Abelian and non-abelian Hall liquids and charge-density wave: quantum number fractionalization in one and two dimensions

Previously, we have demonstrated that, on a torus, the Abelian quantum Hall liquid is adiabatically connected to a charge-density wave as the smaller dimension of the torus is varied. In this work, we extend this result to the non-Abelian bosonic Hall state. The outcome of these works is the realization that the paradigms of quantum number fractionalization in one dimension (polyacetylene) and two dimensions (fractional quantum Hall effect) are, in fact, equivalent.     

Role of lateral alkyl chains in modulation of molecular structures on metal surfaces

We use low energy electron diffraction, scanning tunneling microscopy, first-principles density-functional theory, and molecular mechanics calculations to analyze the adsorption and growth of quinacridone derivatives (QA) with alkyl chains of 4 and 16 carbon atoms on a Ag(110) substrate. Surprisingly, we find that the alkyl chains determine the orientation of the molecular overlayers. While the interaction of QA and the Ag substrate is primarily due to chemical bonding of oxygen to the silver substrate, determining the molecular orientation and preferred adsorption site, the intermolecular arrangement can be adjusted via the length of alkyl chains. We are thus able to fabricate uniform QA films with very well controlled physical properties.     

Critical revision of the ZEPLIN-I sensitivity to WIMP interactions

The ZEPLIN Collaboration has recently published its first result presenting a maximum sensitivity of 1.1×¹⁰⁻⁶$1.1\times {10}^{\mathrm{-6}}$ picobarn for a WIMP mass of ≈60 GeV$\approx 60\text{ GeV}$. The analysis is based on a discrimination method using the different time distribution of scintillation light generated in electron recoil and nuclear recoil interactions. We show that the methodology followed both for the calibration of the ZEPLIN-I detector response and for the estimation of the discrimination power is not reliable enough to claim any background discrimination at the present stage. The ZEPLIN-I sensitivity appears then to be in the order of 10⁻³ picobarn, three orders of magnitude above the claimed 1.1×¹⁰⁻⁶$1.1\times {10}^{\mathrm{-6}}$ picobarn.     

Localization for Involutions in Floer Cohomology

We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included.     

Turnaround Students in High School Mathematics: Constructing Identities of Competence Through Mathematical Worlds

This study investigates prospective secondary teachers’ cognitive difficulties and mathematical ideas involved in making connections among representations. We implemented a three-week teaching unit to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to formulating connections among representations, in the context of conic curves. Qualitative analysis of data showed that most undergraduate mathematics majors and minors in this study struggled with variation, the Cartesian Connection, and other affiliated ideas such as graph as a locus of points. Furthermore, they were unable to identify basic metric relations encoded in algebraic expressions such as the distance between points, which further compounded their difficulties in making connections among representations. We argue that mathematics teacher education needs more focus on these ideas so that their graduates can successfully teach these big ideas in their future instruction.     

Halperin (m,m',n) bilayer quantum Hall states on thin cylinders

The Halperin (m,m',n) bilayer quantum Hall states are studied on thin cylinders. In this limit, charge-density-wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the (331) state and the non-Abelian Moore-Read state in the thin cylinder limit.     

Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser

We demonstrate the imaging of ferroelectric domains in BaTiO3, using an infrared-emitting free-electron laser as a tunable optical source for scattering scanning near-field optical microscopy and spectroscopy. When the laser is tuned into the spectral vicinity of a phonon resonance, ferroelectric domains can be resolved due to the anisotropy of the dielectric properties of the material. Slight detuning of the wavelength gives rise to a contrast reversal clearly evidencing the resonant character of the excitation. The near-field domain contrast shows that the orientation of the dielectric tensor with respect to the sample surface has a clear influence on the near-field signal.     

Tunable optical frequency comb with a crystalline whispering gallery mode resonator

We report on the experimental demonstration of a tunable monolithic optical frequency comb generator. The device is based on four-wave mixing in a crystalline calcium fluoride whispering gallery mode resonator. The frequency spacing of the comb is given by an integer number of the free spectral range of the resonator. We select the desired number by tuning the frequency of the pumping laser with respect to the corresponding resonator mode. We also observe a rich variety of optical combs and high-frequency hyperparametric oscillation, depending on the experimental conditions. A potential application of the comb for generating tunable narrow band frequency microwave signals is demonstrated.     

Volatile organic compounds in head and neck squamous cell carcinoma—An in vitro pilot study

Owing to the lack of specific symptoms, diagnosis of head and neck squamous cell carcinoma (HNSCC) may be delayed. We evaluated volatile organic compounds in tumor samples from patients suffering from HNSCC and tested the hypothesis that there is a characteristic altered composition in the headspace of HNSCC compared with control samples from the same patient with normal squamous epithelium. These results provide the basis for future noninvasive breath analysis in HNSCC. Headspace air of suspected tumor and contralateral control samples in 20 patients were analyzed using ion-mobility spectrometry. Squamous cell carcinoma was diagnosed in 16 patients. In total, we observed 93 different signals in headspace measurements. Squamous cell carcinomas revealed significantly higher levels of volatile cyclohexanol (0.54 ppb_v, 25th to 75th percentiles 0.35–0.86) compared with healthy squamous epithelium (0.24 ppb_v, 25th to 75th percentiles 0.12–0.3; p < 0.001). In conclusion, head and neck squamous cell carcinoma emitted significantly higher levels of volatile cyclohexanol in headspace compared with normal squamous epithelium. These findings form the basis for future breath analysis for diagnosis, therapy control and the follow-up of HNSSC to improve therapy and aftercare.