Jose Gaite

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• PhD
• Professor (Associate) at Universidad Politécnica de Madrid

The critical behavior of three-state statistical models invariant under the full symmetry group S_3 and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale i...

The critical behavior of three-state statistical models invariant under the full symmetry group $S_3$ and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale...

Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the $\lambda\phi^4$ theory in three dimensions and make a comparison between the sharp-cutoff regularization method and ot...

Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the λϕ4 theory in three dimensions and make a comparison between the sharp-cutoff regularization method and other more rec...

We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al.’s idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple se...

We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It boils down to a sim...

We present a new statistical analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey (data release 7). A set of volume-limited samples shows that the stellar mass of galaxies is concentrated in a range of galaxy luminosities that is very different from the range selected by the usual analysis of galaxy positions. Never...

Brief description of the space environment and, in particular, radiation in outer space to Earth. We study radiation (solar and cosmic), its interaction with matter, and the possible effects of that radiation on space vehicles. Written in Spanish.

Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale invariant distribution of matter, namely it gives rise to a fractal geometry. A suitable explanation of the features o...

Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale invariant distribution of matter, namely it gives rise to a fractal geometry. A suitable explanation of the features o...

The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body simulations or the Sloan Digital Sky Survey are elucidated by means of multifractal geometry. A nonlacunar multif...

A statistical analysis of the angular projection of the large-scale stellar mass distribution, as obtained from the Sloan Digital Sky Survey (data release 7) with the stellar masses of galaxies, finds values of the clustering length $r_0$ and the power-law exponent $\gamma$ of the two-point correlation function that are larger than the standard val...

The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in N-body simulations or the Sloan Digital Sky Survey are elucidated by means of multifractal geometry. Multifractal geometry can encomp...

A novel fractal analysis of the cosmic web structure is carried out, employing the Sloan Digital Sky Survey, data release 7. We consider the large-scale stellar mass distribution, unlike other analyses, and determine its multifractal geometry, which is compared with the geometry of the cosmic web generated by cosmological N-body simulations. We fin...

A novel fractal analysis of the cosmic web structure is carried out, employing the Sloan Digital Sky Survey, data release 7. We consider the large-scale stellar mass distribution, unlike other analyses, and determine its multifractal geometry, which is compared with the geometry of the cosmic web generated by cosmological N-body simulations. We fin...

The penetration of a fast projectile into a resistant medium is a complex process that is suitable for simple modeling, in which basic physical principles can be profitably employed. This study connects two different domains: the fast motion of macroscopic bodies in resistant media and the interaction of charged subatomic particles with matter at h...

The penetration of a fast projectile into a resistant medium is a complex process that is suitable for simple modeling, in which basic physical principles can be profitably employed. This study connects two different domains: the fast motion of macroscopic bodies in resistant media and the interaction of charged subatomic particles with matter at h...

Dark matter halos can be defined as smooth distributions of dark matter placed in a non-smooth cosmic web structure. This definition of halos demands a precise definition of smoothness and a characterization of the manner in which the transition from smooth halos to the cosmic web takes place. We introduce entropic measures of smoothness, related t...

The current cold dark matter cosmological model explains the large scale cosmic web structure but is challenged by the observation of a relatively smooth distribution of matter in galactic clusters. We consider various aspects of modeling the dark matter around galaxies as distributed in smooth halos and, especially, the smoothness of the dark matt...

The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as th...

Halo models of the large scale structure of the Universe are critically examined, focusing on the definition of halos as smooth distributions of cold dark matter. This definition is essentially based on the results of cosmological N-body simulations. By a careful analysis of the standard assumptions of halo models and N-body simulations and by taki...

The Kolmogorov approach to turbulence is applied to the Burgers turbulence in the stochastic adhesion model of large-scale structure formation. As the perturbative approach to this model is unreliable, here a new, non-perturbative approach, based on a suitable formulation of Kolmogorov's scaling laws, is proposed. This approach suggests that the po...

We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in therm...

