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Quantum thermodynamics of the resonant-level model with driven system-bath coupling
http://hdl.handle.net/10993/34083
Title: Quantum thermodynamics of the resonant-level model with driven system-bath coupling
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<br/>Author, co-author: Schmidt, Thomas; Esposito, Massimiliano; Haughian, PatrickModular classes of Q-manifolds: a review and some applications
http://hdl.handle.net/10993/34045
Title: Modular classes of Q-manifolds: a review and some applications
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<br/>Author, co-author: Bruce, Andrew
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<br/>Abstract: A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including $L_{\infty}$-algebroids and higher Poisson manifolds.A generalization of the concept of distance based on the simplex inequality
http://hdl.handle.net/10993/34025
Title: A generalization of the concept of distance based on the simplex inequality
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<br/>Author, co-author: Kiss, Gergely; Marichal, Jean-Luc; Teheux, Bruno
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<br/>Abstract: We introduce and discuss the concept of \emph{$n$-distance}, a generalization to $n$ elements of the classical notion of distance obtained by replacing the triangle inequality with the so-called simplex inequality
\[
d(x_1, \ldots, x_n)~\leq~K\, \sum_{i=1}^n d(x_1, \ldots, x_n)_i^z{\,}, \qquad x_1, \ldots, x_n, z \in X,
\]
where $K=1$. Here $d(x_1,\ldots,x_n)_i^z$ is obtained from the function $d(x_1,\ldots,x_n)$ by setting its $i$th variable to $z$. We provide several examples of $n$-distances, and for each of them we investigate the infimum of the set of real numbers $K\in\left]0,1\right]$ for which the inequality above holds. We also introduce a generalization of the concept of $n$-distance obtained by replacing in the simplex inequality the sum function with an arbitrary symmetric function.Weakly Inscribed Polyhedra
http://hdl.handle.net/10993/33903
Title: Weakly Inscribed Polyhedra
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<br/>Author, co-author: chen, hao; Schlenker, Jean-MarcNotes on the Schwarzian tensor and measured foliations at infinity of quasifuchsian manifolds.
http://hdl.handle.net/10993/33902
Title: Notes on the Schwarzian tensor and measured foliations at infinity of quasifuchsian manifolds.
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<br/>Author, co-author: Schlenker, Jean-Marc
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<br/>Abstract: The boundary at infinity of a quasifuchsian hyperbolic manifold is equiped with a holomorphic quadratic differential. Its horizontal measured foliation $f$ can be interpreted as the natural analog of the measured bending lamination on the boundary of the convex core. This analogy leads to a number of questions. We provide a variation formula for the renormalized volume in terms of the extremal length $\ext(f)$ of $f$, and an upper bound on $\ext(f)$. \par We then describe two extensions of the holomorphic quadratic differential at infinity, both valid in higher dimensions. One is in terms of Poincar\'e-Einstein metrics, the other (specifically for conformally flat structures) of the second fundamental form of a hypersurface in a "constant curvature" space with a degenerate metric, interpreted as the space of horospheres in hyperbolic space. This clarifies a relation between linear Weingarten surfaces in hyperbolic manifolds and Monge-Amp\`ere equations.
Notes aiming at clarifying the relations between different points of view and introducing one new notion, no real result. Not intended to be submitted at this pointHyperbolic ends with particles and grafting on singular surfaces
http://hdl.handle.net/10993/33901
Title: Hyperbolic ends with particles and grafting on singular surfaces
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<br/>Author, co-author: chen, qiyu; Schlenker, Jean-Marc
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<br/>Abstract: We prove that any hyperbolic end with particles (cone singularities along infinite curves of angles less than π) admits a unique foliation by constant Gauss curvature surfaces. Using a form of duality between hyperbolic ends with particles and convex globally hyperbolic maximal (GHM) de Sitter spacetime with particles, it follows that any convex GHM de Sitter spacetime with particles also admits a unique foliation by constant Gauss curvature surfaces. We prove that the grafting map from the product of Teichm\"uller space with the space of measured laminations to the space of complex projective structures is a homeomorphism for surfaces with cone singularities of angles less than π, as well as an analogue when grafting is replaced by "smooth grafting".Elucidating the fine details of cholesteric liquid crystal shell reflection patterns
http://hdl.handle.net/10993/33853
Title: Elucidating the fine details of cholesteric liquid crystal shell reflection patterns
