Vibrational branching ratios and shape resonant photoionization dynamics in N_2O

Vibrational branching ratios and photoelectron asymmetry parameters for alternative vibrational modes in the photoionization of N_2O(7σ^(−1)) have been studied using accurate photoelectron continuum orbitals. Earlier dispersed ionic fluorescence measurements [E. D. Poliakoff, M. H. Ho, M. G. White, and G. E. Leroi, Chem. Phys. Lett. 130, 91 (1986)] revealed strong non‐Franck–Condon vibrational ion distributions for both the symmetric and antisymmetric stretching modes at low photoelectron energies. Our results establish that these features arise from a σ shape resonance which, based on its dependence on internuclear geometry, must be associated with the molecular framework as a whole and not with either of its fragments, N–N or N–O. This behavior accounts for the more pronounced deviations of the vibrational branching ratios from Franck–Condon values observed in the symmetric than in the antisymmetric mode. The σ continuum also supports a second shape resonance at higher energy which does not influence the vibrational branching ratios but is quite evident in the photoelectron asymmetry parameters around a photon energy of 40 eV. These vibrationally resolved studies of the photoelectron spectra of this polyatomic system provide an interesting example of the rich shape resonant behavior that can be expected to arise in polyatomic molecules with their alternative vibrational modes

Shape resonance behavior in 1π_g photoionization of O_2

We report calculations of vibrationally resolved cross sections and photoelectron angular distributions for photoionization of O_2 leading to the X^ 2 Π_g (ν^+ =0–4) states of O^+_2 using Hartree–Fock continuum photoelectron orbitals. These studies were motivated by recent results which show that a σ_u shape resonance plays a dominant role in producing non‐Franck–Condon vibrational distributions in resonant multiphoton ionization of O_2 via the C ^3Π_g (1π_g3sσ_g) Rydberg state. In the present study, we investigate how this shape resonance influences photoionization dynamics in single‐photon ionization. Below 21 eV photon energy, we find significant non‐Franck–Condon effects in the vibrational branching ratios as well as in the vibrationally resolved photoelectron angular distributions. Substantial autoionization hinders a direct comparison between theory and experiment

Multiplet-specific shape resonant features in vibrationally resolved 3σ_g photoionization of O_2

We report multiplet‐specific vibrationally resolved photoionization cross sections and photoelectron angular distributions for the 3σ_g orbital of O_2 leading to the v^+=0–3 levels of the b^4Σ^−_g and B^2Σ^−_g states of O^+_2. These studies were motivated by recent work which shows significant nonstatistical behavior in the vibrationally unresolved spectrum at low photoelectron energies arising from the sensitivity of the kσ_u shape resonance to the multiplet‐specific exchange potentials. In addition to the anticipated non‐Franck–Condon vibrational distributions arising from the kσ_u shape resonance, we also find substantial nonstatistical effects in our vibrationally resolved cross sections and particularly in our photoelectron angular distributions over a broad energy range. Extensive electronic autoionization due to Rydberg levels leading to the c^ 4Σ^−_u (2σ^(−1)_u) ion makes it difficult to assess these effects in the available experimental data

A rigorous analysis of the cavity equations for the minimum spanning tree

We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations techniques. For the limit case of the Spanning tree we prove that the fixed point of the algorithm arising from the cavity equations leads to the global optimum.Comment: 5 pages, 1 figur

Characterization of Collective Gaussian Attacks and Security of Coherent-State Quantum Cryptography

We provide a simple description of the most general collective Gaussian attack in continuous-variable quantum cryptography. In the scenario of such general attacks, we analyze the asymptotic secret-key rates which are achievable with coherent states, joint measurements of the quadratures and one-way classical communication.Comment: 4 pages, 1 figure + 1 Table, REVteX. More descriptive titl

Exponentially Enhanced Quantum Metrology

We show that when a suitable entanglement generating unitary operator depending on a parameter is applied on N qubits in parallel, and an appropriate observable is measured, a precision of order 2 raised to the power (-N) in estimating the parameter may be achieved. This exponentially improves the precision achievable in classical and in quantum non-entangling parallel strategies. We propose a quantum-optics model of laser light interacting with an N-qubit system, say a polyatomic molecule, via a generalized Jaynes-Cummings interaction which, in principle, could achieve the exponentially enhanced precision.Comment: 4 pages, 1 postscript figure ; typos correcte

On Strong Superadditivity of the Entanglement of Formation

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation $E_F$ and the conjugate function $E^*$ of the entanglement function E(\rho)=S(\trace_A\rho). We then consider the conjectured strong superadditivity of the entanglement of formation $E_F(\rho) \ge E_F(\rho_I)+E_F(\rho_{II})$, where $\rho_I$ and $\rho_{II}$ are the reductions of $\rho$ to the different Hilbert space copies, and prove that it is equivalent with subadditivity of $E^*$. As an application, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for all non-trace-preserving quantum channels, when purity is measured by Schatten $p$-norms for $p$ tending to 1.Comment: 11 pages; refs added, explanatory improvement

Shape-resonance-induced non-Franck–Condon effects in (2+1) resonance enhanced multiphoton ionization of the C 3Πg state of O2

We show that strong non-Franck–Condon effects observed in (2+1) resonance enhanced multiphoton ionization of the C 3Pig state of O2 are due to the ksigmau shape resonance previously observed in single-photon studies of diatomic molecules. Calculated vibrational branching ratios for the v=2,3 levels of the C 3Πg state are in reasonable agreement with experiment. Certain discrepancies remain in comparing theoretical results with the measured spectra, and possible electron-correlation effects which underly this are discussed

Clustering by soft-constraint affinity propagation: Applications to gene-expression data

Motivation: Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing techniques was proposed by Frey and Dueck \cite{Frey07}. In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to, and exemplars have to refer to themselves. Albeit its proved power, AP in its present form suffers from a number of drawbacks. The hard constraint of having exactly one exemplar per cluster restricts AP to classes of regularly shaped clusters, and leads to suboptimal performance, {\it e.g.}, in analyzing gene expression data. Results: This limitation can be overcome by relaxing the AP hard constraints. A new parameter controls the importance of the constraints compared to the aim of maximizing the overall similarity, and allows to interpolate between the simple case where each data point selects its closest neighbor as an exemplar and the original AP. The resulting soft-constraint affinity propagation (SCAP) becomes more informative, accurate and leads to more stable clustering. Even though a new {\it a priori} free-parameter is introduced, the overall dependence of the algorithm on external tuning is reduced, as robustness is increased and an optimal strategy for parameter selection emerges more naturally. SCAP is tested on biological benchmark data, including in particular microarray data related to various cancer types. We show that the algorithm efficiently unveils the hierarchical cluster structure present in the data sets. Further on, it allows to extract sparse gene expression signatures for each cluster.Comment: 11 pages, supplementary material: http://isiosf.isi.it/~weigt/scap_supplement.pd