Geodesic
Quantum analogue of unstable limit cycles of a~periodically perturbed inverted oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 19-31

Voir la notice de l'article provenant de la source Math-Net.Ru

To study the quantum analogue of classical limit cycles, we consider the behavior of a particle in a negative quadratic potential perturbed by a sinusoidal field. We propose a type of wave function asymptotically satisfying the operator of initial conditions and still admitting analytic integration of the nonstationary Schrödinger equation. The solution demonstrates that for certain perturbation phases determined by the forcing frequency and the initial indeterminacy of the coordinate, the wave-packet center temporarily stabilizes near the potential maximum for approximately two "natural periods" of the oscillator and then moves to infinity with bifurcations in the drift direction. The effect is not masked by packet spreading, because the packet undergoes anomalous narrowing (collapse) to a size of the order of the characteristic length on the above time interval and its unbounded spreading begins only after this.
Keywords: inverted quantum oscillator, limit cycle, nonstationary Schrödinger equation, generalized Gaussian type, collapse, dynamical stabilization
Mots-clés : periodic perturbation, bifurcation. 
@article{TMF_2019_198_1_a1,
     author = {V. V. Chistyakov},
     title = {Quantum analogue of unstable limit cycles of a~periodically perturbed inverted oscillator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {19--31},
     publisher = {mathdoc},
     volume = {198},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a1/}
}
TY  - JOUR
AU  - V. V. Chistyakov
TI  - Quantum analogue of unstable limit cycles of a~periodically perturbed inverted oscillator
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 19
EP  - 31
VL  - 198
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a1/
LA  - ru
ID  - TMF_2019_198_1_a1
ER  - 
%0 Journal Article
%A V. V. Chistyakov
%T Quantum analogue of unstable limit cycles of a~periodically perturbed inverted oscillator
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 19-31
%V 198
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a1/
%G ru
%F TMF_2019_198_1_a1
V. V. Chistyakov. Quantum analogue of unstable limit cycles of a~periodically perturbed inverted oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 19-31. http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a1/