Entropic measures of Rydberg-like harmonic states

Abstract

The Shannon entropy, the desequilibrium and their generalizations (Rényi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts. The radial part depends on the analytical form of the potential, but the angular part does not. In this paper we first calculate the angular entropy of any central potential by means of two analytical procedures. Then, we explicitly find the dominant term of the radial entropy for the highly energetic (i.e., Rydberg) stationary states of the oscillator-like systems. The angular and radial contributions to these entropic measures are analytically expressed in terms of the quantum numbers which characterize the corresponding quantum states and, for the radial part, the oscillator strength. In the latter case we use some recent powerful results of the information theory of the Laguerre polynomials and spherical harmonics which control the oscillator-like wavefunctions.

arXiv commentAccepted in International Journal of Quantum Chemistry

References in corpus (24)

• Area laws for the entanglement entropy - a review
• Entropy and Area
• Formulation of the uncertainty relations in terms of the Renyi entropies
• A class of Rényi information estimators for multidimensional densities
• Direct measurement of non-linear properties of bipartite quantum states
• Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
• Pinning of Fermionic Occupation Numbers
• On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles
• Quantum entanglement in exactly soluble atomic models: The Moshinsky model with three electrons, and with two electrons in a uniform magnetic field
• On the Role of Information Theoretic Uncertainty Relations in Quantum Theory
• Position-momentum uncertainty relations based on moments of arbitrary order
• Spreading lengths of Hermite polynomials
• Entanglement in N-harmonium: bosons and fermions
• Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics
• The Shannon-entropy-based uncertainty relation for $D$-dimensional central potentials
• Analytic solutions of topologically disjoint systems
• One-parameter class of uncertainty relations based on entropy power
• Virial expansion coefficients in the harmonic approximation
• Entanglement in S states of two-electron quantum dots with Coulomb impurities at the center
• The lowest excited configuration of harmonium
• Condensation and interaction range in harmonic boson traps: a variational approach
• Quantum Statistics and Thermodynamics in the Harmonic Approximation
• Entropy and complexity analysis of the D-dimensional rigid rotator and hyperspherical harmonics
• Momentum distribution of confined bosons: temperature dependence

Cited by in corpus (13)

• Rényi and Tsallis entropies: three analytic examples
• Rényi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields
• Analytical Shannon information entropies for all discrete multidimensional hydrogenic states
• Exact Shannon entropies for the multidimensional harmonic states
• Heisenberg and entropic uncertainty measures for large-dimensional harmonic systems
• Rényi entropies for multidimensional hydrogenic systems in position and momentum spaces
• Exact Rényi entropies of $D$-dimensional harmonic systems
• Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells
• Fisher information in confined isotropic harmonic oscillator
• Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots
• Complexity-like properties and parameter asymptotics of ${\mathfrak{L}}_q$-norms of Laguerre and Gegenbauer polynomials
• Convexity properties of superpositions of degenerate bipartite eigenstates