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We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange–Poincaré bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in M. C. Nucci and R. Campoamor-Stursberg. Minimally superintegrable systems in flat three-dimensional space are also linearizable. J Math Phys. 63 (2022), no. 12, 123510, and may be found at https://doi.org/10.1063/5.0086431., It is shown that all minimally superintegrable Hamiltonian systems in a three-dimensional flat space derived in the work of Evans [Phys. Rev. A 41, 5666–5676 (1990)] possess hidden symmetries leading to their linearization., Ministerio de Ciencia e Innovación, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

We use cluster expansion methods to establish local the indistiguishability of the finite volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our estimates imply that the model satisfies local topological quantum order, and so, the spectral gap above the ground state is stable against local perturbations., EU Horizon 2020, MCIN/AEI/10.13039/501100011033, ESF Investing in your future, Comunidad de Madrid, DFG, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

A coupled massive Thirring model of two interacting Dirac spinors in 1 + 1 dimensions with fields taking values in a Grassmann algebra is introduced, which is closely related to a SU(1) version of the Grassmannian Thirring model also introduced in this work. The Lax pair for the system is constructed, and its equations of motion are obtained from a zero curvature condition. It is shown that the system possesses several infinite hierarchies of conserved quantities, which strongly confirms its integrability. The model admits a canonical formulation and is invariant under space-time translations, Lorentz boosts and global U(1) gauge transformations, as well as discrete symmetries like parity and time reversal. The conserved quantities associated to the continuous symmetries are derived using Noether's theorem, and their relation to the lower-order integrals of motion is spelled out. New nonlocal integrable models are constructed through consistent nonlocal reductions between the field components of the general model. The Lagrangian, the Hamiltonian, the Lax pair and several infinite hierarchies of conserved quantities for each of these nonlocal models are obtained substituting its reduction in the expressions of the analogous quantities for the general model. It is shown that, although the Lorentz symmetry of the general model breaks down for its nonlocal reductions, these reductions remain invariant under parity, time reversal, global U(1) gauge transformations and space-time translations., Universidad Complutense de Madrid, Council of Scientific and Industrial Research (CSIR) (India), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

The no-programing theorem prohibits the existence of a universal programmable quantum processor. This statement has several implications in relation to quantum computation but also to other tasks of quantum information processing, making this construction a central notion in this context. Nonetheless, it is well known that, even when the strict model is not implementable, it is possible to conceive of it in an approximate sense. Unfortunately, the minimal resources necessary for this aim are still not completely understood. Here, we investigate quantitative statements of the theorem, improving exponentially previous bounds on the resources required by such a hypothetical machine. The proofs exploit a new connection between quantum channels and embeddings between Banach spaces which allows us to use classical tools from geometric Banach space theory in a clean and simple way., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We study the thermodynamics and critical behavior of su(m) spin chains of Haldane-Shastry type at zero chemical potential, both in the AN-1 and BCN cases. We evaluate in closed form the free energy per spin for arbitrary values of m, from which we derive explicit formulas for the energy, entropy, and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for m <= 10 by the corresponding temperature for an m-level system with uniformly spaced levels. We show that at low temperatures the free energy per spin of the models under study behaves as that of a one-dimensional conformal field theory with central charge c = m - 1 (with the only exception of the Frahm-Inozemtsev chain at zero value of its parameter). However, from a detailed study of the ground-state degeneracy and the low-energy excitations, we conclude that these models are only critical in the antiferromagnetic case, with a few exceptions that we fully specify., Ministerio de Ciencia e Innovación (España), Universidad Complutense de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Editor's pick, We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of G with a chain of n sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States approach from [Abdul-Rahman et al., Analytic Trends in Mathematical Physics, Contemporary Mathematics (American Mathematical Society, 2020), Vol. 741, p. 1.], we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy., DFG, Agencia Estatal de Investigación, Comunidad de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

