Ergodic semigroups of positivity preserving self-adjoint operators

We prove that an ergodic semigroup of positivity preserving self-adjoint operators is positivity improving. We also present a new proof (using Markov techniques) of the ergodicity of semigroups generated by spatially cutoff P(?)₂ Hamiltonians.     

Geometric methods in multiparticle quantum systems

Technically simple proofs are given of the HVZ theorem on the bottom of the essential spectrum of multiparticle systems and of Combes' result on completeness below the lowest three body threshold. The first proof is a variant of a proof of Enss and a decendent of Zhislin's original proof. Finally, we apply our methods to the bound state spectrum.On leave from Princeton University. Research support in part by U.S. National Science Foundation under grants MPS-75-11864 and MPS-75-20638     

Aspects of supersymmetric quantum mechanics

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E₀ = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P_c(y) is identical to |Ψ₀(y)|² in the quantum theory.     

Range of the screened coulomb interaction in electrolytes and double layer problems

It is shown that the range of the Coulomb interaction in unsymmetric electrolytes at large distances is determined not by the Debye screening length, but by a rather more complicated function of the density, which is evaluated explicitly.     

Stimulus-dependent spatial patterns of response in SI cortex

Background  

Recently we reported that vibrotactile flutter stimulation of a skin locus at different amplitudes evokes an optical response confined to the same local region of the primary somatosensory cortex (SI), where its overall magnitude varies proportionally to the flutter amplitude. In this report, we characterize the impact of the flutter amplitude on the spatial patterns of activity evoked within the responding SI region.     

Synthesis of the carbocyclic skeleton of abyssomicins C and D

[reaction: see text] Intramolecular Diels-Alder substrate trienyl methylenebutenolide 5 was prepared in six steps by coupling 3-methoxy-4-methylenebutenolide (6) with trienone keto aldehyde 7. Heating 5 in CHCl(3) for 2 d at 70 degrees C afforded 80% of a single Diels-Alder adduct 4 with the complete carbon skeleton of abyssomicin C. Addition of thiophenoxide to the enone double bond of 4 followed by an intramolecular Michael addition afforded 15 with the abyssomicin D carbon skeleton.     

Electrochemistry in ultrahigh vacuum: underpotential deposition of Al on polycrystalline W and Au from room temperature AlCl(3)/1-ethyl-3-methylimidazolium chloride melts

The voltammetric characteristics of polycrystalline Au and W electrodes cleaned (thermal annealing at 1100 K) and characterized (Auger electron spectroscopy) in ultrahigh vacuum (UHV) have been examined in ultrapure AlCl(3)/1-ethyl-3-methylimidazolium chloride (EtMeImCl) melts in UHV. These experiments were performed using a custom-designed transfer system that allows for the all-Al electrochemical cell to be filled with EtMeImCl in an auxiliary UHV chamber and later transferred under UHV to the main UHV chamber that houses the Auger electron spectrometer. The results obtained for the underpotential (UPD) and bulk deposition of Al on Au were found to be very similar to those reported in the literature for measurements carried out under 1 atm of an inert gas in a glovebox. For the far more reactive W surfaces, voltammetric features ascribed to the stripping of underpotential-deposited Al could be observed following a single scan from 1.0 V vs Al(3+)/Al to a potential negative enough for bulk deposition of Al to ensue. This behavior is unlike that reported in the literature for experiments performed in a glovebox, which required either extensive potential cycling in the Al bulk deposition and stripping region or excursions to potentials positive enough for chlorine evolution to ensue for Al UPD features to be clearly discerned. These observations open new prospects for fundamental electrochemical studies of well-characterized, highly reactive metals, including single crystals, in a variety of low vapor pressure ionic liquids.     

Schrödinger Operators with Few Bound States

We show that whole-line Schrödinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast. We also prove the following result for one- and two-dimensional Schrödinger operators, H, with bounded positive ground states: Given a potential V, if both H±V are bounded from below by the ground-state energy of H, then V≡0.D. D. was supported in part by NSF grant DMS–0227289.R. K. was supported in part by NSF grant DMS–0401277.B. S. was supported in part by NSF grant DMS–0140592.     

Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging

We describe a novel microscopy technique for quantitative phase-contrast imaging of a transparent specimen. The technique is based on depth-resolved phase information provided by common path spectral-domain optical coherence tomography and can measure minute phase variations caused by changes in refractive index and thickness inside the specimen. We demonstrate subnanometer level path-length sensitivity and present images obtained on reflection from a known phase object and human epithelial cheek cells.