Large-scale structure formation can be modeled as a nonlinear process that transfers energy from the largest scales to successively smaller scales until it is dissipated, in analogy with Kolmogorov's cascade model of incompressible turbulence. However, cosmic turbulence is very compressible, and vorticity plays a secondary role in it. The simplest...

The Kolmogorov approach to turbulence is applied to the Burgers turbulence in the stochastic adhesion model of large-scale structure formation. As the perturbative approach to this model is unreliable, here is proposed a new, non-perturbative approach, based on a suitable formulation of Kolmogorov's scaling laws. This approach suggests that the pow...

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a consta...

We develop a method of multifractal analysis of N-body cosmological simulations that improves on the customary counts-in-cells method by taking special care of the effects of discreteness and large scale homogeneity. The analysis of the Mare-Nostrum simulation with our method provides strong evidence of self-similar multifractal distributions of da...

We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like distributions. The last two distributions are connected with two types of fractal geometry of the matter distributi...

CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. AIMS: Our objecti...

We analyse a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential e...

The dark matter distribution is arguably scale invariant in a range of scales, so that it has a fractal geometry, observable in the clustering of galaxies and in cosmic voids. We review evidence of fractal geometry in recent observations, which shows, in particular, that a simple fractal model is not sufficient. Therefore, we propose a multifractal...

The effect of the large-scale cosmological expansion on small systems is studied in the light of modern cosmological models of large-scale structure. We identify certain assumptions of earlier works which render them unrealistic regarding these cosmological models. The question is reanalyzed by dropping these assumptions to conclude that a given sm...

We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power law profile, as opposed to a fractal model, can account for the observed power law galaxy-galaxy correlations. We conclude that such model, which can actually be considered as a degenerate multifractal model, is not realistic...

There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of cosmological structure formation seems to be driven to a multifractal attractor. This supports previous studies, w...

On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos are recognized as prominent features of that structure. Therefore, we propose to model the dark matter distribution as sets of fractal distributions of halos. This model relies on the concept of multifractal model as the most general scal...

The matter distribution is arguably scale invariant in a range of scales. On the other hand, halos and voids are recognized as prominent features of that structure. We review evidence of scale invariance in recent observations of the galaxy distribution, in particular, the Sloan Digital Sky Survey and observations of the Local Volume. This evidence...

“Cut-out sets” are fractals that can be obtained by removing a sequence of disjoint regions from an initial region of d-dimensional euclidean space. Conversely, a description of some fractals in terms of their void complementary set is possible. The essential property of a sequence of fractal voids is that their sizes decrease as a power law, that...

On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter distribution as a set of fractal distributions of halos of different kinds. This model relies on the concept o...

The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems defined on a chain, an optimal formulation is given by White's "density matrix renormalization group". This formula...

Context: .The question of the stability of steady spherical accretion has been studied for many years and, recently, the concept of spatial instability has been introduced.Aims.Here we study the perturbations of steady spherical accretion flows (Bondi solutions), restricting ourselves to the case of a self-similar flow, as a case that is amenable t...

Spherical accretion flows are simple enough for analytical study, by solution of the corresponding fluid dynamic equations. The solutions of stationary spherical flow are due to Bondi. The questions of the choice of a physical solution and of stability have been widely discussed. The answer to these questions is very dependent on the problem of bo...

Voids are a prominent feature of the galaxy distribution but their quantitative study is hindered by the lack of a precise definition of what constitutes a void. Here we propose a definition of voids in point distributions that uses methods of discrete stochastic geometry, in particular, Delaunay and Voronoi tessellations, and we construct a new vo...

Voids are a prominent feature of fractal point distributions but there is no precise definition of what is a void (except in one dimension). Here we propose a definition of voids that uses methods of discrete stochastic geometry, in particular, Delaunay and Voronoi tessellations, and we construct a new algorithm to search for voids in a point set....

We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We conclude that such model, which can actually be considered as a degenerate multifractal model, is not realistic...

The density matrix renormalization group can be formulated as a method that sequentially splits some quantum system into two subsystems and chooses the reduced Hilbert spaces for the subsystems such that the entropy of bipartite entanglement is maximized. This method is optimal for removing the negative effect of a boundary in the performance of re...

