Information analysis in free and confined harmonic oscillator

Abstract

In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology,etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information, Shannon entropy, Renyi entropy , Tsallis entropy, Onicescu energy and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been invoked to explain several physico-chemical properties of a system under investigation. Kullback-Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the change of information in going from one state to another.

References in corpus (29)

• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Matrix product states represent ground states faithfully
• An information-theoretic security proof for QKD protocols
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Features of the Extension of a Statistical Measure of Complexity to Continuous Systems
• Tendency to Maximum Complexity in a Non-Equilibrium Isolated System
• Rényi generalization of the operational entanglement entropy
• On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
• Some extensions of the uncertainty principle
• A generalized skew information and uncertainty relation
• An elementary formula for entanglement entropies of fermionic systems
• Renyi Entropy of the Interacting Fermi Liquid
• Any order imaginary time propagation method for solving the Schrodinger equation
• Calculation of the spiked harmonic oscillators through a generalized pseudospectral method
• A Parallel Algorithm for Solving the 3d Schrodinger Equation
• A method to discern complexity in two-dimensional patterns generated by coupled map lattices
• Spherically confined isotropic harmonic oscillator
• Studies on some singular potentials in quantum mechanics
• Fisher information in confined hydrogen-like ions
• Supersymmetric variational energies of 3d confined potentials
• Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields
• Bound state spectra of the 3D rational potential
• Quantum mechanical virial-like theorem for confined quantum systems
• Ground and excited states of Li${}^{-}$, Be${}^{-}$ through a density-based approach
• Legendre transform structure and extremal properties of the relative Fisher information
• Non-linear relativistic diffusions
• Renyi-alpha entropies of quantum states in closed form: Gaussian states and a class of non-Gaussian states
• Moments of Wigner function and Renyi entropies at freeze-out