Quantum information measures of the Dirichlet and Neumann hyperspherical dots

• URL: http://arxiv.org/abs/2103.13094v2
• Date: Mon, 12 Apr 2021 09:49:38 GMT
• Title: Quantum information measures of the Dirichlet and Neumann hyperspherical dots
• Authors: O. Olendski
• Abstract summary: $mathttd$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) This paves the way to an efficient computation in either space of Shannon, R'enyi and Tsallis entropies, Onicescu energies and Fisher informations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: $\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schr\"{o}dinger equation in position space and the Fourier transform of the corresponding wave function leads to the analytic form of its momentum counterpart too. This paves the way to an efficient computation in either space of Shannon, R\'{e}nyi and Tsallis entropies, Onicescu energies and Fisher informations; for example, for the latter measure, some particular orbitals exhibit simple expressions in either space at any BC type. A comparative study of the influence of the edge requirement on the quantum information measures proves that the lower threshold of the semi-infinite range of the dimensionless R\'{e}nyi/Tsallis coefficient where one-parameter momentum entropies exist is equal to $\mathtt{d}/(\mathtt{d}+3)$ for the Dirichlet hyperball and $\mathtt{d}/(\mathtt{d}+1)$ for the Neumann one what means that at the unrestricted growth of the dimensionality both measures have their Shannon fellow as the lower verge. Simultaneously, this imposes the restriction on the upper value of the interval $[1/2,\alpha_R)$ inside which the R\'{e}nyi uncertainty relation for the sum of the position $R_\rho(\alpha)$ and wave vector $R_\gamma\left(\frac{\alpha}{2\alpha-1}\right)$ components is defined: $\alpha_R$ is equal to $\mathtt{d}/(\mathtt{d}-3)$ for the Dirichlet geometry and to $\mathtt{d}/(\mathtt{d}-1)$ for the Neumann BC. Some other properties are discussed from mathematical and physical points of view. Parallels are drawn to the corresponding properties of the hydrogen atom and similarities and differences are explained based on the analysis of the associated wave functions.

Related papers

• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Spatial Wavefunctions of Spin [0.0]
  We present an alternative formulation of quantum mechanical angular momentum. The wavefunctions are Wigner D-functions, $D_n ms (phi, theta, chi)$. Some implications of the quantum number $n$ for fundamental particles are discussed.
  arXiv  Detail & Related papers  (2023-07-25T15:48:56Z)
• Quantum-information theory of magnetic field influence on circular dots with different boundary conditions [0.0]
  2D circular quantum dots (QDs) whose circumference supports homogeneous either Dirichlet or Neumann boundary condition (BC) Physical interpretation is based on the different roles of the two BCs and their interplay with the field: Dirichlet (Neumann) surface is a repulsive (attractive) interface.
  arXiv  Detail & Related papers  (2023-06-28T11:33:11Z)
• 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)
• On parametric resonance in the laser action [91.3755431537592]
  We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
  arXiv  Detail & Related papers  (2022-08-22T09:43:57Z)
• Learning a Single Neuron with Adversarial Label Noise via Gradient Descent [50.659479930171585]
  We study a function of the form $mathbfxmapstosigma(mathbfwcdotmathbfx)$ for monotone activations. The goal of the learner is to output a hypothesis vector $mathbfw$ that $F(mathbbw)=C, epsilon$ with high probability.
  arXiv  Detail & Related papers  (2022-06-17T17:55:43Z)
• Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field [0.0]
  Shannon information entropies $S_rho,gamma$, Fisher informations $I_rho,gamma$, Onicescu energies $O_rho,gamma$ and R'enyi entropies $R_rho,gamma(alpha)$ are calculated.
  arXiv  Detail & Related papers  (2022-02-09T19:26:56Z)
• Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
  The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
  arXiv  Detail & Related papers  (2021-12-14T16:29:53Z)
• Random matrices in service of ML footprint: ternary random features with no performance loss [55.30329197651178]
  We show that the eigenspectrum of $bf K$ is independent of the distribution of the i.i.d. entries of $bf w$. We propose a novel random technique, called Ternary Random Feature (TRF) The computation of the proposed random features requires no multiplication and a factor of $b$ less bits for storage compared to classical random features.
  arXiv  Detail & Related papers  (2021-10-05T09:33:49Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• R\'{e}nyi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells [0.0]
  Dirichlet and Neumann boundary conditions (BCs) of 1D quantum well are studied. For either BC the dependencies of the R'enyi position components on the parameter $alpha$ are the same for all orbitals. The gap between the thresholds $alpha_TH$ of the two BCs causes different behavior of the R'enyi uncertainty relations as functions of $alpha$.
  arXiv  Detail & Related papers  (2020-03-09T18:34:00Z)

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.