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<br/>Author, co-author: Geng, Yong; Noh, Junghyun; Drevensek-Olenik, Irena; Rupp, Romano; Lagerwall, Jan
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<br/>Abstract: Clusters of planar-aligned short-pitch cholesteric liquid crystal spheres generate dynamic colourful patterns due to multiple selective reflections from the radially oriented cholesteric helices in neighbour shells at varying distances. These photonic communication patterns were widely investigated for the cases of both droplets and shells, demonstrating not only intriguing optical phenomena but also potential for applications as new optical elements for photonics, sensing or security pattern generation. However, the optics of these clusters is truly complex and until now only the strongest and most fundamental reflections have been analysed and explained. In this report, we elucidate the origin of a number of more subtle reflections and we explain the extension in space of various spots as well as their internal colour variations.Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials
http://hdl.handle.net/10993/33844
Title: Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials
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<br/>Author, co-author: Poltavskyi, Igor; DiStasio, Robert; Tkatchenko, Alexandre
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<br/>Abstract: Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems [I. Poltavsky and A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the “quantumness” associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials.Recording Belgium's Gravitational History
http://hdl.handle.net/10993/33826
Title: Recording Belgium's Gravitational History
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<br/>Author, co-author: Van Camp, Michel; Francis, Olivier; Lecocq, ThomasThickness dependence of the resistivity of platinum-group metal thin films
http://hdl.handle.net/10993/33813
Title: Thickness dependence of the resistivity of platinum-group metal thin films
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<br/>Author, co-author: Dutta, S.; Sankaran, K.; Moors, Kristof; Pourtois, G.; Van Elshocht, S.; Bömmels, J.; Vandervorst, W.; Tokei, Z.; Adelmann, C.
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<br/>Abstract: We report on the thin film resistivity of several platinum-group metals (Ru, Pd, Ir, and Pt). Platinum-group thin films show comparable or lower resistivities than Cu for film thicknesses below about 5 nm due to a weaker thickness dependence of the resistivity. Based on experimentally determined mean linear distances between grain boundaries as well as ab initio calculations of the electron mean free path, the data for Ru, Ir, and Cu were modeled within the semiclassical Mayadas-Shatzkes model [Phys. Rev. B 1, 1382 (1970)] to assess the combined contributions of surface and grain boundary scattering to the resistivity. For Ru, the modeling results indicated that surface scattering was strongly dependent on the surrounding material with nearly specular scattering at interfaces with SiO2 or air but with diffuse scattering at interfaces with TaN. The dependence of the thin film resistivity on the mean free path is also discussed within the Mayadas-Shatzkes model in consideration of the experimental findings.Finite Size Effects in Highly Scaled Ruthenium Interconnects
http://hdl.handle.net/10993/33812
Title: Finite Size Effects in Highly Scaled Ruthenium Interconnects
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<br/>Author, co-author: Dutta, Shibesh; Moors, Kristof; Vandemaele, Michiel; Adelmann, Christoph
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<br/>Abstract: Ru has been considered a candidate to replace Cu-based interconnects in VLSI circuits. Here, a methodology is proposed to predict the resistivity of (Ru) interconnects. First, the dependence of the Ru thin film resistivity on the film thickness is modeled by the semiclassical Mayadas-Shatzkes (MS) approach. The fitting parameters thus obtained are then used as input in a modified MS model for nanowires to calculate wire resistivities. Predicted experimental resistivities agreed within about 10%. The results further indicate that grain boundary scattering was the dominant scattering mechanism in scaled Ru interconnects.Multi-oriented props and homotopy algebras with branes
http://hdl.handle.net/10993/33801
Title: Multi-oriented props and homotopy algebras with branes
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<br/>Author, co-author: Merkulov, Sergei
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<br/>Abstract: We introduce a new category of differential graded {\em multi-oriented}\, props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k$ linear subspaces
in that space, $k$ being the number of extra directions (if $k=0$ this structure recovers an ordinary prop); symplectic vector spaces equipped with $k$ Lagrangian subspaces play a distinguished role in this theory.