A spin-oscillator system models unzipping of biomolecules (such as DNA, RNA, or proteins) subject to an external force. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value Fc of an applied external force F, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates, whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to F − Fc as in an Arrhenius law., Ministerio de Economía y Competitividad, UCM/BSCH, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Está depositada la versión enviada a la revista del artículo, We establish a direct connection between inhomogeneous XX spin chains (or free fermion systems with nearest-neighbors hopping) and certain QES models on the line giving rise to a family of weakly orthogonal polynomials. We classify all such models and their associated XX chains, which include two families related to the Lame (finite gap) quantum potential on the line. For one of these chains, we numerically compute the Renyi bipartite entanglement entropy at half filling and derive an asymptotic approximation thereof by studying the model's continuum limit, which turns out to describe a massless Dirac fermion on a suitably curved background. We show that the leading behavior of the entropy is that of ac= 1 critical system, although there is a subleading log(logN) correction (whereNis the number of sites) unusual in this type of models., Ministerio de Ciencia e Innovación (España), Universidad Complutense de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Está depositada la versión enviada a la revista del artículo, We study the thermodynamics and criticality of the su(m|n) Haldane-Shastry chain of BC ( N ) type with a general chemical potential term. We first derive a complete description of the spectrum of this model in terms of BC ( N )-type motifs, from which we deduce a representation for the partition function as the trace of a product of site-dependent transfer matrices. In the thermodynamic limit, this formula yields a simple expression for the free energy per spin in terms of the Perron-Frobenius eigenvalue of the continuum limit of the transfer matrix. Evaluating this eigenvalue we obtain closed-form expressions for the thermodynamic functions of the chains with m, n <= 2. Using the motif-based description of the spectrum derived here, we study in detail the ground state of these models and their low energy excitations. In this way we identify the critical intervals in chemical potential space and compute their corresponding Fermi velocities. By contrast with previously studied models of this type, we find in some cases two types of low energy excitations with linear energy-quasimomentum relation. Finally, we determine the central charge of all the critical phases by analyzing the low-temperature behavior of the expression for the free energy per spin., Ministerio de Ciencia e Innovación (España), Universidad Complutense de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Each oscillator in a linear chain (a string) interacts with a local Ising spin in contact with a thermal bath. These spins evolve according to Glauber dynamics. Below a critical temperature, there appears an equilibrium, time-independent, rippled state in the string that is accompanied by a nonzero spin polarization. On the other hand, the system is shown to form “metastable,” nonequilibrium long-lived ripples in the string for slow spin relaxation. The system vibrates rapidly about these quasistationary states, which can be described as snapshots of a coarse-grained stroboscopic map. For moderate observation times, ripples are observed irrespective of the final thermodynamically stable state (rippled or not). Interestingly, the system can be considered as a “minimal” model to understand rippling in clamped graphene sheets., Ministerio de Economía y Competitividad, UCM/BSCH, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: d/dt (mx˙/√1 −|˙x|2/c2) = ∇V(x), x ∈ ⊂ Rn, where m, c > 0 and V : → R is a function of class C1. As an application, we prove the existence of multiple periodic solutions with prescribed energy for a relativistic N-centre type problem in the plane., Depto. de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar (IMI), Fac. de Ciencias Matemáticas, TRUE, pub

The Bose equation of state has not progressed significantly since the universality regime discovery in terms of the s-wave scattering length, a. Nowadays no expansion exists to calculate the energy at higher densities, which does not show universality anymore and differs depending on the interaction potential of the particles. Current proposals are reviewed to study the possibility of extending the universality in terms of the s-wave effective range, r_0, and p-wave scattering length, a_1. We do so by achieving agreement using the Diffusion Monte Carlo (DMC) method between the energies of systems presenting interaction potentials that share up to the aforementioned 2-body scattering parameters. It is obtained that potentials sharing at least the additional parameter r_0, of similar or less magnitude than a, show this better consensus in their energies at higher densities. Dependencies between the scattering parameters and the energy are explored to validate current theories and present a preliminary proposal for the next term in the series expansion., La ecuación de estado de Bose no ha progresado significativamente desde el descubrimiento del régimen de universalidad en términos de la longitud de dispersión en onda s, a. Hoy en día no existe una expansión para calcular la energía a mayores densidades, la cual ya no muestra universalidad y difiere según el potencial de interacción de las partículas. Se revisan las propuestas actuales para estudiar la posibilidad de extender la universalidad en términos del rango efectivo en onda s, r_0 y la longitud de dispersión en onda p, a_1. Lo hacemos logrando un acuerdo usando el método Diffusion Monte Carlo (DMC) entre las energías de los sistemas que presentan potenciales de interacción que comparten hasta los parámetros de dispersión de 2 cuerpos antes mencionados. Se obtiene que los potenciales que comparten al menos el parámetro adicional r_0, de similar o menor magnitud que a, muestran este mejor consenso en sus energías a mayores densidades. Se exploran las dependencias entre los parámetros de dispersión y la energía para validar las teorías actuales y presentar una propuesta preliminar para el próximo término en la expansión de la serie., L'equació d'estat de Bose no ha avançat significativament des del descobriment del règim d'universalitat en termes de la longitud de dispersió en ona s, a. Actualment no existeix cap expansió per calcular l'energia a densitats més altes, que ja no mostra universalitat i difereix en funció del potencial d'interacció de les partícules. Es revisen les propostes actuals per a estudiar la possibilitat d'extendre la universalitat en termes del rang efectiu en ona s, r_0 i la longitud de dispersió en ona p, a_1. Ho fem aconseguint un acord mitjançant el mètode Diffusion Monte Carlo (DMC) entre les energies de sistemes que presenten potencials d'interacció que comparteixen els paràmetres de dispersió de 2 cossos esmentats anteriorment. S'obté que els potencials que comparteixen almenys el paràmetre addicional r_0, de magnitud similar o menor que a, mostren aquest millor consens en les seves energies a densitats més altes. S'exploren les dependències entre els paràmetres de dispersió i l'energia per validar les teories actuals i presentar una proposta preliminar per al proper terme de l'expansió de la sèrie.

