Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators

• URL: http://arxiv.org/abs/2009.02017v1
• Date: Fri, 4 Sep 2020 06:29:49 GMT
• Title: Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators
• Authors: J. S. Dehesa and I. V. Toranzo
• Abstract summary: Spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are discussed. We have used a methodology where the theoretical determination of the integral functionals of the Laguerre and Gegenbauers are discussed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like quantities (Fisher information, Shannon and R\'enyi entropies, disequilibrium) of its quantum probability distribution together with their associated uncertainty relations. They are explicitly given, at times in a closed compact form, by means of the potential parameters (oscillator strength, dimensionality, $D$) and the hyperquantum numbers $(n_r,\mu_1,\mu_2,\ldots,\mu_{D-1})$ which characterize the state. Emphasis is placed on the highly-excited Rydberg (high radial hyperquantum number $n_r$, fixed $D$) and the high-dimensional (high $D$, fixed hyperquantum numbers) states. We have used a methodology where the theoretical determination of the integral functionals of the Laguerre and Gegenbauer polynomials, which describe the spreading quantities, leans heavily on the algebraic properties and asymptotical behavior of some weighted $\mathfrak{L}_{q}$-norms of these orthogonal functions.

Related papers

• Emergent Anomalous Hydrodynamics at Infinite Temperature in a Long-Range XXZ Model [14.297989605089663]
  We find anomalous hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. We quantify the degree of quantum chaos using the Kullback-Leibler divergence. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of non-integrable quantum many-body systems.
  arXiv  Detail & Related papers  (2024-03-26T17:50:04Z)
• Symmetry shapes thermodynamics of macroscopic quantum systems [0.0]
  We show that the entropy of a system can be described in terms of group-theoretical quantities. We apply our technique to generic $N$ identical interacting $d$-level quantum systems.
  arXiv  Detail & Related papers  (2024-02-06T18:13:18Z)
• One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory [0.0]
  Motion of a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered. The dependence on the particle energy and the factor $mathfraka$ describing a relative strength of its constituents is described.
  arXiv  Detail & Related papers  (2023-04-13T11:50:51Z)
• Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling [22.20907440445493]
  We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) This formulation does not depend on the discretization of the Schr"odinger equation and recurrence relations of special functions. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator.
  arXiv  Detail & Related papers  (2023-04-04T03:02:03Z)
• Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics [0.0]
  Non-equilibrium and instability features of prey-predator-like systems are investigated in the framework of the Weyl-Wigner quantum mechanics. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters are shown to be affected by quantum distortions.
  arXiv  Detail & Related papers  (2023-03-16T19:55:36Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Asymptotic Equipartition Theorems in von Neumann algebras [24.1712628013996]
  We show that the smooth max entropy of i.i.d. states on a von Neumann algebra has an rate given by the quantum relative entropy. Our AEP not only applies to states, but also to quantum channels with appropriate restrictions.
  arXiv  Detail & Related papers  (2022-12-30T13:42:35Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• Complexity-like properties and parameter asymptotics of $\mathfrak{L}_{q}$-norms of Laguerre and Gegenbauer polynomials [0.0]
  Main monotonic statistical complexity-like measures of the Rakhmanov's probability density associated to the hypergeometrics (HOP) in a real continuous variable. The degree and parameters of these two-fold spreading measures are shown for the parameter-dependent families of HOPs of Laguerre and Gegenbauer types.
  arXiv  Detail & Related papers  (2021-08-16T16:49:49Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)
• Multidimensional hydrogenic states: Position and momentum expectation values [0.0]
  The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $langle ralpha rangle$ and $leftlangle palpha rightrangle$, respectively. These quantities have not been calculated in an analytical and effective manner up until now except for a number of three-dimensional hydrogenic states.
  arXiv  Detail & Related papers  (2020-11-24T17:34:14Z)

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.