Phase dynamics of a relativistic electron excited by the potential field of a wave packet: Reconstruction of phase space

1998 ◽  
Vol 41 (5) ◽  
pp. 442-446
Author(s):  
A. S. Krotov ◽  
A. A. Tel’nikhin
Keyword(s):  
Phase Space ◽  
Wave Packet ◽  
Relativistic Electron ◽  
Potential Field ◽  
Phase Dynamics

scholarly journals The distribution of electrons in a metal

1928 ◽  
Vol 120 (786) ◽  
pp. 727-735 ◽  
Keyword(s):  
Phase Space ◽  
Potential Field ◽  
Nuclear Charge ◽  
Electron Gas ◽  
Interesting Application ◽  
Heavy Atoms ◽  
Upper Limit ◽  
Dimensional Phase Space ◽  
New Statistics ◽  
Number Of Cells

1. The Statistics of a Degenerate Gas . An interesting application of the new statistics of Fermi and Dirac has been made by Thomas (and also independently by Fermi) to the distribution of electrons in heavy atoms. The basic idea of these researches is that the “electron gas” surrounding a nuclues “degenerate,” so that every cell of extension h 3 of a six dimensional phase space contains two electrons, one electron spinning in one direction and another in the opposite direction. An upper limit to the possible translational energies of the electrons is imposed by the condition that electrons shall not have enough energy to escape from the field of the nucleus, viz:— ϵ≼ e . V, (1) where ϵ and e represent the energy and charge of the electron and V is the potential field. The possible range of momentum co-ordinates (neglecting relativity considerations) is then limited by p ≼(2 me V) ½ (2) and the total number of cells of extension h 3 in the phase space is given by 4π(2 me V) 3/2 /3 h 3 (3) for every unit of ordinary (co-ordinate) space available. If every cell contains two electrons, the density is given by ρ = —8π e (2 me V) 3/2 /3 h 3 . (4) Since, however, the potential V is determined by the nuclear charge and the distribution of electrons, we have ∇ 2 = —4πρ = (32π 2 e (2 me V) 3/2 /3 h 3 ,(5) an equation to determine V, subject to V → 0 as r → ∞ V r as r → 0}, (6) where E is the charge on the nucleus.

scholarly journals Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: An integrated investigation during geomagnetic storm times

2007 ◽  
Vol 112 (A11) ◽  
pp. n/a-n/a ◽  
Author(s):  
Y. Chen ◽  
R. H. W. Friedel ◽  
G. D. Reeves ◽  
T. E. Cayton ◽  
R. Christensen
Keyword(s):  
Phase Space ◽  
Relativistic Electron ◽  
Geomagnetic Storm ◽  
Geosynchronous Orbit ◽  
Phase Space Density ◽  
Space Density

Reconstructing slow-time dynamics from fast-time measurements

2007 ◽  
Vol 366 (1866) ◽  
pp. 729-745 ◽  
Author(s):  
David Chelidze ◽  
Ming Liu
Keyword(s):  
Phase Space ◽  
Potential Field ◽  
Damage Identification ◽  
Feature Space ◽  
Operating Conditions ◽  
Fast Time ◽  
Slow Time ◽  
Time Dynamics ◽  
Feature Vectors ◽  
Nonlinear Potential

This paper considers a dynamical system subjected to damage evolution in variable operating conditions to illustrate the reconstruction of slow-time (damage) dynamics using fast-time (vibration) measurements. Working in the reconstructed fast-time phase space, phase space warping-based feature vectors are constructed for slow-time damage identification. A subspace of the feature space corresponding to the changes in the operating conditions is identified by applying smooth orthogonal decomposition (SOD) to the initial set of feature vectors. Damage trajectory is then reconstructed by applying SOD to the feature subspace not related to the changes in the operating conditions. The theory is validated experimentally using a vibrating beam, with a variable nonlinear potential field, subjected to fatigue damage. It is shown that the changes in the operating condition (or the potential field) can be successfully separated from the changes caused by damage (or fatigue) accumulation and SOD can identify the slow-time damage trajectory.

Wave packet dynamics and phase space structure of HCN molecule

1990 ◽  
Vol 142 (3) ◽  
pp. 345-359 ◽  
Author(s):  
S.C. Farantos ◽  
M. Founargiotakis
Keyword(s):  
Phase Space ◽  
Wave Packet ◽  
Space Structure ◽  
Phase Space Structure ◽  
Wave Packet Dynamics

A Gaussian wave packet phase-space representation of quantum canonical statistics

2015 ◽  
Vol 143 (4) ◽  
pp. 044102 ◽  
Author(s):  
David J. Coughtrie ◽  
David P. Tew
Keyword(s):  
Phase Space ◽  
Wave Packet ◽  
Gaussian Wave Packet ◽  
Space Representation ◽  
Phase Space Representation
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