We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both secondand third-harmonic generation via χ (2) and χ (3) nonlinearities. We find that conversion efficiency is optimized for a certain “critical” power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. Thes...

The multipartite entangled state n p χ χ χ ,..., , , 3 2 for the total momentum and relative coordinates of n particles is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p p e 1 λ → , i i i e χ χ λ → , n i ,..., 2 = , in the state n p χ χ χ ,..., , , 3 2 is investigated.

The chromatic vertex (resp. edge) stability number vsχ(G) esχ(G)) of a graph G is the minimum vertices edges) whose deletion results in H with χ(H)=χ(G)−1. In main result it proved that if χ(G)∈{Δ(G),Δ(G)+1}, then vsχ(G)=ivsχ(G), where ivsχ(G) independent number. need not hold for graphs χ(G)≤Δ(G)+12. It χ(G)>Δ(G)2+1, vsχ(G)=esχ(G). A Nordhaus–Gaddum-type on also given.

The expected trilepton signals from p¯ p → χ ± 1 χ 0 2 → (χ 0 1 ℓ ± ν)(χ 0 1 ℓ ′+ ℓ ′−) will be converted into hadronically quiet multilepton signals, if the two final χ 0 1 have leptonic R-parity-violating (RPV) decays χ 0 1 → ℓℓ ′ ν. We make illustrative calculations of the acceptance for these spectacular RPV signals, and point out that distinctive multilepton signals are possible even when ...

A k-decomposition (G1, . . . , Gk) of a graph G is a partition of its edge set to form k spanning subgraphs G1, . . . , Gk. The classical theorem of Nordhaus and Gaddum bounds χ(G1) + χ(G2) and χ(G1)χ(G2) over all 2-decompositions of Kn. For a graph parameter p, let p(k;G) denote the maximum of ∑k i=1 p(Gi) over all k-decompositions of the graph G. The clique number ω, chromatic number χ, list ...

Using a sample of 9.7 × 10 BB meson pairs collected with the CLEO detector, we study B decays to the χc1 and χc2 charmonia states, which are reconstructed via their radiative decays to J/ψ. We first measure the branching fraction for inclusive χc1 production in B decays to be B(B → χc1X) = (4.14 ± 0.31 ± 0.40) × 10 , where the first uncertainty is statistical and the second one is systematic. W...

A set of problems is offered to accompany the set of lectures with the above title. Topic 1: Coherent States 1.1 Let {|n〉}, n = 0, 1, 2, 3, . . ., denote a complete set of orthonormal vectors in an abstract Hilbert space , with 〈m|n〉 = δmn. Next, let |χ〉 = √ 1 − |χ|2 |0〉 + χ|1〉 , for all complex χ, 0 ≤ |χ| ≤ 1, denote a family of two-dimensional vectors. a) If χ→ χ in the sense of complex numbe...