ORBi<sup>lu</sup> Community: Physical, chemical, mathematical & earth Sciences
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Moment maps and closed Fedosov's star products
http://hdl.handle.net/10993/37319
Title: Moment maps and closed Fedosov's star products
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<br/>Author, co-author: La Fuente-Gravy, LaurentMoment map and closed Fedosov star products
http://hdl.handle.net/10993/37318
Title: Moment map and closed Fedosov star products
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<br/>Author, co-author: La Fuente-Gravy, LaurentSymplectic Dirac operators: Construction and kernels
http://hdl.handle.net/10993/37317
Title: Symplectic Dirac operators: Construction and kernels
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<br/>Author, co-author: La Fuente-Gravy, LaurentFutaki invariant for Fedosov star products
http://hdl.handle.net/10993/37316
Title: Futaki invariant for Fedosov star products
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<br/>Author, co-author: La Fuente-Gravy, Laurent
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<br/>Abstract: We study obstructions to the existence of closed Fedosov star products on a
given Kähler manifold (M, omega, J). In our previous paper [11], we proved that if the
Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of
Connes-Flato-Sternheimer [4]) Fedosov’s star product then it is a zero of a moment
map μ on the space of symplectic connections. By analogy with the Futaki invariant
obstructing the existence of cscK metrics, we build an obstruction for the existence
of zero of μ and hence for the existence of closed Fedosov’s star product on a Kähler
manifold.On Mpc-structures and symplectic Dirac operators
http://hdl.handle.net/10993/37312
Title: On Mpc-structures and symplectic Dirac operators
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<br/>Author, co-author: Cahen, Michel; Gutt, Simone; La Fuente-Gravy, Laurent; Rawnsley, John
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<br/>Abstract: We prove that the kernels of the restrictions of the symplectic Dirac operator and one
of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial
valued spinor fields are finite dimensional on a compact symplectic manifold. We compute
these kernels explicitly for complex projective spaces and show that the remaining
Dirac–Dolbeault operator has infinite dimensional kernels on these finite rank sub-bundles.
We construct injections of subgroups of the symplectic group (the pseudo-unitary group
and the stabiliser of a Lagrangian subspace) in the Mpc group and classify G-invariant
Mpc-structures on symplectic manifolds with a G-action. We prove a variant of
Parthasarathy’s formula for the commutator of two symplectic Dirac-type operators on
general symmetric symplectic spaces.Infinite dimensional moment map geometry and closed Fedosov star products
http://hdl.handle.net/10993/37311
Title: Infinite dimensional moment map geometry and closed Fedosov star products
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<br/>Author, co-author: La Fuente-Gravy, Laurent
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<br/>Abstract: We study the Cahen–-Gutt moment map on the space of symplectic connections of a
symplectic manifold. Given a Kähler manifold (M, ω, J ), we define a Calabi-type functional
F on the space M of Kähler metrics in the class [ω]. We study the space of zeroes
of F. When (M, ω, J ) has non-negative Ricci tensor and ω is a zero of F, we show the
space of zeroes of F near ω has the structure of a smooth finite dimensional submanifold.
We give a new motivation, coming from deformation quantization, for the study of moment
maps on infinite dimensional spaces. More precisely, we establish a strong link between
trace densities for star products (obtained from Fedosov-type methods) and moment map
geometry on infinite dimensional spaces. As a byproduct, we provide, on certain Kähler
manifolds, a geometric characterization of a space of Fedosov star products that are closed
up to order 3.The group of Hamiltonian automorphisms of a star product
http://hdl.handle.net/10993/37310
Title: The group of Hamiltonian automorphisms of a star product
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<br/>Author, co-author: La Fuente-Gravy, Laurent
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<br/>Commentary: We deform the group of Hamiltonian diffeomorphisms into a group of
Hamiltonian automorphisms, Ham(M, ∗), of a formal star product ∗ on a symplectic
manifold (M, ω). We study the geometry of that group and deform the Flux
morphism in the framework of deformation quantization.Grenzüberschreitende Umwelten
http://hdl.handle.net/10993/37303
Title: Grenzüberschreitende Umwelten
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<br/>Author, co-author: Schulz, ChristianNonequilibrium Thermodynamics in Biology: From Molecular Motors to Metabolic Pathways
http://hdl.handle.net/10993/37273
Title: Nonequilibrium Thermodynamics in Biology: From Molecular Motors to Metabolic Pathways
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<br/>Author, co-author: Wachtel, Artur
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<br/>Abstract: Biological systems need to exchange energy and matter with their environment in order to stay functional or “alive”. This exchange has to obey the laws of thermodynamics: energy cannot be created and exchange comes at the cost of dissipation, which limits the efficiency of biological function. Additionally, subcellular processes that involve only few molecules are stochastic in their dynamics and a consistent theoretical modeling has to account for that.
