Premium
Time‐evolution operator for a forced parametric oscillator
Author(s) -
A. José Récamier,
Jáuregui Rocío
Publication year - 1997
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/(sici)1097-461x(1997)62:2<125::aid-qua1>3.0.co;2-y
Subject(s) - anharmonicity , quartic function , unitarity , operator (biology) , harmonic oscillator , position operator , ladder operator , unitary state , momentum operator , time evolution , physics , momentum (technical analysis) , parametric statistics , quantum mechanics , algebraic number , perturbation theory (quantum mechanics) , statistical physics , mathematics , mathematical analysis , computer science , extension (predicate logic) , repressor , law , compact operator , chemistry , biochemistry , political science , transcription factor , programming language , statistics , finance , pure mathematics , economics , gene
We apply an algebraic technique to describe the evolution of a parametric harmonic oscillator forced by a constant quartic potential. As the first step, we make use of iterative Bogolubov transformations (IBT) to incorporate information from the anharmonic part of the interaction in a nonperturbative form, yielding a unitary time‐evolution operator. Later on, we make use of first‐order perturbation theory to deal with that part of the interaction which was not incorporated previously. We show numerically that the resulting time‐evolution operator is closer to unitarity than is the one obtained if no IBT is applied. The quantum fluctuations of position and momentum are evaluated for “the ground” state. Squeezing and correlation effects are observed. © 1997 John Wiley & Sons, Inc.