scholarly journals Information Entropy of Zero-Point Oscillations of a Harmonic Oscillator

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
A.V. Stepanov ◽  
◽  
M.A. Stepanov ◽  
Keyword(s):  
Harmonic Oscillator ◽  
Information Entropy ◽  
Zero Point

scholarly journals INFORMATION ENTROPY AND NUCLEON CORRELATIONS IN NUCLEI

2005 ◽  
Vol 14 (08) ◽  
pp. 1251-1266 ◽  
Author(s):  
S. E. MASSEN ◽  
V. P. PSONIS ◽  
A. N. ANTONOV
Keyword(s):  
Experimental Data ◽  
Harmonic Oscillator ◽  
Electron Scattering ◽  
Information Entropy ◽  
Linear Relation ◽  
Short Range ◽  
Harmonic Oscillator Model ◽  
Momentum Distributions ◽  
The Mean

We evaluated the information entropies in coordinate and momentum spaces and their sum (Sr, Sk, S) for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator model and with the short-range correlated distributions. Suppose A is the number of nuclei, it is found that Sr depends strongly on ln A and does not depend very much on the model. The behavior of Sk is the opposite. The various cases that we consider can be classified according to either the quantity of the experimental data that we use or by the values of S, i.e., the increase in the quality of the density and in the momentum distributions leads to an increase in the values of S. In all cases, apart from the linear relation S=a+b ln A, the linear relation S=aV+bV ln V also holds. V is the mean volume of the nucleus. If S is considered as an ensemble entropy, a relation between A or V and the ensemble volume can be found. Finally, comparing many different electron scattering experiments for the same nucleus, we found that the larger the momentum transfer ranges, the larger the information entropy is. It is concluded that S might be used to compare different experiments for the same nucleus, and to choose the most reliable one.

scholarly journals Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Wayne Cheng-Wei Huang ◽  
Herman Batelaan
Keyword(s):  
Probability Distribution ◽  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Zero Point ◽  
Simulation Method ◽  
Vacuum Field ◽  
Stochastic Electrodynamics ◽  
Validity Range ◽  
Gaussian Probability Distribution ◽  
Dynamical Information

Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.

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