Quantum Nonlocality of Photon Pairs in Interference in a Mach-Zehnder Interferometer

Nonlocal character of entangled photon pairs generated in spontaneous parametric downconversion is demonstrated. One photon from a pair propagates through a Mach-Zehnder interferometer and is detected in coincidence-count measurement with its twin. Width of the coincidence-count interference pattern (measured for various values of path difference in the Mach-Zehnder interferometer) depends on spectral width of the twin as a result of entanglement of photons in a pair. The experimental setup is analyzed for a Gaussian spectral filter and a Fabry-Perot resonator. It is shown that nonlocal interference is much stronger for cw pumping in comparison with femtosecond pulsed pumping for values of parameters commonly used in spontaneous parametric downconversion experiments.     

Profinite groups of finite cohomological dimension

Let 1→N→G→G/N→1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n:=cd_p(G)<∞ and if the order of $\text{H}{}^{\mathrm{k}}\text{(N,}\text{F}{}_{\mathrm{p}}\text{)}$ is finite for k:=cd_p(N), the virtual cohomological p-dimension of G/N equals n?k. To cite this article: T. Weigel, P. Zalesskii, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

An exponential lower bound to the size of bounded depth frege proofs of the pigeonhole principle

We prove lower bounds of the form exp(n^{ε d}), ε_d > 0, on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d, for any constant d. This is the largest lower bound for the strongest proof system, for which any superpolynomial lower bounds are known.     

Oxidative dehydrogenation of crotonaldehyde overK2HPMo12O40catalyst

Summary The oxidative dehydrogenation of crotonaldehyde to furan and maleic anhydride was carried out over K₂HPMo₁₂O₄₀catalyst. A positive effect of water vapor on furan formation is explained by ability of the catalyst to isomerize 2E- to 2Z-crotonaldehyde.</o:p>     

An engine breaking the ΩEP-property

We present a construction which shows that some special continua do not have the nonwandering-eventually-periodic property. The construction applies e.g. to the topologist's sin curve and to the harmonic fan.     

Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces

Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D₄,E₆,E₇,E₈). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z², where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D₄ is the Cherednik algebra of type C^∨C₁, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI.     

Diffractive dissociation reaction np → Λ0K0p for incident neutron momenta between 30 and 70 GeV/c BIS-2 collaboration

We present results of the exclusive diffractive reaction np ⁰K⁰p at 0·08 < |t|< 0·53 GeV²/c² and momenta between 30–70 GeV/c at the Serpukhov neutron beam. Thet-dependence is exp (Bt) withB= 11·4± 2·3 (GeV/c)^–2 and it exhibits the diffractive minimum at ¦t¦ 0·28 GeV²/c² for ⁰K⁰ massesM < 1·8 GeV/c².B decreases with increasingM. Correlation with the beam direction is observed in the rest frame of the ⁰K⁰ system: the cross section rises for the forward-going ⁰. The rise is more pronounced for higherM. The cross section of reaction np ⁰K⁰p for 0<|t|< 0·53 GeV²/c² is 10·3 ± 2·5 ± 2·8 b.