Документ взят из кэша поисковой машины. Адрес оригинального документа : http://lmmqsp.sinp.msu.ru/mat/present_ICPEAC_popov.pdf Дата изменения: Wed Sep 16 15:08:16 2015 Дата индексирования: Sat Apr 9 22:20:01 2016 Кодировка:

New look at the strong field approximation in laser-matter interactions
Yuri V. Popov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia


In collaboration with: A.Galstyan, A.Hamido, N. Janssens, B. Piraux ­ Inst. Condensed Matter and Nanosciences, Univ. Catholique de Louvain, Louvain-la-Neuve, Belgium F.Mota-Furtado, P.F.O'Mahony ­ Dept. of Mathematics, Royal H o l l o w a y, U n i v e r s i t y o f L o n d o n , E g h a m , Surrey, United Kingdom O. Chuluunbaatar -- Joint Institute for Nuclear Research, Dubna, Moscow region, Russia

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MOTIVATIONS:

-- People say, that SFA calculations are gauge dependent.

Is it correct ?
-- Papers are published with the statements, that SFA in the

length gauge is in better agreement with the experiment, than that in the velocity gauge, or vice versa. What is in a reality?

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Definitions for laser pulse:


Time dependent Schroedinger equation

V - gauge LV - transformation

L - gauge


Lipmann-Schwinger (Dyson) equation

Green's function

V-Volkov wave


Lipmann-Schwinger (Dyson) equation


Eq. (4) is correct for an arbitrary initial wave packet, NOT for the hydrogen ground state!


V-gauge ansatz

LS-equation

V-SFA (first Born, Bauer)


V-gauge ansatz

The corresponding L-gauge ansatz

gives the same V-SFA.
Formula (10) generates the gauge-invariant family.


L-gauge ansatz

LS-equation

L-SFA (first Born, Keldysh)


L-gauge ansatz

The ansatz (11) generates now another gaugeinvariant family. They can be compared only with the exact solutions of the corresponding TDSE and the phase connection of the L and V wave packets. X = a+b = c+d a+b ­ one family, c+d ­ another family


Calculation of energy spectra


Calculation of energy spectra


Conclusions

SFA is the first Born term, if the Coulomb potential is considered like a perturbation. Correct perturbation means that higher terms are smaller than the first one. This is a domain of high frequencies and low intensities.


Conclusions

Correct gauge transformation of the chosen ansatz gives the gauge invariant Born series, which can be called as the gauge invariant family. The V-SFA and L-SFA are related to DIFFERENT families. They are different and CANNOT be gauge invariant by definition. But the full Born series of different families are gauge invariant.



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