Person: Martínez Alonso, Luis
Universidad Complutense de Madrid
Faculty / Institute
Now showing 1 - 10 of 65
PublicationPhase space and phase transitions in the Penner matrix model with negative coupling constant(IOP Publishing Ltd, 2017-03-24) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina Reus, ElenaThe partition function of the Penner matrix model for both positive and negative values of the coupling constant can be explicitly written in terms of the Barnes G function. In this paper we show that for negative values of the coupling constant this partition function can also be represented as the product of an holomorphic matrix integral by a nontrivial oscillatory function of n. We show that the planar limit of the free energy with 't Hooft sequences does not exist. Therefore we use a certain modification that uses Kuijlaars-McLaughlin sequences instead of 't Hooft sequences and leads to a well-defined planar free energy and to an associated two-dimensional phase space. We describe the different configurations of complex saddle points of the holomorphic matrix integral both to the left and to the right of the critical point, and interpret the phase transitions in terms of processes of gap closing, eigenvalue tunneling, and Bose condensation. PublicationEcuaciones Diferenciales II(Departamento de Física Teórica II (Métodos Matemáticos de la Física), 2015) Mañas Baena, Manuel; Martínez Alonso, LuisEn este manual se revisan diferentes aspectos sobre las ecuaciones diferenciales en derivadas parciales de utilidad para los físicos. Se elaboraron como notas de clase de la asignatura Ecuaciones II, del plan 1993 de la Licenciatura de Física de la UCM. Actualmente cubre un 75% de la asignatura Métodos Matemáticos II del Grado de Física de la UCM. PublicationExplicit solutions of supersymmetric KP hierarchies: Supersolitons and solitinos(American Institute of Physics, 1996-12) 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. PublicationGravitational lensing by eigenvalue distributions of random matrix models(IOP Publishing Ltd, 2018-05-10) 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. PublicationKinetic dominance and the wave function of the Universe(Amer Physical Soc, 2022-04-06) 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. PublicationDispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical δ̅ -dressing method(American Institute of Physics, 2002-07) 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. PublicationComplex saddle points in the Gross-Witten-Wadia matrix model(Amer Physical Soc, 2016-11-14) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina, ElenaWe give an exhaustive characterization of the complex saddle point configurations of the Gross-WittenWadia matrix model in the large-N limit. In particular, we characterize the cases in which the saddles accumulate in one, two, or three arcs, in terms of the values of the coupling constant and of the fraction of the total unit density that is supported in one of the arcs, and derive an explicit condition for gap closing associated with nonvacuum saddles. By applying the idea of large-N instanton we also give direct analytic derivations of the weak- coupling and strong-coupling instanton actions. PublicationIntegrable quasiclassical deformations of cubic curves(American Institute of Physics, 2005-11) 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. PublicationMultiple orthogonal polynomials, string equations and the large-n limit(IOP Publishing Ltd, 2009-03-22) Martínez Alonso, Luis; Medina Reus, ElenaThe Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the phase space of the Whitham hierarchy of dispersionless integrable systems is provided. Applications to the analysis of the large-n limit of multiple orthogonal polynomials and their associated random matrix ensembles and models of non-intersecting Brownian motions are given. PublicationOn twistor solutions of the DKP equation(IOP Publishing, 2003-06-13) Guil Guerrero, Francisco; Mañas Baena, Manuel; Martínez Alonso, LuisThe factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for the construction of classes of nontrivial solutions of the dKP equation.