Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

2016 ◽  
Vol 25 (8) ◽  
pp. 080301
Author(s):  
Salim Medjber ◽  
Hacene Bekkar ◽  
Salah Menouar ◽  
Jeong Ryeol Choi
1997 ◽  
Vol 491 ◽  
Author(s):  
J. S. Graves ◽  
R. E. Allen

ABSTRACTA method is introduced for simulations of the coupled dynamics of electrons and ions in a molecule or material. It is applicable to general nonadiabatic processes, including interactions with an arbitrarily intense radiation field. The field is included in the electronic Hamiltonian through a time-dependent Peierls substitution. The time-dependent Schrödinger equation is solved with an algorithm that preserves orthogonality, and the atomic forces are obtained from a generalized Ehrenfest theorem. Calculations for GaAs and Si demonstrate that the method is reliable and quantitative.


2019 ◽  
Vol 20 (04) ◽  
pp. 2050025 ◽  
Author(s):  
Olli Hella ◽  
Juho Leppänen

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate of convergence. For maps chosen from a certain parameter range, but without additional assumptions on how the maps vary with time, we obtain a self-norming CLT provided that the variances of the partial sums grow sufficiently fast. When the maps are chosen randomly according to a shift-invariant probability measure, we identify conditions under which the quenched CLT holds, assuming fiberwise centering. Finally, we show a multivariate CLT for intermittent quasi-static systems. Our approach is based on Stein’s method of normal approximation.


2008 ◽  
Vol 22 (24) ◽  
pp. 4225-4241
Author(s):  
CHI-SHUNG TANG ◽  
PI-GANG LUAN

We consider wave packet propagation in mesoscopic quantum systems. A number of approaches are compared to look at the general solution of a time-dependent Schrödinger equation and the validity of the Ehrenfest theorem. Detailed calculations are presented to illustrate the results of a charged particle motion in the time-dependent systems, and show that the Ehrenfest theorem is not directly applicable in topologically nontrivial systems.


1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.


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