561975 research outputs found
Sort by
Canonicalizing zeta generators: genus zero and genus one
Get PDFZeta generators are derivations associated with odd Riemann zeta values thatact freely on the Lie algebra of the fundamental group of Riemann surfaces withmarked points. The genus-zero incarnation of zeta generators are Iharaderivations of certain Lie polynomials in two generators that can be obtainedfrom the Drinfeld associator. We characterize a canonical choice of thesepolynomials, together with their non-Lie counterparts at even degrees , through the action of the dual space of formal and motivic multizetavalues. Based on these canonical polynomials, we propose a canonicalisomorphism that maps motivic multizeta values into the -alphabet. Thecanonical Lie polynomials from the genus-zero setup determine canonical zetagenerators in genus one that act on the two generators of Enriquez' ellipticassociators. Up to a single contribution at fixed degree, the zeta generatorsin genus one are systematically expanded in terms of Tsunogai's geometricderivations dual to holomorphic Eisenstein series, leading to a wealth ofexplicit high-order computations. Earlier ambiguities in defining thenon-geometric part of genus-one zeta generators are resolved by imposing a newrepresentation-theoretic condition. The tight interplay between zeta generatorsin genus zero and genus one unravelled in this work connects the constructionof single-valued multiple polylogarithms on the sphere withiterated-Eisenstein-integral representations of modular graph forms.<br
Probing fundamental physics with Extreme Mass Ratio Inspirals: a full Bayesian inference for scalar charge
Get PDFExtreme Mass Ratio Inspirals (EMRIs) are key sources for the futurespace-based gravitational wave detector LISA, and are considered promisingprobes of fundamental physics. Here, we present the first complete Bayesiananalysis of EMRI signals in theories with an additional massless scalar, whichcould arise in an extension of General Relativity or of the Standard Model ofParticle Physics. We develop a waveform model accurate at adiabatic order forequatorial eccentric orbits around spinning black holes. Using full Bayesianinference, we forecast LISA's ability to probe the presence of new fundamentalfields with EMRI observations.<br
Origin of the insulating phase and metal-insulator transition in the organic molecular solid κ-(BEDT-TTF)<sub>2</sub>Cu<sub>2</sub>(CN)<sub>3</sub>
Get PDFRecent studies of organic molecular solids have focused on their complex phase diagram and on light-induced phenomena, including a Mott insulating state, a spin liquid phase, and light-enhanced superconductivity. However, discrepancies between experiments and first-principles calculations for the κ-(BEDT-TTF)2X family hinder a comprehensive understanding of their properties. Here, we revisit the electronic structure of κ-(BEDT-TTF)2Cu2(CN)3 with a recently developed method for applying the Hubbard U potential on generalized orbital states, within the framework of density functional theory, to correct the orbital energy levels of the molecular solid. Our work focuses on the electronic structure of κ-(BEDT-TTF)2Cu2(CN)2, whose insulating state originates from an energy gap between the highest occupied and the lowest unoccupied molecular orbital states of the BEDT-TTF dimers, which constitute the periodic unit of the molecular solid. Our calculations provide results in alignment with experiments for band gaps, optical conductivities, and evolution of the metal-insulator transition as a function of pressure. Especially, the observed superconducting dome of κ-(BEDT-TTF)2Cu2(CN)3, which derives from the flat band state at the Fermi level, is qualitatively reproduced. Additionally, we construct a new low-energy lattice model based on our first-principles computed band structure that can be exploited to address many-body physics, such as quantum spin liquid states and double-holon dynamics. Our work can be extended to achieve deeper insight into the complex phase diagram and light-induced phenomena in the κ-(BEDT-TTF)2X family and other complex organic molecular solids
The Topology of Rayleigh-Levy Flights in Two Dimensions
No full textRayleigh-Lévy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference for studying the highly non-linear regime of structure formation. Unlike standard Markovian processes, they exhibit long-range correlations at all orders. Following on recent work on one dimensional flights, this study explores the one-point statistics and Minkowski functionals (density PDF, perimeter, Euler characteristic) of Rayleigh-Lévy flights in two dimensions. We derive the Euler characteristic in the mean field approximation and the density PDF and iso-field perimeter in beyond mean field calculations, and validate the results against simulations. The match is excellent throughout, even for fields with large variances, in particular when finite volume effects in the simulations are taken into account and when the calculation is extended beyond the mean field