Manin triples is a classical example of an algebraic structure (concretely, a Lie bialgebra structure) given in terms of a vector space and its subspace; in the context of this paper Manin triples are precisely symplectic Lagrangian representations of the {\em 2-oriented} generalization of the classical operad of Lie algebras. In a sense, the theory of multi-oriented props provides us with a far reaching strong homotopy generalization
of Manin triples type constructions.Calculating the Malliavin derivative of some stochastic mechanics problems
http://hdl.handle.net/10993/33796
Title: Calculating the Malliavin derivative of some stochastic mechanics problems
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<br/>Author, co-author: Hauseux, Paul; Hale, Jack; Bordas, Stéphane
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<br/>Abstract: The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper.Workshop on Supergeometry and Applications
http://hdl.handle.net/10993/33780
Title: Workshop on Supergeometry and Applications
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<br/>Author, co-author: Bruce, Andrew; Poncin, NorbertHomotopical Geometry over Differential Operators and Batalin-Vilkovisky Complex
http://hdl.handle.net/10993/33779
Title: Homotopical Geometry over Differential Operators and Batalin-Vilkovisky Complex
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<br/>Author, co-author: Poncin, NorbertHigher Supergeometry Revisited
http://hdl.handle.net/10993/33778
Title: Higher Supergeometry Revisited
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<br/>Author, co-author: Poncin, NorbertSome naturally defined star products for Kaehler manifolds
http://hdl.handle.net/10993/33776
Title: Some naturally defined star products for Kaehler manifolds
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<br/>Author, co-author: Schlichenmaier, MartinAn elementary proof of the formal rigidity of the Witt and Virasoro algebra
http://hdl.handle.net/10993/33775
Title: An elementary proof of the formal rigidity of the Witt and Virasoro algebra
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<br/>Author, co-author: Schlichenmaier, MartinCONTRIBUTIONS TO THE STATISTICS OF RANDOM PROCESSES USING MALLIAVIN CALCULUS
http://hdl.handle.net/10993/33767
Title: CONTRIBUTIONS TO THE STATISTICS OF RANDOM PROCESSES USING MALLIAVIN CALCULUS
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<br/>Author, co-author: Krein, Christian Yves Léopold
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<br/>Abstract: In this dissertation we present several applications of Malliavin calculus, both to the statistical analysis of continuous time stochastic processes and to limit theorems for non-linear functionals of Gaussian Fields. Malliavin calculus extends techniques of classical calculus of variations from deterministic functions to random variables. In Malliavin calculus, the so called Malliavin derivative and its adjoint, the divergence operator, are combined with the theory of Hilbert spaces. Just as classical calculus, this theory has proved to be a powerful tool and its applications vary from the existence of densities, to the construction of estimators and the study of weak convergence of sequences of random variables and random vectors, with a special focus on normal approximations.
The first part of the present document is essentially a generalization of a result of Privault and Réveillac (2008), which extends a seminal paper of Stein (1956). Stein has shown that, under certain conditions, there are biased estimators which perform better than the standard estimator for the mean of a multivariate normal vector. It has been shown by Privault and Réveillac that a similar statement holds for Gaussian processes and we shall present a generalization of their work to continuous time models, where the noise is either a chaotic Brownian martingale or a non-martingale noise living in the second Wiener chaos. This first part of the work corresponds to the paper "Drift estimation with non-gaussian noise using Malliavin Calculus" (2015) which has been published by the Electronic Journal of Statistics.
In the second part of the work we give necessary and sufficient criteria for the convergence of sequences of random variables, living in a fixed sum of Wiener chaoses, to a limit which lives in the sum of the first two Wiener chaoses. Our results extend the important findings of Nualart and Peccati (2005), the so-called Fourth Moment Theorem, and a recent finding of Azmoodeh, Peccati and Poly (2014). Our criteria make use of the so-called Gamma-operators which are derived from scalar products of Malliavin derivatives and the infinitesimal generator of the Ornstein-Uhlenbeck semi-group, see for instance Azmoodeh, Peccati and Poly (2014). This part corresponds to the paper "Weak convergence on Wiener space: targeting the first two chaoses" (2017) which has been submitted to the Latin American Journal of Probability and Mathematical Statistics (ALEA).
In the last part of the present work we consider a sequence living in a fixed Wiener chaos and converging in law to a normal variable. A second sequence is supposed to converge in law to a target variable which is the sum of a linear combination of independent chi-square distributed random variables and an independent normal variable. We derive conditions under which the sequence of random vectors, formed by both sequences of random variables, converges in law. We use again Gamma-operators and cumulants to derive necessary and sufficient conditions which can be seen as generalization of results of Peccati and Tudor (2005) for Gaussian limits in the case of sequences of random vectors which converge componentwise. We apply methods developed by Nourdin and Peccati (2009) to examine the rate of convergence of a sequence of double Wiener integrals towards a normal variable.Charge pumping through a polaron quantum dot
http://hdl.handle.net/10993/33766
Title: Charge pumping through a polaron quantum dot
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<br/>Author, co-author: Haughian, Patrick; Yap, Han Hoe; Walter, Stefan; Nunnenkamp, Andreas; Gong, Jiangbin; Schmidt, Thomas
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<br/>Abstract: Nanoelectromechanical systems exhibit a rich phenomenology due to the interaction of electronic and mechanical degrees of freedom. If this interaction is sufficiently strong, it leads to drastic suppression of conductance ("Franck-Condon blockade''). We show that this blockade can be exponentially lifted by application of an AC voltage. Multi-parameter drive protocols generate a pump current which enjoys the same enhancement.