Topological Correlations in a Layer Adsorbed on a Crystal Surface

The incoherent scattering of electrons by a layer adsorbed at a single crystal surface is determined by the topological correlations of elements forming the adsorbed layer. The model for the description of atoms or molecules adsorbed on the surface is formulated in terms of occupation operators which are expressed in terms of pseudospin operators with a given spin value. The correlations can be determined by the fluctuation dissipation theorem in connection with the susceptibility or given directly by means of the Green functions properly chosen. An example of the topological or chemical disorder of two components is considered in detail. The calculations of the topological correlations allow us to find the incoherent scattering amplitude as a function of the surface coverage which can be experimentally detected.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Pseudodifferential multi-product representation of the solution operator of a parabolic equation

By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on $\R^n$ as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof is based on an effective use of the Weyl calculus and the Fefferman-Phong inequality.Comment: Comm. Partial Differential Equations to appear (2009) 28 page

Experimental observation of spatial antibunching of photons

We report an interference experiment that shows transverse spatial antibunching of photons. Using collinear parametric down-conversion in a Young-type fourth-order interference setup we show interference patterns that violate the classical Schwarz inequality and should not exist at all in a classical description.Comment: 4 pages, 7 figure

A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement

Mucin Variable Number Tandem Repeat Polymorphisms and Severity of Cystic Fibrosis Lung Disease: Significant Association with MUC5AC

Variability in cystic fibrosis (CF) lung disease is partially due to non-CFTR genetic modifiers. Mucin genes are very polymorphic, and mucins play a key role in the pathogenesis of CF lung disease; therefore, mucin genes are strong candidates as genetic modifiers. DNA from CF patients recruited for extremes of lung phenotype was analyzed by Southern blot or PCR to define variable number tandem repeat (VNTR) length polymorphisms for MUC1, MUC2, MUC5AC, and MUC7. VNTR length polymorphisms were tested for association with lung disease severity and for linkage disequilibrium (LD) with flanking single nucleotide polymorphisms (SNPs). No strong associations were found for MUC1, MUC2, or MUC7. A significant association was found between the overall distribution of MUC5AC VNTR length and CF lung disease severity (p = 0.025; n = 468 patients); plus, there was robust association of the specific 6.4 kb HinfI VNTR fragment with severity of lung disease (p = 6.2 x 10(-4) after Bonferroni correction). There was strong LD between MUC5AC VNTR length modes and flanking SNPs. The severity-associated 6.4 kb VNTR allele of MUC5AC was confirmed to be genetically distinct from the 6.3 kb allele, as it showed significantly stronger association with nearby SNPs. These data provide detailed respiratory mucin gene VNTR allele distributions in CF patients. Our data also show a novel link between the MUC5AC 6.4 kb VNTR allele and severity of CF lung disease. The LD pattern with surrounding SNPs suggests that the 6.4 kb allele contains, or is linked to, important functional genetic variation

High-sensitivity AC-charge detection with a MHz-frequency fluxonium qubit

Owing to their strong dipole moment and long coherence times, superconducting qubits have demonstrated remarkable success in hybrid quantum circuits. However, most qubit architectures are limited to the GHz frequency range, severely constraining the class of systems they can interact with. The fluxonium qubit, on the other hand, can be biased to very low frequency while being manipulated and read out with standard microwave techniques. Here, we design and operate a heavy fluxonium with an unprecedentedly low transition frequency of $1.8~\mathrm{MHz}$. We demonstrate resolved sideband cooling of the ``hot'' qubit transition with a final ground state population of $97.7~\%$, corresponding to an effective temperature of $23~\mu\mathrm{K}$. We further demonstrate coherent manipulation with coherence times $T_1=34~\mu\mathrm{s}$, $T_2^*=39~\mu\mathrm{s}$, and single-shot readout of the qubit state. Importantly, by directly addressing the qubit transition with a capacitively coupled waveguide, we showcase its high sensitivity to a radio-frequency field. Through cyclic qubit preparation and interrogation, we transform this low-frequency fluxonium qubit into a frequency-resolved charge sensor. This method results in a charge sensitivity of $33~\mu\mathrm{e}/\sqrt{\mathrm{Hz}}$, or an energy sensitivity (in joules per hertz) of $2.8~\hbar$. This method rivals state-of-the-art transport-based devices, while maintaining inherent insensitivity to DC charge noise. The high charge sensitivity combined with large capacitive shunt unlocks new avenues for exploring quantum phenomena in the $1-10~\mathrm{MHz}$ range, such as the strong-coupling regime with a resonant macroscopic mechanical resonator