Archive ouverte UNIGE | last documents for author 'Santiago Codesido Sanchez'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Santiago Codesido Sanchez'engApparent efficiency of serially coupled columns in isocratic and gradient elution modeshttps://archive-ouverte.unige.ch/unige:113095https://archive-ouverte.unige.ch/unige:113095The goal of this work was to understand the variation of apparent efficiency when serially couplingcolumns with identical stationary phase chemistries, but with differences in their kinetic performance.For this purpose, a mathematical treatment was developed both for isocratic and gradient modes to assessthe change in plate numbers and peak widths when coupling arbitrary several columns. To validate thetheory, experiments were also carried out using various mixtures of compounds, on columns packed withdifferent particle sizes, to mimic highly efficient (new, not used) and poorly efficient columns (used onewith many injections). Excellent agreement was found between measured and calculated peak widths.The average error in prediction was about 5% (which may be explained by the additional volume of thecoupling tubes).In isocratic mode, the plate numbers are not additive when the coupled columns possess differentefficiencies, and a limiting plate count value can be calculated depending on the efficiency and length ofthe individual columns. Theoretical efficiency limit can also be determined assuming one column in therow with infinite efficiency.In gradient elution mode, the columns’ order has a role (non-symmetrical system). When the lastcolumn has high enough efficiency, the gradient band compression effect may outperform the competingband broadening caused by dispersive and diffusive processes (peak sharpening). Therefore, in gradientmode, the columns should generally be sequentially placed according to their increasing efficiency.Mon, 21 Jan 2019 12:58:13 +0100A geometric approach to non-perturbative quantum mechanicshttps://archive-ouverte.unige.ch/unige:102512https://archive-ouverte.unige.ch/unige:102512This work explores the connection between spectral theory and topological strings. A concrete example (the Y(3,0) geometry) of a conjectured exact relation between both based on mirror symmetry (TS/ST correspondence) is analysed in detail, to find a complete agreement. This is used as motivation to apply string theory tools, and in particular the refined holomorphic anomaly, to other Schrödinger-type spectral problems. With it, we efficiently compute their all-orders WKB expansion. We also upgrade the refined holomorphic anomaly to include non-perturbative corrections to the WKB series. This is used to retrieve the transseries generated by previously known exact quantization conditions for quantum mechanical problems. Via resurgence, it will allows us to reproduce the large order behaviour of the WKB coefficients, for both the Schrödinger problems and the quantum mirror curves of the TS/ST correspondence.Fri, 23 Feb 2018 11:03:14 +0100Non-Perturbative Quantum Mechanics from Non-Perturbative Stringshttps://archive-ouverte.unige.ch/unige:101100https://archive-ouverte.unige.ch/unige:101100This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of topological string theory. The method can be applied to traditional spectral problems governed by the Schr"odinger equation, where it both reproduces and extends the results of well-established approaches, such as the exact WKB method. It can be also applied to spectral problems based on the quantization of mirror curves, where it leads to new results on the trans-series structure of the spectrum. Various examples are discussed, including the modified Mathieu equation, the double-well potential, and the quantum mirror curves of local P2 and local F0. In all these examples, it is verified in detail that the trans-series obtained with this new method correctly predict the large-order behavior of the corresponding perturbative sectors.Wed, 03 Jan 2018 16:11:57 +0100Spectral Theory and Mirror Curves of Higher Genushttps://archive-ouverte.unige.ch/unige:101099https://archive-ouverte.unige.ch/unige:101099Recently, a correspondence has been proposed between spectral theory and topological strings on toric Calabi-Yau manifolds. In this paper we develop in detail this correspondence for mirror curves of higher genus, which display many new features as compared to the genus one case studied so far. Given a curve of genus g, our quantization scheme leads to g different trace class operators. Their spectral properties are encoded in a generalized spectral determinant, which is an entire function on the Calabi-Yau moduli space. We conjecture an exact expression for this spectral determinant in terms of the standard and refined topological string amplitudes. This conjecture provides a non-perturbative definition of the topological string on these geometries, in which the genus expansion emerges in a suitable 't Hooft limit of the spectral traces of the operators. In contrast to what happens in quantum integrable systems, our quantization scheme leads to a single quantization condition, which is elegantly encoded by the vanishing of a quantum-deformed theta function on the