FM - Artículos de revistaFM - Artículos de revistahttp://uvadoc.uva.es/handle/10324/221552020-02-20T07:36:53Z2020-02-20T07:36:53ZAn Integro-Differential Equation of the Fractional Form: Cauchy Problem and SolutionOlivar Romero, FernandoRosas Ortiz, Óscarhttp://uvadoc.uva.es/handle/10324/400992020-02-03T12:36:23Z2019-01-01T00:00:00ZWe solve the Cauchy problem defined by the fractional partial differential
equation [∂tt − κD]u = 0, with D the pseudo-differential Riesz operator of first
order, and certain initial conditions. The
solution of the Cauchy problem resulting from the substitution of the Gaussian pulse
u(x, 0) by the Dirac delta distribution ϕ(x) = μδ(x) is obtained as corollary.
2019-01-01T00:00:00ZOn the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the SphereGonzález León, Miguel ÁngelMateos Guilarte, JuanTorre Mayado, Marina de lahttp://uvadoc.uva.es/handle/10324/400982020-02-03T12:36:23Z2019-01-01T00:00:00ZSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space
to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context.
2019-01-01T00:00:00ZKink dynamics in the MSTB modelAlonso Izquierdo, A.http://uvadoc.uva.es/handle/10324/400972020-02-03T12:36:23Z2019-01-01T00:00:00ZIn this paper kink scattering processes are investigated in the Montonen–Sarker–Trullinger–Bishop (MSTB) model. The MSTB model is in fact a one-parametric family of relativistic scalar field theories living in a one-time one-space Minkowski space-time which encompasses two coupled scalar fields. Among the static solutions of the model two kinds of topological kinks are distinguished in a precise range of the family parameter. In that regime there exists one unstable kink exhibiting only one non-null component of the scalar field. Another type of topological kink solutions, stable in this case, includes two different kinks for which the two components of the scalar field are non-null. Both one-component and two-component topological kinks are accompanied by their antikink partners. The decay of the unstable kink to one of the stable solutions plus radiation is numerically computed. The pair of stable two-component kinks living
respectively on upper and lower semi-ellipses in the field space belongs to the same topological sector in the configuration space and provides an ideal playground to address several scattering events involving one kink and either its own antikink or the antikink of the other stable kink. By means of numerical analysis we shall find and describe interesting physical phenomena. Bion (kink–antikink oscillations) formation, kink reflection, kink–antikink annihilation, kink transmutation and resonances are examples of these types of events. The appearance of these phenomena emerging in the kink–antikink scattering depends critically on the initial collision velocity and the chosen value of the coupling constant parametrizing the family of MSTB models.
2019-01-01T00:00:00ZSoliton fermionic number from the heat kernel expansionAlonso Izquierdo, A.Fresneda, RodrigoMateos Guilarte, JuanVassilevich, D.http://uvadoc.uva.es/handle/10324/400962020-02-03T12:36:23Z2019-01-01T00:00:00ZWe consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized η function that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in amulti flavor extension of the Goldstone–Wilczek model. We also propose an improved expansion of the heat
kernel that allows the tackling of the convergence issues and permits an automated computation of the coefficients.
2019-01-01T00:00:00ZA generalized Holling type II model for the interaction between dextral-sinistral snails and Pareas snakesAlonso Izquierdo, A.González León, Miguel ÁngelTorre Mayado, Marina de lahttp://uvadoc.uva.es/handle/10324/400952020-02-03T12:36:22Z2019-01-01T00:00:00ZPareatic snakes possess outstanding asymmetry in the mandibular tooth number, which has probably been caused by its evolution to improve the feeding on the predominant dextral snails. Gene mutation can generate chiral inversion on the snail body. A sinistral snail population can thrive in this ecological context. The interactions between dextral/sinistral snails and Pareas snakes are modeled in this paper by using a new generalized functional response of Holling type II. Distinct Pareas species show different bilateral asymmetry degrees. This parameter plays an essential role in our model and determines the evolution of the populations. Stability of the solutions is also analyzed for different regimes in the space of parameters.
2019-01-01T00:00:00ZAsymmetric kink scattering in a two-component scalar field theory modelAlonso-Izquierdo, A.http://uvadoc.uva.es/handle/10324/400942020-02-03T12:36:23Z2019-01-01T00:00:00ZIn this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian
space-time is addressed. The potential term U(fi_1; fi_2) is given by a polynomial of fourth degree in the
first field component and of sixth degree in the second one. The novel characteristic of this model is
that the kink variety describes two different types of extended particles. These particles are characterized
by its topological charge but also by a new feature determined by a discrete charge L = 0,1,-1.
For this reason, the kink scattering involves a very rich variety of processes, which comprises kink
annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final
velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are
very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type
II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric
scattering events are also discussed.
2019-01-01T00:00:00ZNonlinear symmetries of perfectly invisible PT-regularized conformal and superconformal mechanics systemsGuilarte, Juan MateosPlyushchay, Mikhail S.http://uvadoc.uva.es/handle/10324/400932020-02-03T12:36:22Z2019-01-01T00:00:00ZWe investigate how the Lax-Novikov integral in the perfectly invisible PT-regularized
zero-gap quantum conformal and superconformal mechanics systems affects
on their (super)-conformal symmetries. We show that the expansion of the conformal
symmetry with this integral results in a nonlinearly extended generalized Shrödinger
algebra. The PT-regularized superconformal mechanics systems in the phase of the
unbroken exotic nonlinear N = 4 super-Poincare symmetry are described by nonlinearly super-extended Schrödinger algebra with the osp(2|2) sub-superalgebra. In the partially broken phase, the scaling dimension of all odd integrals is indefinite, and the osp(2|2) is not contained as a sub-superalgebra.
