Demkov-Fradkin tensor for curved harmonic oscillators

• URL: http://arxiv.org/abs/2409.03900v2
• Date: Mon, 9 Sep 2024 08:27:43 GMT
• Title: Demkov-Fradkin tensor for curved harmonic oscillators
• Authors: Şengül Kuru, Javier Negro, Sergio Salamanca,
• Abstract summary: We obtain the Demkov-Fradkin tensor of symmetries for a quantum curved harmonic oscillator in a space with constant curvature given by a parameter $kappa$. As a by-product, the classical Demkov-Fradkin tensor has been obtained by the same method.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we obtain the Demkov-Fradkin tensor of symmetries for the quantum curved harmonic oscillator in a space with constant curvature given by a parameter $\kappa$. In order to construct this tensor we have firstly found a set of basic operators which satisfy the following conditions: i) their products give symmetries of the problem; in fact the Hamiltonian is a combination of such products; ii) they generate the space of eigenfunctions as well as the eigenvalues in an algebraic way; iii) in the limit of zero curvature, they come into the well known creation/annihilation operators of the flat oscillator. The appropriate products of such basic operators will produce the curved Demkov-Fradkin tensor. However, these basic operators do not satisfy Heisenberg commutators but close another Lie algebra. As a by-product, the classical Demkov-Fradkin tensor for the classical curved harmonic oscillator has been obtained by the same method. The case of two dimensions has been worked out in detail: the operators close a $so_\kappa(4)$ Lie algebra; the spectrum and eigenfunctions are explicitly solved in an algebraic way and in the classical case the trajectories have been computed.

Related papers

• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass [0.0]
  We have found three basis elements of this algebra. The algebra defined through those basis elements is a $mathfraksuleft (1,1 right)$ Heisenberg-Lie algebra.
  arXiv  Detail & Related papers  (2023-05-19T14:30:04Z)
• Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
  The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes. We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator. As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
  arXiv  Detail & Related papers  (2023-04-28T19:20:52Z)
• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field [0.0]
  We have considered a two-dimensional anisotropic harmonic oscillator placed in a time-dependent magnetic field. An orthonormal basis of the Hilbert space consisting of the eigenvectors of $hatmathcalI$ is obtained. Separability Criterion for the bipartite coherent states corresponding to our system has been demonstrated.
  arXiv  Detail & Related papers  (2022-06-30T17:19:09Z)
• The eigenvalues and eigenfunctions of the toroidal dipole operator in a mesoscopic system [0.0]
  We find the quantization rules for the eigenvalues, which are essential for describing measurements of $hatT_3$. While these kernels appear to be problematic at first glance due to singularities, they can actually be used in practical computations.
  arXiv  Detail & Related papers  (2022-03-19T17:49:20Z)
• Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space [62.997667081978825]
  We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. We extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces.
  arXiv  Detail & Related papers  (2022-02-09T19:14:13Z)
• Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature [0.0]
  This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. Their symmetries are obtained by the Jordan-Schwinger representations in the family of the Cayley-Klein algebras.
  arXiv  Detail & Related papers  (2021-12-27T07:09:02Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Intrinsic decoherence dynamics in the three-coupled harmonic oscillators interaction [77.34726150561087]
  We give an explicit solution for the complete equation, i.e., beyond the usual second order approximation used to arrive to the Lindblad form.
  arXiv  Detail & Related papers  (2021-08-01T02:36:23Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Quantum dynamics of the classical harmonic oscillator [0.0]
  A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space.
  arXiv  Detail & Related papers  (2019-12-27T21:00:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.