cage, or in the plane perpendicular to it. The excitation produces an oscillatory, non-stationary, electronic state that exhibits localization of the electron density in different parts of the molecule both during and after the pulse. The coherent oscillations of the non-stationary electronic state are also demonstrated through the alternation of the dipole moment of the molecule.     

The weight twoK-theory of fields

We verify the weight-two portion of the Quillen-Lichtenbaum conjectures, relating the modn weight-twoK-groups of a field with the appropriate étale cohomology groups. This extends the work of Merkurjev and Suslin onK ₂ of a field, and the works of Suslin and the author on the indecomposableK ₃ of a field.Partially supported by the NSF.     

Relativistic field formulation of simultaneous quantum measurement

The simultaneous measurement of Dirac field operators is formulated in analogy to the work of von Neumann and Arthurs-Kelly. Meter fields are coupled to the system field with a relativistically invariant bilinear interaction. Measurement of vacuum meter field expectation values provides for the simultaneous measurement of noncommuting system components. It is shown that two meter coupling allows for a simultaneous minimum in the variance of the subsequent meter measurements. A pseudoscalar self-interaction of the Dirac field is shown to allow simultaneous measurement of positive energy field operators with negative energy meters. The simultaneous measurement ofn noncommuting field operators is obtained by coupling the system ton fermionic fields. Also, in this paper the related concept of mutual simultaneous measurement is developed. This requires that any operators in the enlarged Hilbert space are measurable by the remaining fields as meters. System embedding into a larger Hilbert space results in added noise due to the zero point motion of the meter fields. By the negentropy principle of Brillouin, the added noise is equivalent to entropy. A criterion determining the interaction among fields is that the averaged added noise in the components of each quantum field is minimized. This criterion defines an optimum fermionic mass matrix through the determination of the entangling interaction.1. This work was sponsored by the Department of the Air Force under contract F19628-90-C-0002.     

Fluorescence lifetime imaging of oxygen in living cells

The usefulness of the fluorescent probe ruthenium tris(2,2′-dipyridyl) dichloride hydrate (RTDP) for the quantitative imaging of oxygen in single cells was investigated utilizing fluorescence lifetime imaging. The results indicate that the fluorescence behavior of RTDP in the presence of oxygen can be described by the Stem-Volmer equation. This shows that fluorescence quenching by oxygen is a dynamic quenching process. In addition, it was demonstrated that the fluorescence lifetime of RTDP is insensitive to pH, ion concentration, and cellular contents. This implies that a simple calibration procedure in buffers can be used to quantify oxygen concentrations within cells. First fluorescence imaging experiments on J774 macrophages show a nonuniform fluorescence intensity and a uniform fluorescence lifetime image. This indicates that the RTDP is heterogeneously partitioned throughout the cells, while the oxygen concentration is constant.     

Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population is governed by correlation functions that although being formally down by powers ofN (the population size), nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean-field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.     

On the simultaneous measurement of position and momentum: Naimark embeddings and projections

Single and double meter simultaneous measurements of a harmonic oscillator are reviewed and compared. Naimark extensions are constructed and relevant projection properties are exhibited for both cases. The theory is extended to the simultaneous measurement of squeezed position and momentum measurements.     

Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity

Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity. Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309–318) who obtained such results for the eigenvalues of the fixed membrane problem.     

Information content analysis for reaction of oreinted molecules

Experimental data on the orientation dependence of the reactivity in NO + O₃ and Rb + CH₃I collisions is analyzed. Error limits of the measurements are used to conclude that one low-order, or “Legendre moment” accounts for much of the observed dependence on the orientation. The same procedure applies also to data on the polarization of the products.