CRUE-CSIC (Acuerdos Transformativos 2023). 19 páginas., We present a computational investigation of a problem of hadron collisions from recent years, that of baryon anticorrelations. This is an experimental dearth of baryons near other baryons in phase space, not seen upon examining numerical Monte Carlo simulations. We have addressed one of the best known Monte Carlo codes, PYTHIA, to see what baryon (anti)correlations it produces, where they are originated at the string-fragmentation level in the underlying Lund model, and what simple modifications could lead to better agreement with data. We propose two ad-hoc alterations of the fragmentation code, a "one-baryon" and an "always-baryon" policies that qualitatively reproduce the data behaviour, i.e anticorrelation, and suggest that lacking Pauli-principle induced corrections at the quark level could be the culprit behind the current disagreement between computations and experiment., Unión Europea. H2020, U.S. Department of Energy, Ministerio de Ciencia e Innovación (España), Universidad Complutense de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, Instituto de Física de Partículas y del Cosmos (IPARCOS), TRUE, pub

We reexamine different examples of reduction chains g ⊃ g′ of Lie algebras in order to show how the polynomials determining the commutant with respect to the subalgebra g′ leads to polynomial deformations of Lie algebras. These polynomial algebras have already been observed in various contexts, such as in the framework of superintegrable systems. Two relevant chains extensively studied in Nuclear Physics, namely the Elliott chain su(3) ⊃ so(3) and the chain so(5) ⊃ su(2) ×u(1) related to the Seniority model, are analysed in detail from this perspective. We show that these two chains both lead to three-generator cubic polynomial algebras, a result that paves the way for a more systematic investigation of nuclear models in relation to polynomial structures arising from reduction chains. In order to show that the procedure is not restricted to semisimple algebras, we also study the chain Ŝ(3) ⊃ sl(2, R) × so(2) involving the centrally-extended Schrödinger algebra in (3 + 1)-dimensional space–time. The approach chosen to construct these polynomial algebras is based on the use of the Lie-Poisson bracket, so that all the results are presented in the Poisson (commutative) setting. The advantage of considering this approach vs the enveloping algebras is emphasized, commenting on the main formal differences between the polynomial Poisson algebras and their noncommutative analogue. As an illustrative example of the latter, the three-generator cubic algebra associated to the Elliott chain is reformulated in the Lie algebraic (noncommutative) setting., Ministerio de Ciencia e Innovación, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

CRUE-CSIC (Acuerdos Transformativos 2023) © The Author(s) 2023 Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Amilcar Branquinho thanks Centre for Mathematics of the University of Coimbra-UIDB/00324/2020 (funded by the Portuguese Government through FCT/MCTES) and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020Ana Foulquie acknowledges Center for Research & Development in Mathematics and Applications, supported through the Portuguese Foundation for Science and Technology (FCT- Fundacao para a Ciencia e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. Manuel Manas: Thanks financial support from the Spanish "Agencia Estatal de Investigacion" research project [PGC2018-096504-B-C33], Ortogonalidad y Aproximacion: Teoria y Aplicaciones en Fisica Matematica and [PID2021- 122154NB-I00], Ortogonalidad y Aproximacion con Aplicaciones en Machine Learning y Teoria de la Probabilidad., Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pineiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin., Ministerio de Ciencia e Innovación (MICINN)/AEI, Ministerio de Cienncia e Innovación (MICINN), Fundação para a Ciência e a Tecnologia (FCT), Center for Mathematics of the University of Coimbra, Portuguese Government through FCT/MCTES, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2023 The Autor(s) This project has received funding from the Spanish Ministerio de Ciencia e Innovacion Grant No. PID2019-106080 GB-C21 and the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 824093 (STRONG2020). A. R. acknowledges the financial support of the U.S. Department of Energy Contract No. DE-SC0018416 at the College of William & Mary, and Contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Lab. J. R. E. acknowledges financial support from the Swiss National Science Foundation under Project No. PZ00P2 174228 and from the Ramon y Cajal program (RYC2019-027605-I) of the Spanish MINECO., We establish the existence of the long-debated f(0)(1370) resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at (1245 +/- 40) - i(300(-70)(+30)) MeV in pi pi scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at (1380(-60)(+70)) - i(220(-70)(+80)) MeV also appears in the pi pi -> K (K) over bar over bar data analysis with partial-wave dispersion relations. Despite settling its existence, our model-independent dispersive and analytic methods still show a lingering tension between pole parameters from the pi pi and K (K) over bar channels that should be attributed to data., Unión Europea. H2020, Ministerio de Ciencia e Innovación (MICINN), Swiss National Science Foundation (SNSF), United States Department of Energy (DOE), Programa Ramón y Cajal, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2023 American Physical Society B. A., J. K., and J. L. B. S. would like to gratefully acknowledge support by DAAD, the DFG Research Training Group 1620 Models of Gravity, DFG Project No. Ku612/18-1, FCT Project No. PTDC/FIS-AST/3041/2020, and MICINN Project No. PID2021-125617NB-I00 “QuasiMode”. J. L. B. S. gratefully acknowledges support from Santander-UCM Project No. PR44/21-29910. X. Y. C. andD. Y. are supported by the National Research Foundation of Korea (Grants No. 2021R1C1C1008622 and No. 2021R1A4A5031460). We thank Fech Scen Khoo, Luis Manuel González-Romero, and Francisco Navarro- Lérida for discussions., We consider polar perturbations of static Ellis-Bronnikov wormholes and derive the coupled set of perturbation equations for the gravitational and the scalar field. For massless wormholes the perturbations decouple, and we obtain two identical master equations for the scalar and gravitational modes, which moreover agree with the master equation for the axial modes. Consequently there is isospectrality with threefold degenerate modes. For a finite mass of the background wormhole solutions, the equations are coupled. We then obtain two distinct branches of polar quasinormal modes for a given multipole number l, associated with the presence of the two types of fields. We calculate the quasinormal mode frequencies and decay rates for the branches with l = 2, 3 and 4. For a given l the real frequencies of the two branches get the closer, the higher the multipole number gets., Ministerio de Ciencia e Innovación (MICINN), German Research Foundation (DFG), Fundação para a Ciência e a Tecnologia (FCT), National Research Foundation of Korea (NRF), Banco de Santander/Universidad Complutense de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