2019-01-01T00:00:00ZNonclassical States for Non-Hermitian Hamiltonians with the Oscillator SpectrumZelaya, KevinDey, SanjibHussin, VeroniqueRosas Ortiz, Óscarhttp://uvadoc.uva.es/handle/10324/400922020-02-03T12:36:22Z2019-01-01T00:00:00ZIn this paper, we show that the standard techniques that are utilized to study the
classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non-PT-symmetric and PT-symmetric oscillators exhibiting real spectra.
2019-01-01T00:00:00ZRevisiting the Casimir Energy with General Boundary Conditions, and applications in 1D CrystalsMuñoz Castañeda, José MaríaBordag, M.Santamaría Sanz, Lucíahttp://uvadoc.uva.es/handle/10324/400912020-02-04T10:05:45Z2020-01-01T00:00:00ZWe obtain new expressions for the Casimir energy between plates that are mimicked
by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.
2020-01-01T00:00:00ZEvolution of quantum observables: from non-commutativity to commutativityFortin, S.Gadella Urquiza, ManuelHolik, F.Losada, M.http://uvadoc.uva.es/handle/10324/400902020-02-03T12:36:20Z2020-01-01T00:00:00ZA fundamental aspect of the quantum-to-classical limit is the transition from a non-
commutative algebra of observables to commutative one.However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infinite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.
2020-01-01T00:00:00ZSymmetries of certain double integrals related to Hall effect devicesAusserlechner, UdoGlasser, M. LawrenceZhou, Yajunhttp://uvadoc.uva.es/handle/10324/400892020-02-12T09:25:24Z2020-01-01T00:00:00ZOne encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz–Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical parameters of the underlying Hall effect devices. We give a unified mathematical treatment of such symmetric double integrals, in the context of Hall effect devices with three and four contacts.
2020-01-01T00:00:00ZDirac-Weyl equation on a hyperbolic graphene surface under perpendicular magnetic fieldsDemir Kizilirmk, D.Kuru, SengulNegro Vadillo, Francisco Javierhttp://uvadoc.uva.es/handle/10324/400882020-02-03T12:36:20Z2020-01-01T00:00:00ZIn this paper the Dirac-Weyl equation on a hyperbolic surface of graphene under magnetic fields is considered. In order to solve this equation analytically for some
cases, we will deal with vector potentials symmetric under rotations around the z axis. Instead of using tetrads we will get this equation from a more intuitive point of view by restriction from the Dirac-Weyl equation of an ambient space. The eigenvalues and corresponding eigenfunctions for some magnetic fields are found by means of the factorization method. The existence of a zero energy ground level and its degeneracy is also analysed in relation to the Aharonov-Casher theorem valid for
at graphene.
2020-01-01T00:00:00ZSU(2), Associated Laguerre Polynomials and Rigged Hilbert SpacesCeleghini, EnricoGadella Urquiza, ManuelOlmo Martínez, Mariano Antonio delhttp://uvadoc.uva.es/handle/10324/400872020-02-03T12:36:20Z2018-01-01T00:00:00ZWe present a family of unitary irreducible representations of SU(2)
realized in the plane, in terms of the Laguerre polynomials. These functions
are similar to the spherical harmonics defined on the sphere. Relations with
an space of square integrable functions defined on the plane, L^2(R^2), are
analyzed. We have also enlarged this study using rigged Hilbert spaces that
allow to work with iscrete and continuous bases like is the case here.
2018-01-01T00:00:00ZSpectral Algorithms for MRA Orthonormal WaveletsGómez Cubillo, Fernando MaríaVillullas Merino, Sergiohttp://uvadoc.uva.es/handle/10324/400862020-02-12T07:49:31Z2018-01-01T00:00:00ZOperator techniques lead to spectral algorithms to compute scaling
functions and wavelets associated with multiresolution analyses (MRAs). The
spectral algorithms depend on the choice of pairs of suitable orthonormal
bases (ONBs). This work presents the spectral algorithms for three different
pairs of ONBs: Haar bases, Walsh–Paley bases and trigonometric bases. The
Walsh–Paley bases connect wavelet theory and dyadic harmonic analysis. The
results for trigonometric bases are the first viable attempt to do a discrete
Fourier analysis of the problem.
2018-01-01T00:00:00ZExactly Solvable One-Qubit Driving Fields Generated via Nonlinear EquationsEnríquez, MarcoCruz y Cruz, Sarahttp://uvadoc.uva.es/handle/10324/400852020-02-03T12:36:20Z2018-01-01T00:00:00ZUsing the Hubbard representation for SU(2), we write the time-evolution operator of a
two-level system in the disentangled form. This allows us to map the corresponding dynamical law
into a set of nonlinear coupled equations. In order to find exact solutions, we use an inverse approach
and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with
the Ermakov equation. A physical model with the so-obtained Hamiltonians is discussed in the
context of the nuclear magnetic resonance phenomenon.
2018-01-01T00:00:00ZA functional identity involving elliptic integralsGlasser, M. LawrenceZhou, Yajunhttp://uvadoc.uva.es/handle/10324/400842020-02-03T12:36:20Z2018-01-01T00:00:00ZWe show that adouble integral remains invariant as one trades some parameters. This invariance property is suggested from symmetry considerations in the operating characterstics of a semiconductor Hall-effect device.
2018-01-01T00:00:00Z