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Stability of the Rydberg atom in the crossed magnetic and electric fields
Author(s) -
Guirao Juan L. G.,
Vera Juan A.
Publication year - 2011
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22462
Subject(s) - hamiltonian (control theory) , rydberg atom , physics , third order , rydberg formula , instability , atom (system on chip) , quantum mechanics , mathematical physics , atomic physics , chemistry , mathematics , ion , mathematical optimization , computer science , embedded system , ionization , philosophy , theology
The stability of equilibrium positions of the Rydberg atom exposed to the uniform crossed electric and magnetic fields is analyzed. The dynamics of the system is described by an autonomous Hamiltonian depending on parameters a and f . By the normalization of the quadratic part of the Hamiltonian expansion in the neighborhood of the equilibrium position it is proved that for any f < 0 and ${1 \over 2} < a < {1 \over 2} + {{( - f)^{3/2} } \over {3\sqrt 3 }}$ , the equilibrium solution of the equations of motion is stable in Liapunov sense, while for f > 0 and a < 1/2, there is a domain of instability in the plain of parameters Ofa bounded by the curve d 3 = 0. In the domain of linear stability, it is proved that there are two curves in the plane Ofa , where the resonance conditions of third (ω 1 = 2ω 2 ) and fourth (ω 1 = 3ω 2 ) order are fulfilled. Moreover, by the normalization of the third‐ and fourth‐order terms in the Hamiltonian expansion it is proved that in the case of the third‐order resonance, the equilibrium position is unstable for all f > 0 different from f = 0.111572 and f = 0.281144, for which the stability takes place. In the case of the fourth‐order resonance, there are two intervals of parameters for which the equilibrium position is unstable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011