CRUE-CSIC (Acuerdos Transformativos 2022), We show global existence of classical solutions for the nonlinear Nordström theory with a source term and a cosmological constant under the assumption that the source term is small in an appropriate norm, while in some cases no smallness assumption on the initial data is required. In this theory, the gravitational field is described by a single scalar function that satisfies a certain semi-linear wave equation. We consider spatial periodic deviation from the background metric, that is why we study the semi-linear wave equation on the three-dimensional torus T3 in the Sobolev spaces Hm(T3). We apply two methods to achieve the existence of global solutions, the first one is by Fourier series, and in the second one, we write the semi-linear wave equation in a non-conventional way as a symmetric hyperbolic system. We also provide results concerning the asymptotic behavior of these solutions and, finally, a blow-up result if the conditions of our global existence theorems are not met., CRUE-CSIC agreement with Springer Nature, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

© The Author(s) 2023 We wish to thank the anonymous referees for many useful observations. This work has been partly supported by the research project PGC2018-094898-B-I00, MICINN, Spain, and by the Severo Ochoa Programme for Centres of Excellence in R & D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades y Agencia Estatal de Investigacion, Spain. D. R. N. acknowledges the financial support of EXINA S.L.P. T. and G. T. are members of the Gruppo Nazionale di Fisica Matematica (GNFM)., The theory of generalized Nijenhuis torsions, which extends the classical notions due to Nijenhuis and Haantjes, offers new tools for the study of normal forms of operator fields. We prove a general result ensuring that, given a family of commuting operator fields whose generalized Nijenhuis torsion of level m vanishes, there exists a local chart where all operators can be simultaneously block-diagonalized. We also introduce the notion of generalized Haantjes algebra, consisting of operators with a vanishing higher-level torsion, as a new algebraic structure naturally generalizing standard Haantjes algebras., Ministerio de Ciencia e Innovación (MICINN), Centros de Excelencia Severo Ochoa (MICINN), EXINA S.L.P. T., Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

This paper investigates a dynamical reshaping control method for the station-keeping of unstable resonant libration point orbits (LPO) using the solar radiation pressure (SRP) in the solar-sail-augmented Earth–Moon Quasi-Bicircular Problem. The control strategy aims to reshape the geometrical structures defined by the unstable Floquet modes. Furthermore, asymptotic stability can be achieved by incorporating the central Floquet modes into the procedure. The control variables considered are the two attitude angles of the sail with two scenarios: one with constant lightness number and another with non-constant value. The nominal point, defined as a state on the nominal orbit used to measure the deviation of the spacecraft with respect to the nominal orbit, also plays a role in the stability and convergence rate of the control, and independently of this fact, the Jet Transport technique enables the control laws to be developed in a unified way. In addition, the controllers are obtained as Taylor polynomials in terms of the deviation between the state of the spacecraft and the isochronous point. The numerical simulations analyze the stability, dynamical and long-term behaviors, robustness to orbit determination errors and control costs. The results verify the feasibility of considering SRP for long-term maintenance of LPOs in the Earth–Moon system., C. Gao and J. J. Masdemont thank the Ministerio de Ciencia e Innovación-FEDER, Spain for the grant PID2021-123968NB-I00 and the Catalan government for the grant 2017SGR-1049. G. Gómez thanks the Ministerio de Ciencia e Innovación, Spain for the grant PID2019-104851GB-I00., Peer Reviewed, Postprint (author's final draft)