This dissertation connects recent development in nonequilibrium thermodynamics with approaches taken in biochemical modeling. I start by a short introduction to thermodynamics and statistical mechanics, with a special emphasis on large deviation theory and stochastic thermodynamics. Building on that, I present a general theory for the thermodynamic analysis of networks of chemical reactions that are open to the exchange of matter.
As a particularly insightful concrete example I discuss the mechanochemical energy conversion in stochastic models of a molecular motor protein, and show how a similar analysis can be performed for more general models. Furthermore, I compare the dissipation in stochastically and deterministically modeled open chemical networks, and present a class of chemical networks that displays exact agreement for arbitrary abundance of chemical species and arbitrary distance from thermodynamic equilibrium. My major achievement is a thermodynamically consistent coarse-graining procedure for biocatalysts, which are ubiquitous in molecular cell biology. Finally, I discuss the thermodynamics of unbranched enzymatic chains.The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra
http://hdl.handle.net/10993/37271
Title: The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra
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<br/>Author, co-author: Ecker, Jill Marie-Anne; Schlichenmaier, MartinThe low-dimensional algebraic cohomology of the Witt and the Virasoro algebra
http://hdl.handle.net/10993/37270
Title: The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra
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<br/>Author, co-author: Ecker, Jill Marie-Anne; Schlichenmaier, MartinThe low-dimensional algebraic cohomology of the Virasoro algebra
http://hdl.handle.net/10993/37269
Title: The low-dimensional algebraic cohomology of the Virasoro algebra
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<br/>Author, co-author: Ecker, Jill Marie-Anne; Schlichenmaier, MartinAsymmetries in the spectral density of an interaction-quenched Luttinger liquid
http://hdl.handle.net/10993/37266
Title: Asymmetries in the spectral density of an interaction-quenched Luttinger liquid
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<br/>Author, co-author: Calzona, Alessio; Gambetta, Filippo Maria; Carrega, Matteo; Cavaliere, Fabio; Sassetti, Maura
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<br/>Abstract: The spectral density of an interaction-quenched one-dimensional system is investigated. Both direct and inverse quench protocols are considered and it is found that the former leads to stronger effects on the spectral density with respect to the latter. Such asymmetry is directly reflected on transport properties of the system, namely the charge and energy current flowing to the system from a tunnel coupled biased probe. In particular, the injection of particles from the probe to the right-moving channel of the system is considered. The resulting fractionalization phenomena are strongly affected by the quench protocol and display asymmetries in the case of direct and inverse quench. Transport properties therefore emerge as natural probes for the observation of this quench-induced behavior.Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind
http://hdl.handle.net/10993/37263
Title: Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind
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<br/>Author, co-author: Perucca, Antonella; Fiore, Tom; Lang, AlexanderStatistical significance of trends in Zenith Wet Delay from re-processed GPS solutions
http://hdl.handle.net/10993/37254
Title: Statistical significance of trends in Zenith Wet Delay from re-processed GPS solutions
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<br/>Author, co-author: Klos, Anna; Hunegnaw, Addisu; Teferle, Felix Norman; Abraha, Kibrom Ebuy; Ahmed, Furqan; Bogusz, Janusz
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<br/>Abstract: Long series of Zenith Wet Delay (ZWD) obtained as part of a homogeneous re-processing of Global Positioning System solutions constitute a reliable set of data to be assimilated into climate models. The correct stochastic properties, i.e. the noise model of these data, have to be identified to assess the real value of ZWD trend uncertainties since assuming an inappropriate noise model may lead to over- or underestimated error bounds leading to statistically insignificant trends. We present the ZWD time series for 1995–2017 for 120 selected globally distributed stations. The deterministic model in the form of a trend and significant seasonal signals were removed prior to the noise analysis. We examined different stochastic models and compared them