Dressed tunneling approximation for electronic transport through molecular transistors

A theoretical approach for the non-equilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. It consists in a resummation of the dominant Feynman diagrams from the perturbative expansion in the coupling to the leads. We show that this scheme eliminates the main pathologies found in previous simple analytical approaches for the polaronic regime. The results for the spectral and transport properties are compared with those from several other approaches for a wide range of parameters. The method can be formulated in a simple way to obtain the full counting statistics. Results for the shot and thermal noise are presented.Comment: 11 pages, 11 figures. Accepted for publication in Physical Review

Temperature chaos in 3D Ising Spin Glasses is driven by rare events

Temperature chaos has often been reported in literature as a rare-event driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a large-deviations functional that allows to discuss the size dependencies. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.Comment: 5 pages, 5 figure

Post-Newtonian Dynamics in Dense Star Clusters: Highly-Eccentric, Highly-Spinning, and Repeated Binary Black Hole Mergers

We present models of realistic globular clusters with post-Newtonian dynamics for black holes. By modeling the relativistic accelerations and gravitational-wave emission in isolated binaries and during three- and four-body encounters, we find that nearly half of all binary black hole mergers occur inside the cluster, with about 10% of those mergers entering the LIGO/Virgo band with eccentricities greater than 0.1. In-cluster mergers lead to the birth of a second generation of black holes with larger masses and high spins, which, depending on the black hole natal spins, can sometimes be retained in the cluster and merge again. As a result, globular clusters can produce merging binaries with detectable spins regardless of the birth spins of black holes formed from massive stars. These second-generation black holes would also populate any upper mass gap created by pair-instability supernovae.Comment: 9 pages, 3 figures, 2 appendices. To appear in Physical Review Letter

A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities

The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet series. Since then these inequalities have found applications in various fields of analysis and analytic number theory. The control of the constants involved is crucial for applications, as it became evident in a recent outstanding paper of Defant, Frerick, Ortega-Cerd\'{a}, Ouna\"{\i}es and Seip published in 2011. The present work is devoted to obtain lower estimates for the constants appearing in the Bohnenblust--Hille polynomial inequality and some of its variants. The technique that we introduce for this task is a combination of the Krein--Milman Theorem with a description of the geometry of the unit ball of polynomial spaces on $\ell^2_\infty$.Comment: This preprint does no longer exist as a single manuscript. It is now part of the preprint entitled "The optimal asymptotic hypercontractivity constant of the real polynomial Bohnenblust-Hille inequality is 2" (arXiv reference 1209.4632

Modelling, Mathematical Analysis and Numerical Simulation to Value Derivatives Related to Renewable Energy Certificates

Programa Oficial de Doutoramento en Métodos Matemáticos e Simulación Numérica en Enxeñaría e Ciencias Aplicadas. 551V01[Resumo] O obxectivo principal desta tese céntrase na modelaxe, análise matemática e resolución numérica de problemas de ecuacións en derivadas parciais (EDPs) para a fixación de prezos de certificados de enerxía renovable (RECs, polas súas siglas en inglés) e produtos derivados asociados. Na modelaxe, o prezo do REC xoga un papel importante. Proponse un modelo de EDP non lineal con dous factores estocásticos. Os factores estocásticos son os certificados verdes acumulados e a taxa de xeración de enerxía renovable. Unha novidade desta tese é o tratamento numérico do término convectivo non lineal na EDP. Para resolver o problema linealizado obtido, propóñense esquemas de semi-Lagrange en tempo conxugados con diferenzas finitas, ou m´etodos alternativos de Lagrange-Galerkin. Utilizouse unha metodoloxía semellante para a valoración dos derivados de REC para obter un modelo de EDP lineal unha vez coñecido o prezo do REC. A existencia de solución obtense neste escenario. Abórdase a fixación de prezos de opcións europeas e futuros sobre RECs. Finalmente, móstranse os resultados do comportamento dos modelos e dos métodos numéricos implementados.[Resumen] El objetivo principal de esta tesis se centra en el modelado, análisis matemático y resolución numérica de problemas de ecuaciones en derivadas parciales (EDPs) para la fijación de precios de certificados de energía renovable (RECs, por sus siglas en inglés) y productos derivados asociados. En el modelado, el precio del REC juega un papel relevante. Se propone un modelo de EDP no lineal con dos factores estocásticos. Los factores estocásticos son los certificados verdes acumulados y la tasa de generación de energía renovable. Una novedad de esta tesis es el tratamiento numérico del término convectivo no lineal en la EDP. Para resolver el problema linealizado obtenido, se proponen esquemas de semi-Lagrange en tiempo combinados con diferencias finitas, o métodos alternativos de Lagrange-Galerkin. Se ha utilizado una metodología equivalente para la valoración de los derivados de REC para obtener un modelo de EDP lineal una vez conocido el precio del REC. La existencia de solución se obtiene en este escenario. Se aborda la fijación de precios de opciones europeas y futuros sobre RECs. Finalmente, se muestran resultados del comportamiento de los modelos y de los métodos numéricos implementados.[Abstract] The main objective of this thesis concerns to the modelling, mathematical analysis and numerical solution of partial differential equations (PDEs) models for pricing renewable energy certificates (RECs) and associated derivatives products. In the modelling, the price of the REC plays a relevant role. A non-linear PDE model with two stochastic factors is proposed. The stochastic factors are the accumulated green certificates and the renewable electricity generation rate. One novelty of this thesis comes from the numerical treatment of the non-linear convective term in the PDE. In order to solve the obtained linearized problem, semi-Lagrangian schemes in time combined with finite differences discretizations, or alternative Lagrange-Galerkin methods are proposed. An equivalent methodology has been used for the valuation of the REC derivatives to obtain a linear PDE model once the REC price is known. Existence of solution is obtained in this setting. The application to the pricing of European options and futures on RECs is addressed. Finally, we show illustrative results of the performance of the models and numerical methods that have been implemented.Xunta de Galicia; ED431C 2018/033Xunta de Galicia; ED431G 2019/01This research has been partially funded by the following projects: • Project PID2019-108584RB-I00 from Ministerio de Ciencia e Innovavi_on. • Project MTM2016-76497-R from Ministerio de Economía y Competitividad. • Project ED431C 2018/033 from Xunta de Galicia. • Project ED431G 2019/01 from Xunta de Galicia. All previous projects include FEDER funding