We present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations., The work of F.P.K. and I.G.K. was partially supported by the U.S. Department of Energy, Grant No. SA22-0052- S001 and the U.S. Air Force Office of Scientific Research, Grant No. A9550-21-1-0317. T.M. and C.B. acknowledge financial support from the Deutsche Forschungsgemeinschaft Project No. 318763901–SFB1294. B.E. acknowledges finan- cial support from MICINN/AEI through research Grant No. PID2020-116927RB-C22., Peer Reviewed, Postprint (author's final draft)

Producción Científica, Density functional theory (DFT) calculations are employed to study the oxygen evolution reaction (OER) on the edges of stripes of monolayer molybdenum disulfide. Experimentally, this material has been shown to evolve oxygen, albeit with low efficiency. Previous DFT studies have traced this low catalytic performance to the unfavourable adsorption energies of some reaction intermediates on the MoS2 edge sites. In this work, we study the effects of the aqueous liquid surrounding the active sites. A computational approach is used, where the solvent is modeled as a continuous medium providing a dielectric embedding of the catalyst and the reaction intermediates. A description at this level of theory can have a profound impact on the studied reactions: the calculated overpotential for the OER is lowered from 1.15 eV to 0.77 eV. It is shown that such variations in the reaction energetics are linked to the polar nature of the adsorbed intermediates, which leads to changes in the calculated electronic charge density when surrounded by water. These results underline the necessity to computationally account for solvation effects, especially in aqueous environments and when highly polar intermediates are present., Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 - (Grant PID2019- 104924RB-I00)

Lecture Notes for the matter "Mathematical Methods II" of the second course of the Bachelor in Physics in Universidad Complutense. It treats linear partial differential equations, separation of variables, symmetric operators in Hilbert space, Fourier analysis, eigenfunction expansion method, special functions, and the Helmholtz equation in curvilinear coordinates

Apuntes de clase de análisis en una variable compleja para físicos. Se estudian funciones holomorfas, integrales complejas, series complejas, y la teoría de los residuos. Los elementos clave son las ecuaciones de Cauchy-Rieman, el teorema de Cauchy, la formula integral de Cauchy, y el teorema de los residuos. También, se incluye información histórica.

The effects of microgravity on organisms is an important study field expected to have plenty of applications in the future. The problem is that it is not easy at all to experiment with microgravity. The spatial missions are scarce and expensive, and they are actually the only form of performing experiments in true microgravity conditions. This is why some alternatives have been developed to simulate the microgravity conditions on Earth. In this project, the 3-dimenstional clinostat, one of the methods of simulating microgravity, is studied and an optimization of one is done, with the objective of monitoring cell growth under the effects of the simulated microgravity., Los efectos de la microgravedad en los organismos es un importante campo de estudio que se prevé que tenga muchas aplicaciones en el futuro. El problema es que no es fácil experimentar con microgravedad. Las misiones espaciales son escasas y costosas y, de hecho, son la única forma de realizar experimentos en condiciones de verdadera microgravedad. Es por eso que se han desarrollado algunas alternativas para simular las condiciones de microgravedad en la Tierra. En este proyecto se estudia el clinostato tridimensional, uno de los métodos de simulación de microgravedad, y se realiza una optimización del mismo, con el objetivo de monitorizar el crecimiento celular bajo los efectos de la microgravedad simulada., Els efectes de la microgravetat sobre organismes és un important camp d'estudi que es preveu que tingui moltes aplicacions en el futur. El problema és que no és fàcil experimentar amb microgravetat. Les missions espacials són escasses i costoses i, de fet, són l'única forma de fer experiments en condicions de microgravetat veritable. És per això que s'han desenvolupat alternatives per simular les condicions de microgravetat a la Terra. En aquest projecte s'estudia el clinostat tridimensional, un dels mètodes de simulació de microgravetat, i se'n realitza una optimització, amb l'objectiu de monitoritzar el creixement cel·lular sota els efectes de la microgravetat simulada.

