Phase Space Reduction for Star-Products: An Explicit Construction for CP^n

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we can give an easy algebraic description of this star-product. Moreover, going over to a modified star-product on $C^{n+1} \setminus \{ 0 \}$, obtained by an equivalence transformation, this description can be even further simplified, allowing the explicit computation of a closed formula for the star-product on \CP^n which can easily transferred to the domain $SU(n+1)/S(U(1)\times U(n))$.Comment: LaTeX, 17 page

Integral closure of rings of integer-valued polynomials on algebras

Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic polynomial of least degree such that $\mu_a(a)=0$. The ring ${\rm Int}_K(A)$ consists of polynomials in $K[X]$ that send elements of $A$ back to $A$ under evaluation. If $D$ has finite residue rings, we show that the integral closure of ${\rm Int}_K(A)$ is the ring of polynomials in $K[X]$ which map the roots in an algebraic closure of $K$ of all the $\mu_a(X)$, $a\in A$, into elements that are integral over $D$. The result is obtained by identifying $A$ with a $D$-subalgebra of the matrix algebra $M_n(K)$ for some $n$ and then considering polynomials which map a matrix to a matrix integral over $D$. We also obtain information about polynomially dense subsets of these rings of polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix, integral closure, pullback, polynomially dense set. accepted for publication in the volume "Commutative rings, integer-valued polynomials and polynomial functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201

Toeplitz operators on symplectic manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.Comment: 40 page

Marked changes in electron transport through the blue copper protein azurin in the solid state upon deuteration

Measuring electron transport (ETp) across proteins in the solid-state offers a way to study electron transfer (ET) mechanism(s) that minimizes solvation effects on the process. Solid state ETp is sensitive to any static (conformational) or dynamic (vibrational) changes in the protein. Our macroscopic measurement technique extends the use of ETp meas-urements down to low temperatures and the concomitant lower current densities, because the larger area still yields measurable currents. Thus, we reported previously a surprising lack of temperature-dependence for ETp via the blue copper protein azurin (Az), from 80K till denaturation, while ETp via apo-(Cu-free) Az was found to be temperature de-pendent \geq 200K. H/D substitution (deuteration) can provide a potentially powerful means to unravel factors that affect the ETp mechanism at a molecular level. Therefore, we measured and report here the kinetic deuterium isotope effect (KIE) on ETp through holo-Az as a function of temperature (30-340K). We find that deuteration has a striking effect in that it changes ETp from temperature independent to temperature dependent above 180K. This change is expressed in KIE values between 1.8 at 340K and 9.1 at \leq 180K. These values are particularly remarkable in light of the previously reported inverse KIE on the ET in Az in solution. The high values that we obtain for the KIE on the ETp process across the protein monolayer are consistent with a transport mechanism that involves through-(H-containing)-bonds of the {\beta}-sheet structure of Az, likely those of am-ide groups.Comment: 15 pages, 3 figures, 2 Supplementary figure

An explicit formula for the Berezin star product

We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.Comment: 19 pages, to appear in Lett. Math. Phy

A holomorphic representation of the Jacobi algebra

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI: 10.1142/S0129055X12920018, references update

Light Induced Increase of Electron Diffusion Length in a p n Junction Type CH3NH3PbBr3 Perovskite Solar Cell

High band gap, high open circuit voltage solar cells with methylammonium lead tribromide MAPbBr3 perovskite absorbers are of interest for spectral splitting and photoelectrochemical applications, because of their good performance and ease of processing. The physical origin of high performance in these and similar perovskite based devices remains only partially understood. Using cross sectional electron beaminduced current EBIC measurements, we find an increase in carrier diffusion length in MAPbBr3 Cl based solar cells upon low intensity a few percent of 1 sun intensity blue laser illumination. Comparing dark and illuminated conditions, the minority carrier electron diffusion length increases about 3.5 times from Ln 100 50 nm to 360 22 nm. The EBIC cross section profile indicates a p amp; 8722;n structure between the n FTO TiO2 and p perovskite, rather than the p amp; 8722;i amp; 8722;n structure, reported for the iodide derivative. On the basis of the variation in space charge region width with varying bias, measured by EBIC and capacitance amp; 8722;voltage measurements, we estimate the net doping concentration in MAPbBr3 Cl to be 3 amp; 8722;6 1017 cm amp; 8722;

Near-flat space limit and Einstein manifolds

We study the near-flat space limit for strings on AdS(5)xM(5), where the internal manifold M(5) is equipped with a generic metric with U(1)xU(1)xU(1) isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS(5)xS(5), as the global symmetries are reduced in the most general case. When M(5) is a Sasaki-Einstein space like T(1,1), Y(p,q) and L(p,q,r), whose dual CFT's have N=1 supersymmetry, the near-flat space limit gives the same bosonic sector of the sigma model found for AdS(5)xS(5). This indicates the generic presence of integrable subsectors in AdS/CFT.Comment: 30 pages, 1 figur

On Gammelgaard's formula for a star product with separation of variables

We show that Gammelgaard's formula expressing a star product with separation of variables on a pseudo-Kaehler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal Fock space. We prove this inversion formula directly and thus offer an alternative approach to Gammelgaard's formula which gives more insight into the question why the directed graphs in his formula have no cycles.Comment: 29 pages, changes made in the last two section