Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development
Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 1, pp. 146-149
Cet article a éte moissonné depuis la source Math-Net.Ru
The Bogolyubov–Zubarev fast-phase method [1] is used to give a simple proof of the following well-known proposition [2]: when a perturbation is switched on and off smoothly, the total increment of the adiabatic invariant (the action) for one-dimensional periodic motion in a slowly varying potential is a quantity less than any power of $\alpha$, where $\alpha$ is a parameter that characterizes the rate of change of the potential.
@article{TMF_1986_66_1_a10,
author = {A. N. Vasil'ev and M. A. Guzev},
title = {Simple proof that an adiabatic invariant is conserved to exponential accuracy over a~complete interval of development},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {146--149},
year = {1986},
volume = {66},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/}
}
TY - JOUR AU - A. N. Vasil'ev AU - M. A. Guzev TI - Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1986 SP - 146 EP - 149 VL - 66 IS - 1 UR - http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/ LA - ru ID - TMF_1986_66_1_a10 ER -
%0 Journal Article %A A. N. Vasil'ev %A M. A. Guzev %T Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development %J Teoretičeskaâ i matematičeskaâ fizika %D 1986 %P 146-149 %V 66 %N 1 %U http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/ %G ru %F TMF_1986_66_1_a10
A. N. Vasil'ev; M. A. Guzev. Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development. Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 1, pp. 146-149. http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/