©SISSA/ISAS 2004. The authors thank A.L. Maroto for his comments and careful reading of the manuscript, as well as partial support from the INFN-CICYT Florence-Madrid Collaboration. J.R.P thanks the hospitalit y of the INFN Sezione di Firenze as well as partial support from the Spanish CICYT projects PB98-0782 and BFM2000 1326., We identify the goldstino fields that give mass to the Kaluza Klein modes of five dimensional supergravity, when supersymmetry breaking is induced by brane effects. We then proof the four dimensional Equivalence Theorem that, in renormalizable gauges, allows for the replacement of Kaluza Klein modes of helicity ±1/2 gravitinos in terms of goldstinos. Finally we identify the five dimensional renormalizable gauge fixing that leads to the Equivalence Theorem., INFN-CICYT Florence-Madrid, Spanish CICYT, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1991 The American Physical Society. We are very grateful to Jorma Louko for many useful conversations. L.G. and G.M. would like to thank Massachusetts Institute of Technology (MIT), where most of this work was done, for warm hospitality during their visit. L.G. and G.M. were supported by the Spanish Ministerio de Educacion y Ciencia. J.J.H. was supported in part by funds provided by the U.S. Department of Energy (DOE) under Contract No. DE-aCO2-76ER03069., We study a class of minisuperspace models consisting of a homogenous isotropic universe with a minimally coupled homogenous scalar field with a potential alpha cosh(2-phi) + beta sinh(2-phi), where alpha and beta are arbitrary parameters. This includes the case of a pure exponential potential exp(2-phi), which arises in the dimensional reduction to four dimensions of five-dimensional Kaluza-Klein theory. We study the classical Lorentzian solutions for the model and find that they exhibit exponential or power-law inflation. We show that the Wheeler-DeWitt equation for this model is exactly soluble. Concentrating on the two particular cases of potentials cosh(2-phi) and exp(2-phi), we consider the Euclidean minisuperspace path integral for a propagation amplitude between fixed scale factors and scalar-field configurations. In the gauge N = 0 (where N is the rescaled lapse function), the path integral reduces, after some essentially trivial functional integrations, to a single nontrivial ordinary integral over N. Because the Euclidean action is unbounded from below, N must be integrated along a complex contour for convergence. We find all possible complex contours which lead to solutions of the Wheeler-DeWitt equation or Green's functions of the Wheeler-DeWitt operator, and we give an approximate evaluation of the integral along these contours, using the method of steepest descents. The steepest-descent contours may be dominated by saddle points corresponding to exact solutions to the full Einstein-scalar equations which may be real Euclidean, real Lorentzian, or complex. We elucidate the conditions under which each of these different types of solution arise. For the exp(2-phi) potential, we evaluate the path integral exactly. Although we cannot evaluate the path integral in closed form for the cosh(2-phi) potential, we show that for particular N contours the amplitude may be written as a given superposition of exact solutions to the Wheeler-DeWitt equation. By choosin, U.S. Department of Energy (DOE), Spanish Ministerio de Educacion y Ciencia, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2007 The American Physical Society. C. B. has been funded by the Spanish MEC under Project No. FIS2005-05736-C03-01 with a partial FEDER contribution. G. J. was supported by CSIC Grant No. I3P-BPD2005 of the I3P programme, cofinanced by the European Social Fund, and by he Spanish MEC under Project No. FIS2005-05736-C03-01. L. G. was supported by the Spanish MEC under Project No. FIS2005-05736-C03-02. The authors also acknowledge support from the Spanish MEC Project No. FIS2006-26387-E., We perform a quasinormal mode analysis of black-hole configurations in Bose-Einstein condensates (BECs). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BECs with steplike discontinuities. For this case we show that in the hydrodynamic approximation quasinormal modes do not exist. The full dispersion relation, however, allows the existence of quasinormal modes. Remarkably, the spectrum of these modes is not discrete but continuous., Spanish MEC, CSIC, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

©IOP Publishing Ltd. The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2005-00319) and the European Science Foundation (MISGAM programme) for their support., Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong conditions in the Hermitian matrix model are analysed and the property of doubling of equations is proved. A wide family of sets of critical points is introduced and the corresponding double scaling limit expansions are discussed., Spanish Ministerio de Educación y Ciencia, European Science Foundation (MISGAM programme), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel., Leverhulme early-career fellowship, China Scholarship Council, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

©2010 Elsevier B.V. All rights reserved. This work was partially supported by the Spanish Ministry of Science and Innovation under grant No. FIS2008-00209, and by the Universidad Complutense and Banco Santander under grant No. GR58/08-910556. J.C.B. acknowledges the financial support of the Spanish Ministry of Science and Innovation through an FPU scholarship. The authors would like to thank B. BasuMallick for useful discussions on A_(N−1)-type motifs., In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos., Ministry of Science and Innovation, Spain, UCM-Banco Santander, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© Springer-Verlag / Società Italiana di Fisica 2008. International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (3. 2008. Isla de La Toja, España). We acknowledge financial support from Spanish research projects FPA2004-02602, FPA2005-02327, PR34/07-1856-BSCH, UCM-CAM 910309/08, FPA2007-29115-E and from the F.P.I. Programme (BES-2005-6726). D.C. wishes to thank support from the “Juan de la Cierva” Programme (Ministerio de Educación y Ciencia, Spain), We present a study of the pi pi scattering amplitude in the sigma and rho channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral-symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear-density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar-isoscalar channel to account for finite nuclear-density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear-matter and heavy-ion collision experiments, such as rho mass scaling versus broadening from dilepton spectra and chiral restoration signals in the sigma channel. We also elaborate on the molecular nature of pi pi resonances., Spanish research projects, Ministerio de Educacion y Ciencia (Spain), UCM-CAM, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© Elsevier Science Bv. We thank Prof. A. Martínez Finkelshtein for useful conversations and for calling our attention to the work [20]. The financial support of the Ministerio de Ciencia e Innovación under project FIS2011-22566 is gratefully acknowledged., We apply the method we have described in a previous paper (2013) to determine the phase structure of asymptotic zero densities of the standard cubic model of non-Hermitian orthogonal polynomials. We provide a complete description of the two phases: the one cut phase and the two cut phase, and analyze the phase transition processes of the types: splitting of a cut, birth and death of a cut. (C) 2014 Elsevier B.V. All rights reserved., Ministerio de Ciencia e Innovacion, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