The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings. Indeed, the ordinary renormalization group differential equations can be supplemented with noise, making them into...

In the turbulence that takes place in rotating fluids, the symmetry assumptions of the theory of fully developed turbulence may not hold, in particular, isotropy must be relaxed to axial symmetry. This symmetry reduction leads one to consider the most general axisymmetric viscosity tensor for a Newtonian fluid, which can be obtained by group theory...

The effective stress tensor of a homogeneous turbulent rotating fluid is anisotropic. This leads us to consider the most general axisymmetric four-rank ``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent effective force on large scales that arise from it, in addition to the microscopic viscous force. Some of these terms in...

The effective stress tensor of a homogeneous turbulent rotating fluid is anisotropic. This leads us to consider the most general axisymmetric four-rank "viscosity tensor" for a Newtonian fluid and the new terms in the turbulent effective force on large scales that arise from it, in addition to the microscopic viscous force. Some of these terms invo...

The process of gravitational accretion of initially homogeneous gas on to a solid ball is studied using the methods of fluid dynamics.The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this solution soon becomes discontinuous and gives rise to a shock wave.Afterwards, there is a crossover betwe...

The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate as...

The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between t...

Large-scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity, we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a...

Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event horizon as a boundary that concentrates a large number of quantum states. This allows one to connect with the "de...

Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a (...

We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to the distribution of galaxies. If the distribution of galaxies forms a fractal set, then this property results...

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Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to provide a new interpretation of the density matrix renormalization group: Its efficacy is due to the concentration of quantum states near the boundary.

The coarse-graining operation in hydrodynamics is equivalent to a change of scale which can be formalized as a renormalization group transformation. In particular, its application to the probability distribution of a self-gravitating fluid yields an "exact renormalization group equation" of Fokker-Planck type. Since the time evolution of that distr...

There are two general irreversibility theorems for the renormalization group in more than two dimensions: the first one is of entropic nature, while the second one, by Forte and Latorre, relies on the properties of the stress-tensor trace, and has been recently questioned by Osborn and Shore. We start by establishing under what assumptions this sec...

The relative entropy of the massive free bosonic field theory is studied on various compact Riemann surfaces as a universal quantity with physical significance, in particular, for gravitational phenomena. The exact expression for the sphere is obtained, as well as its asymptotic series for large mass and its Taylor series for small mass. One can al...

The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative entropy analogous to Zamolodchikov’s c function. The one-dimensional quantum thermodynamic entropy gives rise t...

The relative entropy of the massive free bosonic field theory is studied on various compact Riemann surfaces as a universal quantity with physical significance, in particular, for gravitational phenomena. The exact expression for the sphere is obtained, as well as its asymptotic series for large mass and its Taylor series for small mass. One can al...

The classification of symmetric catastrophes is studied to obtain Landau potentials for statistical models. Potentials for symmetric models with two order parameters are thoroughly discussed. The double-cusp catastrophe is used for illustration. Its various symmetries and corresponding statistical models are revealed. As an important example, the t...

There is an ongoing debate in cosmology about the value of the length scale at which ``homogeneity'' in the matter distribution is reached or even if such a scale exists. In the wake of this debate, we intend in this letter to clarify the meaning of the statement transition to homogeneity and of the concept of correlation length. We show that there...

The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative entropy analogous to Zamolodchikov's $c$ function. The one-dimensional quantum thermodynamic entropy gives rise...

In this work we classify the singularities obtained from the Gibbs potential of a lattice gas model with three components, two order parameters and five control parameters applying the general theorems provided by Catastrophe Theory. In particular, we clearly establish the existence of Landau potentials in two variables or, in other words, corank 2...

We present the thermodynamic Bethe ansatz as a way to factorize the partition function of a 2d field theory, in particular, a conformal field theory and we compare it with another approach to factorization due to Schoutens which consists of diagonalizing matrix recursion relations between the partition functions at consecutive levels. We prove that...

