Double-ended queues and joint moments of left-right canonical operators on full Fock space

We follow the guiding line offered by canonical operators on the full Fock space, in order to identify what kind of cumulant functionals should be considered for the concept of bi-free independence introduced in the recent work of Voiculescu. By following this guiding line we arrive to consider, for a general noncommutative probability space (A, phi), a family of "(l,r)-cumulant functionals" which enlarges the family of free cumulant functionals of the space. In the motivating case of canonical operators on the full Fock space we find a simple formula for a relevant family of (l,r)-cumulants of a (2d)-tuple (A_1, ..., A_d, B_1, ..., B_d), with A_1, ... , A_d canonical operators on the left and B_1, ... , B_d canonical operators on the right. This extends a known one-sided formula for free cumulants of A_1, ..., A_d, which establishes a basic operator model for the R-transform of free probability.Comment: In this (final) version, the introduction was re-written to better show the motivation for the question considered in the pape

Exactness of the Fock space representation of the q-commutation relations

We show that for all q in the interval (-1,1), the Fock representation of the q-commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In particular, this implies that the C*-algebra generated by the Fock representation of the q-commutation relations is exact. An immediate consequence is that the q-Gaussian von Neumann algebra is weakly exact for all q in the interval (-1,1).Comment: 20 page

Nb-doped TiO2 thin films deposited by spray pyrolysis method

Undoped TiO2 and Nb-doped TiO2 thin films have been deposited by spray pyrolysis method on ITO/glass substrates. All the as-deposited films are amorphous, as shown by X-Ray Diffraction. Under certain conditions of heat-treatment in air, the films deposited by pyrolysis became pure anatase. The hydrophilic properties of all the films were investigated, and a comparison was made as a function of the heat treatment, and as a function of Nb doping. Contact angles lower then 3 deg. have been obtained, after irradiation times specific for each film

Density of States of Quantum Spin Systems from Isotropic Entanglement

We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.Comment: 4+ pages, content is as in the published versio

Complete diagrammatics of the single ring theorem

Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators. We also rederive the Haagerup-Larsen theorem and show how its recent extension to the eigenvector correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio

Sequential localization of a complex electron fluid

Complex and correlated quantum systems with promise for new functionality often involve entwined electronic degrees of freedom. In such materials, highly unusual properties emerge and could be the result of electron localization. Here, a cubic heavy fermion metal governed by spins and orbitals is chosen as a model system for this physics. Its properties are found to originate from surprisingly simple low-energy behavior, with two distinct localization transitions driven by a single degree of freedom at a time. This result is unexpected, but we are able to understand it by advancing the notion of sequential destruction of an SU(4) spin-orbital-coupled Kondo entanglement. Our results implicate electron localization as a unified framework for strongly correlated materials and suggest ways to exploit multiple degrees of freedom for quantum engineering.Comment: 21 pages, 4 figures (preprint format

Experimental Validation of the Largest Calculated Isospin-Symmetry-Breaking Effect in a Superallowed Fermi Decay

A precision measurement of the gamma yields following the beta decay of 32Cl has determined its isobaric analogue branch to be (22.47^{+0.21}_{-0.19})%. Since it is an almost pure Fermi decay, we can also determine the amount of isospin-symmetry breaking in this superallowed transition. We find a very large value, delta_C=5.3(9)%, in agreement with a shell-model calculation. This result sets a benchmark for isospin-symmetry-breaking calculations and lends support for similarly-calculated, yet smaller, corrections that are currently applied to 0+ -> 0+ transitions for tests of the Standard Model

High-throughput amplicon sequencing reveals distinct communities within a corroding concrete sewer system

This study investigated the variation in microbially induced concrete corrosion communities at different circumferential locations of a real sewer pipe and the effects of a wastewater flooding event on the community. Three distinct microbial community groups were found in different corrosion samples. The physico-chemical properties of the corrosion layers and the microbial communities were distinct for the cross-sectional positions within the pipe, ie ceiling, wall and tidal zones. The microbial communities detected from the same positions in the pipe were consistent over the length of the pipe, as well as being consistent between the replicate pipes. The dominating ceiling communities were members of the bacterial orders Rhodospirillales, Acidithiobacillales, Actinomycetales, Xanthomonadales and Acidobacteriales. The wall communities were composed of members of the Xanthomonadales, Hydrogenophilales, Chromatiales and Sphingobacteriales. The tidal zones were dominated by eight bacterial and one archaeal order, with the common physiological trait of anaerobic metabolism. Sewage flooding within the sewer system did not change the tidal and wall communities, although the corrosion communities in ceiling samples were notably different, becoming more similar to the wall and tidal samples. This suggests that sewage flooding has a significant impact on the corrosion community in sewers

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat