Archive ouverte UNIGE | last documentshttps://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGEengHolomorphic anomaly and quantum mechanicshttps://archive-ouverte.unige.ch/unige:101098https://archive-ouverte.unige.ch/unige:101098We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail the double-well potential and the cubic and quartic oscillators, and we calculate the WKB expansion of their quantum free energies by using the direct integration of the anomaly equations. We reproduce in this way all known results about the quantum periods of these models, which we express in terms of modular forms on the WKB curve. As an application of our results, we study the large order behavior of the WKB expansion in the case of the double well, which displays the double factorial growth typical of string theory.Wed, 03 Jan 2018 16:08:41 +0100On the inequivalence of the CH and CHSH inequalities due to finite statisticshttps://archive-ouverte.unige.ch/unige:94565https://archive-ouverte.unige.ch/unige:94565Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.Wed, 31 May 2017 14:30:44 +0200Extremal correlations of the tripartite no-signaling polytopehttps://archive-ouverte.unige.ch/unige:47359https://archive-ouverte.unige.ch/unige:47359The no-signaling polytope associated with a Bell scenario with three parties, two inputs, and two outputs, is found to have 53 856 extremal points, belonging to 46 inequivalent classes. We provide a classification of these points according to various definitions of multipartite nonlocality and briefly discuss other issues such as the interconversion between extremal points seen as a resource and the relation of the extremal points to Bell-type inequalities.Fri, 27 Feb 2015 14:38:48 +0100Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theorieshttps://archive-ouverte.unige.ch/unige:34932https://archive-ouverte.unige.ch/unige:34932In these lectures, I give a pedagogical presentation of some of the recent progress in supersymmetric Chern–Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N3/2 behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals and large N techniques in matrix models.Mon, 24 Mar 2014 16:35:28 +0100Divergence of the correlation length for critical planar FK percolation with 1≤q≤4 via parafermionic observableshttps://archive-ouverte.unige.ch/unige:30934https://archive-ouverte.unige.ch/unige:30934Parafermionic observables were introduced by Smirnov for planar FK percolation in order to study the critical phase $(p,q)=(p_c(q),q)$. This article gathers several known properties of these observables. Some of these properties are used to prove the divergence of the correlation length when approaching the critical point for FK percolation when $1le qle 4$. A crucial step is to consider FK percolation on the universal cover of the punctured plane. We also mention several conjectures on FK percolation with arbitrary cluster-weight $q>0$.Tue, 05 Nov 2013 14:32:48 +0100Discrete holomorphic parafermions in the Ashkin-Teller model and SLEhttps://archive-ouverte.unige.ch/unige:11910https://archive-ouverte.unige.ch/unige:11910We find discrete holomorphic parafermions of the Ashkin–Teller model on the critical line, by mapping appropriate interfaces of the model onto the O(n = 1) model. We give support to the conjecture that the curve created by the insertion of parafermionic operators at two points on the boundary is SLE(4, ρ, ρ), where ρ varies along the critical line.Mon, 27 Sep 2010 11:29:42 +0200Looking for symmetric Bell inequalitieshttps://archive-ouverte.unige.ch/unige:11839https://archive-ouverte.unige.ch/unige:11839Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins–Gisin–Linden–Massar–Popescu type.Mon, 13 Sep 2010 15:59:23 +0200