Factorization of the Riesz-Feller Fractional Quantum Harmonic OscillatorsRosu, H C; Mancas, S C
doi: 10.1088/1742-6596/1540/1/012005pmid: N/A
Using the Riesz-Feller fractional derivative, we apply the factorization algorithm to the fractional quantum harmonic oscillator along the lines previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results. We solve the non-Hermitian fractional eigenvalue problem in the k space by introducing in that space a new class of Hermite ‘polynomials’ that we call Riesz-Feller Hermite ‘polynomials’. Using the inverse Fourier transform in Mathematica, interesting analytic results for the same eigenvalue problem in the x space are also obtained. Additionally, a more general factorization with two different Lévy indices is briefly introduced.
Prefacedoi: 10.1088/1742-6596/1540/1/011001pmid: N/A
The Quantum Fest is a biennial international conference on quantum phenomena, quantum control and geometry of quantum states, organized by the Center for Research and Advanced Studies (Cinvestav by its acronym in Spanish) and Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del Instituto Politécnico Nacional (UPIITA-IPN) in México City, Mexico. The aim of this meeting is to bring together students and researchers which are engaged in the subjects of the festival, from both theoretical and experimental approaches, in order to enable a closer contact between them by means of lively discussions.The Quantum Fest 2019 is the eighth edition of the festival, it took place from October 28 to November 1 in the facilities of the Physics Department of the Cinvestav. The topics addressed in the talks and poster sessions included quantum entanglement, coherent and squeezed states, Bose-Einstein condensates, quantum optics, quantum resonances, fractional calculus with applications in physics, operator theory, open systems, and spectral design of quantum systems. The conference included 18 plenary talks and 16 short talks, all of them presented by invitation of the festival Organizing Committee. Besides, 26 works were presented in the poster sessions.The present volume of Journal of Physics: Conference Series includes the positively refereed manuscripts that were submitted by the participants of the conference. The accepted contributions have been organized in 16 invited papers and 16 contributed papers.
Peer review statementdoi: 10.1088/1742-6596/1540/1/011002pmid: N/A
All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.
Ladder Operators for the Rosen-Morse System Through Classical AnalogyDelisle-Doray, L; Hussin, V
doi: 10.1088/1742-6596/1540/1/012001pmid: N/A
In quantum mechanics, ladder operators allow to connect the eigenstates of a system together. Ladder functions are algebraically analog objects defined in the framework of classical hamiltonian physics. For a class of exactly solvable one dimensional Hamiltonians, both the ladder operators and ladder functions take a simple form and there is a close similarity between them. In this work, we show how the analogy extends to the case of the Rosen-Morse Hamiltonian, for which the ladder functions have a more complicated structure. We compute a form for the ladder operators, based on the ladder functions of the system and we analyse the correspondences between both cases. Physical mean values are also obtained as a byproduct of the construction.
Unconventional Superfluidity in Ultracold Dipolar GasesDomínguez-Castro, G A; Paredes, R
doi: 10.1088/1742-6596/1540/1/012002pmid: N/A
In this manuscript, we discuss the emergence of p-wave superfluidity in a dipolar Fermi gas confined in a double layer array of parallel optical lattices in two dimensions. The dipole moments of the molecules placed at the sites of the optical lattices, separated a distance L and pointing in opposite directions produce an effective attractive interaction among them, except between those dipoles situated one on top of the other. Such interaction between dipoles is precisely the origin of the non-conventional superfluid state. We present the analysis for the ground state of the many-body system within the mean-field scheme. In particular, we study the stable regions, as a function of the system parameters, namely the effective interaction between dipoles and the filling factor n, for which the superfluid state can exist. Following the BKT scheme, we estimate the critical temperature of the superfluid state.
A Bayesian Analysis for Circular Galaxies Using a Bose—Einstein Condensate as a Dark Matter HaloEscamilla-Rivera, C
doi: 10.1088/1742-6596/1540/1/012003pmid: N/A
In this paper we present an extension of a Bayesian study for a Bose–Einstein Condensate type halo surrounding a Schwarzschild–type black hole. The predictions obtained via the Thomas–Fermi approximation are tested using observations from SPARC galaxy rotation curves sampler with 10 circular galaxies and whose inclination (angle) is less that 80 deg. The statistical analysis is confronted with the Navarro–Frenk–White density profile model where we found that at the centre of galaxies is require a supermassive black hole with a constrain of log10 M/M⊙ = 12.00 ± 0.73 to allow a BEC configuration at this stage. Also, we show that the proposed scenario can fit the galaxy rotation curves on average rate .
Is a Deterministic and Local Interpretation of Quantum Mechanics Possible?… First StepsNahmad-Achar, E; Sánchez-Kuntz, N
doi: 10.1088/1742-6596/1540/1/012006pmid: N/A
Quantum states in superposition cannot be observed, suggesting that they merely embody information on possible measurement results. Yet, we think of them as describing physical systems that evolve in time according to given mathematical equations. Furthermore, evolution takes place in physical space-time, and local causality is imposed on space-time by Special Relativity (a sequence of cause and effect that constitutes a fundamental principle by which we think about and do scientific work).It is therefore strange that there is non–locality and violation of causality embedded in Quantum Mechanics. We try to give here a first step to see whether a deterministic and local interpretation is possible. We will show that Bell’s inequality is not conclusive about the non–local nature of Quantum Mechanics, in that there exists an interpretation of reality (which we put forward) which is local and in which Bell’s inequality cannot be derived. Assuming determinism and locality a new Bell-like inequality is derived, which is always satisfied by Quantum Mechanics and which allows for local hidden variables [1].