It is shown that for particles moving in a plane under the action of attracting central potentials and a perturbing force (potential but not central),orbits representing the falling down of the particle to the center of force exist., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

© IOP Publishing Ltd. We are grateful to J.R.Peláez and E.Ruiz Arriola for useful comments. R.T.A would like to thank Buenaventura Andrés López for invaluable advice. Work partially supported by the Spanish research contracts FPA2008-00592, FIS2008-01323, UCM-Santander 910309 GR58/08, GR35/10-A and the FPI programme (BES-2009-013672)., We analyze the isospin-breaking corrections to quark condensates within one-loop SU(2) and SU(3) chiral perturbation theory including m(u) not equal m(d) as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the m(u) not equal m(d) ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account., UCM-Santander, FPI programme, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

©2004 American Institute of Physics. The present work has been supported by Dirección General de Enseñanza Superior Project PB98-0772. The authors wish to thank F.J. Chinea, F. Navarro-Lérida, and M.J. Pareja for valuable discussions., In this paper we analyze Abelian diagonal orthogonally transitive space–times with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic completeness. A sufficient condition on the metric of these space–times is obtained, that is fairly easy to check and to implement in exact solutions. These results confirm that nonsingular space–times are abundant among stiff fluid cosmologies., Dirección General de Enseñanza Superior, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

©IOP Publishing Ltd. The financial support of the Ministerio de Ciencia e Innovación under project IS2011-22566 is gratefully acknowledged, We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to determine the coefficients of their perturbative expansions in the continuum limit. The method relies on identities satisfied by the resolvent of the Jacobi matrix in the three-term recursion relation of the associated families of orthogonal polynomials. These identities lead to a convenient formulation of the string equations. As an application, we show that in the continuum limit the free energy of certain exactly solvable models like the linear and double Penner models can be written as a sum of Gaussian contributions plus linear terms. To illustrate the one-cut case we discuss the linear, double and cubic Penner models, and for the two- cut case we discuss theoretically and numerically the existence of a double-branch structure of the free energy for the Gaussian Penner model., Ministerio de Ciencia e Innovación (MICINN), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© Geoscienceworld This work has been supported in part by MAT2010–17753 and MAT2010–21088–C03–01 projects. Isabel Sobrados and Jesús Sanz, from Instituto de Ciencia de Materiales de Madrid (ICMM, CSIC) are thanked for the NMR spectra. We thank two anonymous reviewers for the suggestions and comments, and guest editor David London and Robert F. Martin for their help in improving this work. LSM thanks Petr Černý for his efforts in communicating his ideas with such clarity for so many years., K-feldspar in rocks is commonly seen as a heterogeneous mixture of mineral species and varieties with random microstructures. Most consider that observable features arise from incomplete re-equilibrations owing to slow kinetic and localized effects of aqueous fluids (catalyst), with geological environment and chemical impurities playing only a secondary role. Here, an alternative approach is explored by studying well-preserved regularities in the twin patterns of K-feldspar formed in the subsolidus stage from a historical perspective. Selected samples from granitic pegmatites were studied by polarized light optical microscopy (PLOM), electron-probe micro-analysis (EPMA), scanning (SEM) and transmission electron microscopy (TEM), cathodoluminescence imaging (CL), micro-Raman spectroscopy (MRS) and P-31 nuclear magnetic resonance (NMR). We have found that the essential feature of this crystalline medium is the astounding ability to recrystallize into self-organized twin patterns. The mechanism involves coupling between short-range atomic motions and long-range displacive correlations propagated as ideal and non-ideal Albite and Pericline orientations. We suggest a general evolutionary process to explain the development of macroscopic twin patterns in microcline, based on three twin generations as microtwins, macrotwins and cryptotwins. Evolutionary variants also were identified; they depend on both internal crystallochemical features and an external geological stimulus. We suggest a continuous monoclinic-triclinic transformation for impure K-feldspar, whereas a discontinuous inversion occurs where the starting composition is close to the ideal chemical formula. Twin patterns can evolve by twin coarsening to single-orientation microcline if the system "releases" energy, or by twin fragmentation to finely twinned microcline if the system "stores" energy. Hence, K-feldspar is seen here as a very sensitive medium in which precious geological information is recorded in the, ICMM, CSIC, Depto. de Física de Materiales, Fac. de Ciencias Físicas, TRUE, pub