mirror curve. We illustrate our general theory by analyzing in detail the resolved C3/Z5 orbifold, which is the simplest toric Calabi-Yau manifold with a genus two mirror curve. By applying our conjecture to this example, we find new quantization conditions for quantum mechanical operators, in terms of genus two theta functions, as well as new number-theoretic properties for the periods of this Calabi-Yau.Wed, 03 Jan 2018 16:10:28 +0100Holomorphic 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 resummation of the Lee-Yang edge singularity coupled to gravityhttps://archive-ouverte.unige.ch/unige:101097https://archive-ouverte.unige.ch/unige:101097We study the Borel-Pade resummation of the asymptotic series for the string equation of the Lee-Yang edge singularity. Numerical methods are provided to compute a high accuracy exact solution. We find the resummation matches the numerical integration without need for further non-perturbative corrections.Wed, 03 Jan 2018 16:04:51 +0100Operators and higher genus mirror curveshttps://archive-ouverte.unige.ch/unige:92236https://archive-ouverte.unige.ch/unige:92236We perform further tests of the correspondence between spectral theory and topological strings, focusing on mirror curves of genus greater than one with nontrivial mass parameters. In particular, we analyze the geometry relevant to the SU(3) relativistic Toda lattice, and the resolved ℂ 3 / ℤ 6 $$ {\mathbb{C}}^{{}^3}/{\mathbb{Z}}_6 $$ orbifold. Furthermore, we give evidence that the correspondence holds for arbitrary values of the mass parameters, where the quantization problem leads to resonant states. We also explore the relation between this correspondence and cluster integrable systems.Wed, 01 Mar 2017 11:34:31 +0100Holomorphic Anomaly and Quantum Mechanicshttps://archive-ouverte.unige.ch/unige:92110https://archive-ouverte.unige.ch/unige:92110We 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.Mon, 27 Feb 2017 09:50:05 +0100Evaluation of a new low sheath–flow interface for CE-MShttps://archive-ouverte.unige.ch/unige:85990https://archive-ouverte.unige.ch/unige:85990The current trend for increasing technical complexity in the field of CE-ESI-MS interfaces has incited for more accessible alternatives. In this work, a simple low sheath-flow ESI interface operating in the submicroliter nanospray regime without nebulizing gas assistance was evaluated. The use of sheath liquid enabled improving the ionization of the analytes, while the absence of nebulizing gas minimized sample dilution and loss of efficiency. After a rapid qualification, the effect of main operational parameters such as sheath liquid composition and flow rate, working distance and ESI potential was studied. Simulation of the mixing processes inside the Taylor cone proved its size to be of utmost importance in band broadening processes. As a proof of concept, the interface was eventually applied to a set of representative basic drugs analyzed by CE-TOF/MS. Limits of detection reached the 25–100 ppb range with suitable robustness and repeatability results. This design has demonstrated good performance while being simple and accessible to the user.Mon, 15 Aug 2016 10:42:01 +0200Exact results in N = 8 $$ \mathcal{N}=8 $$ Chern-Simons-matter theories and quantum geometryhttps://archive-ouverte.unige.ch/unige:74438https://archive-ouverte.unige.ch/unige:74438We show that, in ABJ(M) theories with N = 8 $$ \mathcal{N}=8 $$ supersymmetry, the non-perturbative sector of the partition function on the three-sphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which determines the full large N asymptotics. Moreover, we find explicit formulae for the generating functionals of their partition functions, for all values of the rank N of the gauge group: they involve Jacobi theta functions on the spectral curve associated to the planar limit. Exact quantization conditions for the spectral problem of the Fermi gas are then obtained from the vanishing of the theta function. We also show that the partition function, as a function of N , can be extended in a natural way to an entire function on the full complex plane, and we explore some possible consequences of this fact for the quantum geometry of M-theory and for putative de Sitter extensions.Fri, 31 Jul 2015 09:43:33 +0200Exact results in N=8 Chern-Simons-matter theories and quantum geometryhttps://archive-ouverte.unige.ch/unige:41315https://archive-ouverte.unige.ch/unige:41315We show that, in ABJ(M) theories with N=8 supersymmetry, the non-perturbative sector of the partition function on the three-sphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which determines the full large N asymptotics. Moreover, we find explicit formulae for the generating functionals of their partition functions, for all values of the rank N of the gauge group. They involve Jacobi theta functions on the spectral curve associated to the planar limit. We also show that the partition function, as a function of N, can be extended in a natural way to an entire function on the full complex plane, and we explore some possible consequences of this fact for the quantum geometry of M-theory and for putative de Sitter extensions.Wed, 29 Oct 2014 15:42:51 +0100