https://uvadoc.uva.es/handle/10324/22154 Física Matemática 2026-04-11T11:44:43Z https://uvadoc.uva.es/handle/10324/41008 We study time evolution of Wigner function of an initially interacting one-dimensional quantum gas following the switch-off of the interactions. For the scenario where at t=0the interactions are suddenly suppressed, we derive a relationship between the dynamical Wigner function and its initial value. A two-particle system initially interacting through two different interactions of Dirac delta type is examined. For a system of particles that is suddenly let to move ballistically (without interactions) in a harmonic trap in d dimensions, and using time evolution of one-body density matrix, we derive a relationship between the time dependent Wigner function and its initial value. Using the inverse Wigner transform we obtain, for an initially harmonically trapped noninteracting particles in ddimensions, the scaling law satisfied by the density matrix at time tafter a sudden change of the trapping frequency. Finally, the effects of interactions are analyzed in the dynamical Wigner function. 2020-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/41002 Ver preprint. 2020-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40883 The nine two-dimensional Cayley–Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogeneous spaces (of points and two kinds of lines), in such a manner that the graded contraction parameters determine their curvature and signature. Secondly, new Poisson homogeneous spaces are constructed by making use of certain Poisson–Lie structures on the corresponding motion groups. Therefore, the quantization of these spaces provides noncommutative analogues of the Cayley–Klein geometries. The kinematical interpretation for the semiRiemannian and pseudo-Riemannian Cayley–Klein geometries is emphasized, since they are just Newtonian and Lorentzian spacetimes of constant curvature. 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40882 Ver abstract 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40881 We employ a symmetric gauge to describe the interaction of electrons in graphene with a magnetic field which is orthogonal to the layer surface and to build the so-called partial and bidimensional coherent states for this system in the Barut-Girardello sense. We also evaluate the corresponding probability and current densities as well as the mean energy value. 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40880 ISBN 978-3-030-20087-9 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40879 We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation. 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40878 Ver abstract 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40877 Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two Hamiltonians through a finite order differential operator. Some related subjects can be simply analyzed, as the algebras ruling both Hamiltonians and the associated coherent states. The technique has been applied also to periodic potentials, where the spectra consist of allowed and forbidden energy bands. In addition, a link with non-linear second-order differential equations, and the possibility of generating some solutions, can be explored. Recent applications concern the study of Dirac electrons in graphene placed either in electric or magnetic fields, and the analysis of optical systems whose relevant equations are the same as those of SUSY QM. These issues will be reviewed briefly in this paper, trying to identify the most important subjects explored currently in the literature. 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40876 Ver abstract 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40875 Ver abstract 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40874 Ver abstract 2019-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40873 We study in detail the behavior of the energy spectrum for the second harmonic generation (SHG) and a family of corresponding quasi-exactly solvable Schrödinger potentials labeled by a real parameter b. The eigenvalues of this system are obtained by the polynomial deformation of the Lie algebra representation space. We have found the bi-confluent Heun equation (BHE) corresponding to this system in a differential realization approach, by making use of the symmetries. By means of a b-transformation from this second-order equation to a Schrödinger one, we have found a family of quasi-exactly solvable potentials. For each invariant n-dimensional subspace of the second harmonic generation, there are either n potentials, each with one known solution, or one potential with n-known solutions. Well-known potentials like a sextic oscillator or that of a quantum dot appear among them. 2020-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40872 The Moll-Arias de Reyna integral is generalized and several values are given. 2020-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40871 We implement a SU(1, 1) covariant integral quantization of functions on the unit disk. The latter can be viewed as the phase space for the motion of a “massive” test particle on (1+1)-anti-de Sitter space-time, and the relevant unitary irreducible representations of SU(1, 1) corresponding to the quantum version of such motions are found in the discrete series and its lower limit. Our quantization method depends on the choice of a weight function on the phase space in such a way that different weight functions yield different quantizations. For instance, the Perelomov coherent states quantization is derived from a particular choice. Semi-classical portraits or lower symbols of main physically relevant operators are determined, and the statistical meaning of the weight function is discussed. 2020-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/40870 Saturn’s convective storms usually fall in two categories. One consists of mid-sized storms ∼2,000 km wide, appearing as irregular bright cloud systems that evolve rapidly, on scales of a few days. The other includes the Great White Spots, planetary-scale giant storms ten times larger than the mid-sized ones, which disturb a full latitude band, enduring several months, and have been observed only seven times since 1876. Here we report a new intermediate type, observed in 2018 in the north polar region. Four large storms with east–west lengths ∼4,000–8,000 km (the first one lasting longer than 200 days) formed sequentially in close latitudes, experiencing mutual encounters and leading to zonal disturbances affecting a full latitude band ∼8,000 km wide, during at least eight months. Dynamical simulations indicate that each storm required energies around ten times larger than mid-sized storms but ∼100 times smaller than those necessary for a Great White Spot. This event occurred at about the same latitude and season as the Great White Spot in 1960, in close correspondence with the cycle of approximately 60 years hypothesized for equatorial Great White Spots. 2020-01-01T00:00:00Z