We show that two different tensors defining the same translational invariant injective Projected Entangled Pair State (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective., Unión Europea. FP7, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

© IOP Publishing Ltd. We would like to thank Robert B Mann and Tim Ralph for their kind invitation to contribute to the Focus issue of Classical and Quantum Gravity on Relativistic Quantum Information. This work was supported by the Spanish MICINN/MINECO Projects FIS2011-29287, FIS2008-06078-C03-03, FIS2011-30145-C03-02, the CAM research consortium QUITEMAD S2009/ESP-1594 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042)., We analyse the evolution of the entanglement of a non-trivial initial quantum field state (which, for simplicity, has been taken to be a bipartite state made out of vacuum and the first excited state) when it undergoes a gravitational collapse. We carry out this analysis by generalizing the tools developed to study entanglement behaviour in stationary scenarios and making them suitable to deal with dynamical spacetimes. We also discuss what kind of problems can be tackled using the formalism spelled out here, as well as single out future avenues of research., Comunidad de Madrid, Spanish MICINN/MINECO, CPAN, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

This research was supported with financial resources from Agencia de Calidad, Acreditación y Prospectiva de las Universidades de Madrid (ACAP), Madrid, Spain., International academic rankings that compare world universities have proliferated recently. In accordance with latter conceptual and methodological advances in academic rankings approaches, five selection criteria are defined and four international university rankings are selected. A comparative analysis of the four rankings is presented taking into account both the indicators frequency and its weights. Results show that, although some indicators differ considerably across selected rankings and even many indicators are unique, indicators referred to research and scientific productivity from university academic staff have a prominent role across all approaches. The implications of obtained data for main rankings consumers are discussed., Agencia de Calidad, Acreditación y Prospectiva de las Universidades de Madrid (ACAP), Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

©Elsevier Science BV. Erice School on Electromagnetic Probes and the Structure of Hadrons and Nuclei (1999. Erice, Italia). This work is partly supported by DGICYT, contract number PB 96-0753, By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in mesonmeson scattering up to 1.2 GeV using the parameters of the O(p²) and O ( p^ 4 ) Chiral Lagrangian. The meson baryon sector can also be tackled along similar lines. We report on an update of these results showing some examples of photon induced reactions where the techniques have been recently applied., DGICYT, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

La ingeniería y la matemática se han retroalimentado desde sus inicios. La ingeniería como la aplicación del conocimiento científico a la invención práctica y la matemática como el conocimiento científico en sí mismo. Este artículo se sitúa en el germen del desarrollo de la física-matemática como herramienta clave en la ingeniería, a través del problema de la cuerda vibrante, con un final envuelto en “armonías”., Engineering and mathematics have been fed back since its inception. Engineering as the application of scientific knowledge to practical invention and mathematics as scientific knowledge itself. This article is placed in the germ of the development of mathematical physics as a key tool in engineering, through the vibrating string problem, with an end wrapped in "harmonies"., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

© 2010 The American Physical Society. This work was partially supported by Spanish Ministerio de Educacion y Ciencia Research Contracts No. FPA2008-00592, No. FIS2006-03438, and No. FIS2008-01323, and by U.Complutense/Banco Santander Grant No. UCM-BSCH GR58/08 910309. We acknowledge the support of the European Community-Research Infrastructure Integrating Activity "Study of Strongly Interacting Matter" (acronym HadronPhysics2, Grant Agreement No. 227431) under the Seventh Framework Programme of the EU., Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within chiral perturbation theory. We define the four-quark condensate as lim(x -> 0) < T((q) over barq)(x)((q) over barq)(0)>, which is equivalent to other definitions commonly used in the literature. Factorization of the four-quark condensate holds to leading and next to leading order. However, at next to next to leading order, a term with a nontrivial space-time dependence in the four-quark correlator yields a divergent four-quark condensate, whereas the two-quark condensate and the scalar susceptibility are finite. Such a nonfactorization term vanishes only in the chiral limit. We also comment on how factorization still holds in the large N-c limit, provided such a limit is taken before renormalization., Unión Europea. FP7, Spanish Ministerio de Educacion y Ciencia, U.Complutense/Banco Santander, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2013 American Physical Society. Useful comments from F. Karsch, S. Mukherjee, and D. Cabrera are acknowledged. This work is partially supported by the EU FP7 HadronPhysics3 project, the Spanish project FPA2011-27853-C02-02, and FPI Programme (BES-2009-013672, R. T. A), and by the German DFG (SFB/TR 16, J. R. E.)., We investigate the charged-neutral difference in the pion self-energy at finite temperature T. Within chiral perturbation theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self-energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T = 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to O(T-2) similar to O(M-pi(2)). Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly p and a(1) exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being O(, Unión Europea. FP7, FPI Programme, German DFG, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub