Invariant Metrics on Nilmanifolds with Positive Topological Entropy

Let T _n denote the group of real n × n upper-triangular matrices with 1s on the diagonal. This paper constructs left-invariant Riemannian and sub-Riemannian metrics on T ₃ T ₄ whose geodesic flow has a subsystem that factors onto a suspended horseshoe. As a corollary, left-invariant Riemannian metrics with positive topological entropy are constructed on all quotients DT _n where D is a discrete subgroup of T _n and n 7.     

Banach space duality of absolute Schur algebras

Matrix Schur product is the entry-wise product of matrices of the same size. It was shown by P. Chaisuriya and S.-C. Ong [1] that (forr1) infinite matrices [a _jk ] such that [|a _jk | ^r ] B(l ² form a Banach algebra under the norm [a _jk ] _r =[|a _jk | ^r ]^1/r and the Schur product. In this paper we demonstrate the existence of Banach space duality within the class of these algebras which is analogous to the classical duality between the spaces of compact, trace class, and bounded operators onl ². Also we obtain a general functional calculus on these algebras, which is used to determine the spectrum and to justify the notion of -norm introduced in [1].This author's research was supported by a sabbatical leave and a Division grant from Colby College.This author's research was supported by a research professorship at Central Michigan University.This author's research was supported by a visiting professorship at Central Michigan University.     

Self-induced shapiro effect in semiconductor superlattices

We observe that the oscillatory motion of photoinjected electron-hole pairs in a biased semiconductor superlattice (Bloch oscillation) is accompanied by a coherent quasi-dc current that is generated by the interaction of the carriers with the self-induced oscillating field. It is shown that this novel macroscopic quantum effect, which is a coherent analog of the Shapiro effect observed in Josephson junctions, can be controlled by changing the spectral position of the exciting laser pulse, which in turn determines the amplitude and phase of the wave packet oscillations. It is thereby possible to coherently drive the electrons either downwards or upwards in the potential of the static field.     

Low temperature scanning force microscopy of the Si(111)-(7x7) surface

A low temperature scanning force microscope (SFM) operating in a dynamic mode in ultrahigh vacuum was used to study the Si(111)- (7x7) surface at 7.2 K. Not only the twelve adatoms but also the six rest atoms of the unit cell are clearly resolved for the first time with SFM. In addition, the first measurements of the short range chemical bonding forces above specific atomic sites are presented. The data are in good agreement with first principles computations and indicate that the nearest atoms in the tip and sample relax significantly when the tip is within a few A of the surface.     

Multiple nano-TiO2 layers to prevent dye/nano-TiO2 from photodegradation under a UV-exposure environment

A device of multiple nano-TiO₂ layers was proposed and fabricated to prevent a dye/nano-TiO₂ region from serious photo-degradation. In this device, the top of the dye/TiO₂ region was designed to be coated using sol-gel nano-TiO₂ thin films to shield UV irradiation from the photo-degradation effect. The sol-gel TiO₂ was prepared in a low temperature (75 °C) and verified as nano-sized particles and an anatase crystalline structure. Different devices of the multi-layer samples fabricated using different compositions of nano-TiO₂ were produced and exposed for UV irradiation tests. Results show that the presence of the sol-gel TiO₂ films coated on top of the dye/TiO₂ region can significantly alleviate the dye photo-degradation under UV irradiation. This multi-layer device can effectively improve the photo-stability of the dye/TiO₂ region in a UV-exposure environment.     

A theoretical approach to substituent effects: Interaction between directly bonded groups in the isoelectronic series XNH3+, XCH3, and XBH3−

Ab initio molecular orbital theory including full geometry optimization at the 4-31G level is used to examine the interactions between substitutents X(X = Li, BeH, BH₂, CH₃, NH₂, OH and F) and substrates Y(Y = NH₃⁺, CH₃, BH₃^?) in the isoelectronic series XNH₃⁺, XCH₃ and XBH₃^?. The results indicate that the interaction energies are dominated by σ-effects. NH₃⁺ is found to interact favorably with the σ-donors (e.g. Li, BeH and BH₂) and unfavorably with the σ-acceptors (e.g. F, OH, NH₂). The reverse pattern a observed for XBH₃^?. The range of interaction energies for XCH₃ is considerably smaller than for XNH₃⁺ and XBH₃^?.     

Collisional frequency shifts in 133Cs fountain clocks

We present a theoretical analysis of the density dependent frequency shift in Cs fountain clocks using the highly constrained binary collision model described by Leo et al. [Phys. Rev. Lett. 85, 2721 (2000)]. We predict a reversal in the clock shift at temperatures near 0.08 microK. Our results show that s waves dominate the collision process. However, as a consequence of the large scattering lengths in Cs the clock shift is strongly temperature dependent and does not reach a constant Wigner-law value until temperatures are less than 0.1 nK.     

A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by David Brown and York (Phys. Rev. D 55, 1977–1984 1997; Phys. Rev. D 47, 1407–1419 1993). We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.