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M. Santander

Publications and source records attributed to M. Santander.

At least 109 records · Page 6Linked to original sources
arXiv2007

Measurement of Aerosols at the Pierre Auger Observatory

The air fluorescence detectors (FDs) of the Pierre Auger Observatory are vital for the determination of the air shower energy scale. To compensate for variations in atmospheric conditions that affect the energy measurement, the Observatory operates an array of monitoring instruments to record hourly atmospheric conditions across the detector site, an area exceeding 3,000 square km. This paper presents results from four instruments used to characterize the aerosol component of the atmosphere: the Central Laser Facility (CLF), which provides the FDs with calibrated laser shots; the scanning backscatter lidars, which operate at three FD sites; the Aerosol Phase Function monitors (APFs), which measure the aerosol scattering cross section at two FD locations; and the Horizontal Attenuation Monitor (HAM), which measures the wavelength dependence of aerosol attenuation.

astro-ph↗
arXiv2007

The Lidar System of the Pierre Auger Observatory

The Pierre Auger Observatory in Malargue, Argentina, is designed to study the origin of ultrahigh energy cosmic rays with energies above 10^18 eV. The energy calibration of the detector is based on a system of four air fluorescence detectors. To obtain reliable calorimetric information from the fluorescence stations, the atmospheric conditions at the experiment's site need to be monitored continuously during operation. One of the components of the observatory's atmospheric monitoring system is a set of four elastic backscatter lidar stations, one station at each of the fluorescence detector sites. This paper describes the design, current status, standard operation procedure, and performance of the lidar system of the Pierre Auger Observatory.

astro-ph↗
arXiv2005

One-dimensional model of a quantum nonlinear harmonic oscillator

In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown to display shape invariance. Its energy spectrum is found by factorization. The linear harmonic oscillator appears as the $λ\to 0$ limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones.

hep-th↗
arXiv2002

Maximal superintegrability on N-dimensional curved spaces

A unified algebraic construction of the classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions for the Hamiltonian and its integrals of motion are given in a linear ambient space $R^{N+1}$, and secondly they are expressed in terms of two geodesic coordinate systems on the ND spaces themselves, with an explicit dependence on the curvature as a parameter. On the sphere, the potential is interpreted as a superposition of N+1 oscillators. Furthermore each Lie algebra generator provides an integral of motion and a set of 2N-1 functionally independent ones are explicitly given. In this way the maximal superintegrability of the ND Euclidean Smorodinsky-Winternitz system is shown for any value of the curvature.

math-ph↗
arXiv2001

Berry phase in homogeneous Kähler manifolds with linear Hamiltonians

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of {\em classical} objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.

math-ph↗
arXiv1999

Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length

An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schrödinger equations on 3D spaces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wavefunction for the hydrogen atom case. Finally, we make a comparison between the ``space curvature" effects and minimal length effects for the hydrogen spectrum

quant-ph↗
arXiv1999

Non-standard quantum so(2,2) and beyond

A new "non-standard" quantization of the universal enveloping algebra of the split (natural) real form $so(2,2)$ of $D_2$ is presented. Some (classical) graded contractions of $so(2,2)$ associated to a $Z_2 \times Z_2$ grading are studied, and the automorphisms defining this grading are generalized to the quantum case, thus providing quantum contractions of this algebra. This produces a new family of "non-standard" quantum algebras. Some of these algebras can be realized as (2+1) kinematical algebras; we explicitly introduce a new deformation of Poincaré algebra, which is naturally linked to the null plane basis. Another realization of these quantum algebras as deformations of the conformal algebras for the two-dimensional Euclidean, Galilei and Minkowski spaces is given, and its new properties are emphasized.

hep-th↗
arXiv1998

Central extensions of the families of quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.

math-ph↗
arXiv1997

Central Extensions of the Quasi-orthogonal Lie algebras

We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as well as a large number of other non-semisimple algebras, all of which have at least a semidirect structure (in some cases two or more). The dimensions of their second cohomology groups H^2(G,R) and the explicit expression of their central extensions are given.

q-alg↗
arXiv1997

Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras

A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a bicrossproduct structure. This is done for both the algebra and, in a low-dimensional example, for the (dual) group aspects of the deformation.

q-alg↗
arXiv1996

The general solution of the real $Z_2^{\otimes N}$ graded contractions of $so(N+1)$

The general solution of the graded contraction equations for a $\zz_2^{\otimes N}$ grading of the real compact simple Lie algebra $so(N+1)$ is presented in an explicit way. It turns out to depend on $2^N-1$ independent real parameters. The structure of the general graded contractions is displayed for the low dimensional cases, and kinematical algebras are shown to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in particular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous space-times.

hep-th↗
arXiv1995

A New Null-Plane Quantum Poincare Algebra

A new quantum deformation, which we call null-plane, of the (3+1) Poincaré algebra is obtained. The algebraic properties of the classical null-plane description are generalized to this quantum deformation. In particular, the classical isotopy subalgebra of the null-plane is deformed into a Hopf subalgebra, and deformed spin operators having classical commutation rules can be defined. Quantum Hamiltonian, mass and position operators are studied, and the null-plane evolution is expressed in terms of a deformed Schrödinger equation.

q-alg↗
arXiv1995

Universal $R$--matrices for non-standard (1+1) quantum groups

A universal quasitriangular $R$--matrix for the non-standard quantum (1+1) Poincaré algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the deformation parameter $z$. A family $g_μ$ of ``quantum graded contractions" of the algebra $U_ziso(1,1)\oplus U_{-z}iso(1,1)$ is obtained; this set of quantum algebras contains as Hopf subalgebras with two primitive translations quantum analogues of the two dimensional Euclidean, Poincaré and Galilei algebras enlarged with dilations. Universal $R$--matrices for these quantum Weyl algebras and their associated quantum groups are constructed.

q-alg↗
arXiv1995

Non-standard quantum (1+1) Poincaré group: a $T$--matrix approach

The Hopf algebra dual form for the non--standard uniparametric deformation of the (1+1) Poincaré algebra $iso(1,1)$ is deduced. In this framework, the quantum coordinates that generate $Fun_w(ISO(1,1))$ define an infinite dimensional Lie algebra. A change in the basis of the dual form is obtained in order to compare this deformation to the standard one. Finally, a non--standard quantum Heisenberg group acting on a quantum Galilean plane is obtained.

q-alg↗
arXiv1994

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases $N=2,3,4$. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations $U_z so(p,q)$. They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincaré and Galilean algebras.

hep-th↗
arXiv1994

Quantum Algebras for Maximal Motion Groups of N-Dimensional Flat Spaces

An embedding method to get $q$-deformations for the non--semisimple algebras generating the motion groups of $N$--dimensional flat spaces is presented. This method gives a global and simultaneous scheme of $q$-deformation for all $iso(p,q)$ algebras and for those ones obtained from them by some Inönü--Wigner contractions, such as the $N$--dimensional Euclidean, Poincaré and Galilei algebras.

hep-th↗
arXiv1994

Poisson--Lie contractions and quantum (1+1) groups

A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction. The quantization of this algebra for the Euclidean, Galilei and Poincaré cases is developed, and their duals are also computed. Contractions on these quantum groups are studied.

hep-th↗