The relative entropy in two-dimensional Field Theory is studied for its application as an irreversible quantity under the Renormalization Group, relying on a general monotonicity theorem for that quantity previously established. In the cylinder geometry, interpreted as finite-temperature field theory, one can define from the relative entropy a mono...

We analyze the thermodynamical potential of a lattice-gas model with three components and five parameters using the methods of the catastrophe theory. We find the highest singularity, which has codimension five, and establish its transversality. Hence the corresponding seven-degree Landau potential, the canonical form wigwam or ${A}_{6},$ constitut...

We consider relative entropy in Field Theory as a well defined (non-divergent) quantity of interest. We establish a monotonicity property with respect to the couplings in the theory. As a consequence, the relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points in decreasing order of criticali...

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a...

We construct Landau-Ginzburg Lagrangians for minimal bosonic ($N=0$) $W$-models perturbed with the least relevant field, inspired by the theory of $N=2$ supersymmetric Landau-Ginzburg Lagrangians. They agree with the Lagrangians for unperturbed models previously found with Zamolodchikov's method. We briefly study their properties, e.g. the perturba...

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a...

We consider the relation between affine Toda field theories (ATFT) and Landau-Ginzburg Lagrangians as alternative descriptions of deformed 2d CFT. First, we show that the two concrete implementations of the deformation are consistent once quantum corrections to the Landau-Ginzburg Lagrangian are taken into account. Second, inspired by Gepner's fusi...

We study the realization of conformal symmetry in the QHE as part of the $W_\infty$ algebra. Conformal symmetry can be realized already at the classical level and implies the complexification of coordinate space. Its quantum version is not unitary. Nevertheless, it can be rendered unitary by a suitable modification of its definition which amounts t...

The Landau potentials of W3-algebra models are analyzed with algebraic-geometric methods. The number of ground states and the number of independent perturbations of every potential coincide and can be computed. This number agrees with the structure of ground states obtained in a previous paper, namely, as the phase structure of the IRF models of Ji...

The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by a few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagra...

The Landau potentials of $W_3$-algebra models are analyzed with algebraic-geometric methods. The number of ground states and the number of independent perturbations of every potential coincide and can be computed. This number agrees with the structure of ground states obtained in a previous paper, namely, as the phase structure of the IRF models of...

We study the Batalin-Vilkovisky master equation for both open and closed string field theory with special attention to anomalies. Open string field theory is anomaly free once the minimal coupling to closed strings induced by loop amplitudes is considered. In closed string field theory the full-fledged master equation has to be solved order by orde...

The quantum Hall effect (QHE) is studied in the context of a conformal field theory (CFT). Winding state vertex operators for an effective field of N "spins" associated with the cyclotron motion of particles are defined. The effective field of spins may be used to define an effective Hamiltonian. This effective Hamiltonian describes the collective...

The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams...

The characterization of singular point sets in phase diagrams is surveyed in the light of catastrophe theory. The critical end point and the phase diagram near it, containing the unstable critical point, are particularly examined. Some diagrams of its sections are given, which extend beyond the standard analysis of the butterfly catastrophe. The in...

The formulation of phase transitions in the framework of catastrophe theory is studied, taking as a reference the tricritical two-fluid system. Adding renormalization-group ideas, a general approach to its classification is explored.

The analytic renormalization procedure for 2D field theory is studied. The consequences for the string effective action are investigated, comparing the R-operation with the Legendre transform. To show where and why they differ, the renormalization is explicitly carried out to third order.

The connection between the renormalization group for the sigma-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

1 EXTENDED ABSTRACT In the last years a deep transformation of the Spanish railway transportation system is being produced due to the large increase of high-speed railway lines, which has given rise to a flourishing period of innovation in both high-speed infrastructure and vehicle technology. In this frame of vehicles travelling at speeds as high...

From November, 2006 to March, 2008 a series of tests were performed onboard a wide variety of trains in order to check their response to pressure waves generated while passing through tunnels. In this communication part of the experimental results are presented, showing the pressure waves generated and focusing on the differences caused by some par...