Critical Galton-Watson processes: The maximum of total progenies within a large window

Consider a critical Galton-Watson process Z={Z_n: n=0,1,...} of index 1+alpha, alpha in (0,1]. Let S_k(j) denote the sum of the Z_n with n in the window [k,...,k+j), and M_m(j) the maximum of the S_k with k moving in [0,m-j]. We describe the asymptotic behavior of the expectation EM_m(j) if the window width j=j_m is such that j/m converges in [0,1] as m tends to infinity. This will be achieved via establishing the asymptotic behavior of the tail probabilities of M_{infinity}(j).Comment: 28 page

Enhanced Binding in non-relativistic QED

We consider a spinless particle coupled to a photon field and prove that even if the Schr\"odinger operator $p^2 + V$ does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant $\alpha$ is small.Comment: simplified versio

Cavity Mode Frequencies and Strong Optomechanical Coupling in Two-Membrane Cavity Optomechanics

We study the cavity mode frequencies of a Fabry-P\'erot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membranes are placed very close to a resonance of the inner cavity formed by them. We also study the cavity finesse of the system and verify that, under the conditions of large coupling, it is not appreciably affected by the presence of the two membranes. The achievable large values of the ratio between the optomechanical coupling and the cavity decay rate, $g/\kappa$, make this two-membrane system the simplest promising platform for implementing cavity optomechanics in the strong coupling regime.Comment: Contribution to the special issue on "Nano-optomechanics" in Journal of Optics, edited by I. Wilson-Rae, J. Sankey and H. Offerhau

Optimal fidelity of teleportation of coherent states and entanglement

We study the Braunstein-Kimble protocol for the continuous variable teleportation of a coherent state. We determine lower and upper bounds for the optimal fidelity of teleportation, maximized over all local Gaussian operations for a given entanglement of the two-mode Gaussian state shared by the sender (Alice) and the receiver (Bob). We also determine the optimal local transformations at Alice and Bob sites and the corresponding maximum fidelity when one restricts to local trace-preserving Gaussian completely positive maps.Comment: 10 pages, 2 figure

Equation of state of two--dimensional 3^3He at zero temperature

We have performed a Quantum Monte Carlo study of a two-dimensional bulk sample of interacting 1/2-spin structureless fermions, a model of $^3$He adsorbed on a variety of preplated graphite substrates. We have computed the equation of state and the polarization energy using both the standard fixed-node approximate technique and a formally exact methodology, relying on bosonic imaginary-time correlation functions of operators suitably chosen in order to extract fermionic energies. As the density increases, the fixed-node approximation predicts a transition to an itinerant ferromagnetic fluid, whereas the unbiased methodology indicates that the paramagnetic fluid is the stable phase until crystallization takes place. We find that two-dimensional $^3$He at zero temperature crystallizes from the paramagnetic fluid at a density of 0.061 \AA$^{-2}$ with a narrow coexistence region of about 0.002 \AA$^{-2}$. Remarkably, the spin susceptibility turns out in very good agreement with experiments.Comment: 7 pages, 7 figure

Local pressure-induced metallization of a semiconducting carbon nanotube in a crossed junction

The electronic and vibrational density of states of a semiconducting carbon nanotube in a crossed junction was investigated by elastic and inelastic scanning tunneling spectroscopy. The strong radial compression of the nanotube at the junction induces local metallization spatially confined to a few nm. The local electronic modifications are correlated with the observed changes in the radial breathing and G-band phonon modes, which react very sensitively to local mechanical deformation. In addition, the experiments reveal the crucial contribution of the image charges to the contact potential at nanotube-metal interfaces

Why do These Match? Explaining the Behavior of Image Similarity Models

Explaining a deep learning model can help users understand its behavior and allow researchers to discern its shortcomings. Recent work has primarily focused on explaining models for tasks like image classification or visual question answering. In this paper, we introduce Salient Attributes for Network Explanation (SANE) to explain image similarity models, where a model's output is a score measuring the similarity of two inputs rather than a classification score. In this task, an explanation depends on both of the input images, so standard methods do not apply. Our SANE explanations pairs a saliency map identifying important image regions with an attribute that best explains the match. We find that our explanations provide additional information not typically captured by saliency maps alone, and can also improve performance on the classic task of attribute recognition. Our approach's ability to generalize is demonstrated on two datasets from diverse domains, Polyvore Outfits and Animals with Attributes 2. Code available at: https://github.com/VisionLearningGroup/SANEComment: Accepted at ECCV 202

Who brings home the bacon? The influence of context on partners' contributions to the household income

Background: Female-breadwinner families represent a relatively new phenomenon in Europe. Little is known about the determinants of this couple type, which sensibly diverts from the traditional economic superiority of men within the household.Objective: This paper studies the contextual correlates of partners’ contribution to the household income, distinguishing between female-breadwinner, male-breadwinner, and equal-income couples. In particular, it focuses on the role of male unemployment rate and the prevalence of gender-egalitarian attitudes as possible explanations for the emergence of female-breadwinner and equal-income couples across European regions and countries.Methods: Using data from the fifth round (2010/2011) of the European Social Survey, integrated with data from the Eurostat database, we model the categorical variable identifying the couple type (male-breadwinner, female-breadwinner, or equal-income couple) by using a multilevel multinomial logistic regression model where individuals are nested within regions and countries.Results: The prevalence of female-breadwinner, male-breadwinner, and equal-income couples varies considerably across European countries as well as within countries. The prevalence of female-breadwinner couples is positively associated with male unemployment, while it is not influenced by the diffusion of gender-egalitarian attitudes. However, the diffusion of gender-egalitarian attitudes matters for explaining the variation in the prevalence of equal-income couples across Europe.Contribution: We add to the literature on partners’ contributions to household income by analysing the spatial distribution and the contextual correlates of female-breadwinner, male-breadwinner, and equal-income couples across European countries and regions.<br/