to widely assumed white noise (WN). A combination of the autoregressive process of first-order plus WN (AR(1) + WN) was proven to be the preferred stochastic representation of the ZWD time series over the generally assumed white-noise-only approach. We found that for 103 out of 120 considered stations, the AR(1) process contributed to the AR(1) + WN model in more than 50% with noise amplitudes between 9 and 68 mm. As soon as the AR(1) + WN model was employed, 43 trend estimates became statistically insignificant, compared to 5 insignificant trend estimates for a white-noise-only model. We also found that the ZWD trend uncertainty may be underestimated by 5–14 times with median value of 8 using the white-noise-only assumption. Therefore, we recommend that AR(1) + WN model is employed before tropospheric trends are to be determined with the greatest reliability.Influence of Sodium and Rubidium Postdeposition Treatment on the Quasi-Fermi Level Splitting of Cu(In,Ga)Se2 Thin Films
http://hdl.handle.net/10993/37253
Title: Influence of Sodium and Rubidium Postdeposition Treatment on the Quasi-Fermi Level Splitting of Cu(In,Ga)Se2 Thin Films
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<br/>Author, co-author: Wolter, Max; Bissig, Benjamin; Avancini, Enrico; Carron, Romain; Buecheler, Stephan; Jackson, Philip; Siebentritt, SusanneCompositionally universal meromorphic functions
http://hdl.handle.net/10993/37238
Title: Compositionally universal meromorphic functions
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<br/>Author, co-author: Meyrath, Thierry
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<br/>Abstract: For a sequence of holomorphic maps $(\vp_n)$ from a domain $\Omega_2$ to a domain $\Omega_1$, we consider meromorphic functions $f$ on $\Omega_1$ for which the sequence of compositions $(f \circ \vp_n)$ is dense in the space of all meromorphic functions on $\Omega_2$, endowed with the topology of spherically uniform convergence on compact subsets. We generalize and unify several known results about universal meromorphic functions and provide new examples of sequences of holomorphic maps, for which there exist universal meromorphic functions. We also consider meromorphic functions that have in some sense a maximally erratic boundary behavior in general domains $\Omega \subset \C, \Omega \neq \C$. As a corollary, we obtain that meromorphic functions on general domains are generically non-extendable.Concentration of the Intrinsic Volumes of a Convex Body
http://hdl.handle.net/10993/37232
Title: Concentration of the Intrinsic Volumes of a Convex Body
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<br/>Author, co-author: Lotz, Martin; McCoy, Michael B.; Nourdin, Ivan; Peccati, Giovanni; Tropp, Joel A.Magnetotransport signatures of three-dimensional topological insulator nanostructures
http://hdl.handle.net/10993/37226
Title: Magnetotransport signatures of three-dimensional topological insulator nanostructures
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<br/>Author, co-author: Moors, Kristof; Schüffelgen, P.; Rosenbach, D.; Schmitt, T.; Schäpers, T.; Schmidt, Thomas
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<br/>Abstract: We study the magnetotransport properties of patterned 3D topological insulator nanostructures with several leads, such as kinks or Y-junctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field, and the spin-momentum locking of the topological surface states lead to a richer magnetoconductance phenomenology as compared to straight nanowires. Similar to straight wires, a quantized conductance with perfect transmission across the nanostructure can be realized across a kink when the input and output channels are pierced by a half-integer magnetic flux quantum. Unlike for straight wires, there is an additional requirement depending on the orientation of the external magnetic field. A right-angle kink shows a unique π -periodic magnetoconductance signature as a function of the in-plane angle of the magnetic field. For a Y-junction, the transmission can be perfectly steered to either of the two possible output legs by a proper alignment of the external magnetic field. These magnetotransport signatures offer new ways to explore topological surface states and could be relevant for quantum transport experiments on nanostructures which can be realized with existing fabrication methods.The Optical Diode Ideality Factor Enables Fast Screening of Semiconductors for Solar Cells
http://hdl.handle.net/10993/37221
Title: The Optical Diode Ideality Factor Enables Fast Screening of Semiconductors for Solar Cells
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<br/>Author, co-author: Babbe, Finn; Choubrac, Leo; Siebentritt, Susanne