Person: Martínez Alonso, Luis
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First Name
Luis
Last Name
Martínez Alonso
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Department
Física Teórica
Area
Física Teórica
Identifiers
65 results
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Now showing 1 - 10 of 65
Item Gravitational lensing by eigenvalue distributions of random matrix models(Classical and quantum gravity, 2018) Martínez Alonso, Luis; Medina, ElenaWe propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.Item Singular sectors of the one-layer Benney and dispersionless Toda systems and their interrelations(Theoretical and mathematical physics, 2011) Konopelchenko, Boris; Martínez Alonso, Luis; Medina, E.We completely describe the singular sectors of the one-layer Benney system (classical long-wave equation) and dispersionless Toda system. The associated Euler-Poisson-Darboux equations E(1/2, 1/2) and E(-1/2,-1/2) are the main tool in the analysis. We give a complete list of solutions of the one-layer Benney system depending on two parameters and belonging to the singular sector. We discuss the relation between Euler-Poisson-Darboux equations E(ɛ, ɛ) with the opposite sign of ɛ.Item An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model(Nuclear Physics B, 2011) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina Reus, ElenaWe present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.Item Explicit solutions of supersymmetric KP hierarchies: Supersolitons and solitinos(Journal of mathematical physics, 1996) Ibort, A.; Martínez Alonso, Luis; Medina Reus, ElenaWide classes of explicit solutions of the Manin-Radul and Jacobian supersymmetric KP hierarchies are constructed by using line bundles over complex supercurves based on the Riemann sphere. Their construction extends several ideas of the standard KP theory, such as wave functions,δ̅ equations and τ-functions. Thus, supersymmetric generalizations of N-soliton solutions, including a new purely odd ‘‘solitino’’ solution, as well as rational solutions, are found and characterized.Item The KP hierarchy in Miwa coordinates(Physics letters A, 1999) Konopelchenko, Boris; Martínez Alonso, LuisA systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay's identities an obtained. It is shown that in terms of these variables the KP hierarchy gives rise to a Darboux system describing an infinite-dimensional conjugate net.Item Determination of S-curves with applications to the theory of nonhermitian orthogonal polynomials(Journal of statistical mechanics : theory and experiment, 2013) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina Reus, ElenaThis paper deals with the determination of the S-curves in the theory of non-hermitian orthogonal polynomials with respect to exponential weights along suitable paths in the complex plane. It is known that the corresponding complex equilibrium potential can be written as a combination of Abelian integrals on a suitable Riemann surface whose branch points can be taken as the main parameters of the problem. Equations for these branch points can be written in terms of periods of Abelian differentials and are known in several equivalent forms. We select one of these forms and use a combination of analytic an numerical methods to investigate the phase structure of asymptotic zero densities of orthogonal polynomials and of asymptotic eigenvalue densities of random matrix models. As an application we give a complete description of the phases and critical processes of the standard cubic model.Item Quasiconformal mappings and solutions of the dispersionless KP hierarchy(Theoretical and mathematical physics, 2002) Konopelchenko, Boris; Martínez Alonso, Luis; Medina Reus, ElenaA ∂¯formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions of the dKP hierarch.Item Integrable quasiclassical deformations of cubic curves(Journal of mathematical physics, 2005) Kodama, Y.; Konopelchenko, Boris; Martínez Alonso, Luis; Medina Reus, ElenaA general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize these deformations.Item Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method(Journal of mathematical physics, 2002) Konopelchenko, Boris; Martínez Alonso, LuisThe quasiclassical limit of the scalar nonlocal δ̅ -problem is derived and a quasiclassical version of the δ̅-dressing method is presented. Dispersionless Kadomtsev– Petviashvili (KP), modified KP, and dispersionless two- dimensional Toda lattice (2DTL) hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy is nothing but the ring of symmetries for the quasiclassical δ̅-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.Item Kinetic dominance and the wave function of the Universe(Physical review D, 2022) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina Reus, ElenaWe analyze the emergence of classical inflationary universes in a kinetic-dominated stage using a suitable class of solutions of the Wheeler-DeWitt equation with a constant potential. These solutions are eigenfunctions of the inflaton momentum operator that are strongly peaked on classical solutions exhibiting either or both a kinetic-dominated period and an inflation period. Our analysis is based on semiclassical WKB solutions of the Wheeler-DeWitt equation interpreted in the sense of Borel (to perform a correct connection between classically allowed regions) and on the relationship of these solutions to the solutions of the classical model. For large values of the scale factor the WKB Vilenkin tunneling wave function and the Hartle-Hawking no-boundary wave functions are recovered as particular instances of our class of wave functions.