Geodesic
Berry phase for time-dependent coupled harmonic oscillators in the noncommutative phase space via path integral techniques
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 1, pp. 58-70

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The purpose of this paper is the description of Berry's phase, in the Euclidean Path Integral formalism, for 2D quadratic system: two time dependent coupled harmonic oscillators. This treatment is achieved by using the adiabatic approximation in the commutative and noncommutative phase space.
Keywords: Berry's phase, noncommutative phase space, coupled oscillators. 
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     title = {Berry phase for time-dependent coupled harmonic oscillators in the noncommutative phase space via path integral techniques},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Leila Khiari; Tahar Boudjedaa; Abdenacer Makhlouf; Mohammed Tayeb Meftah. Berry phase for time-dependent coupled harmonic oscillators in the noncommutative phase space via path integral techniques. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 1, pp. 58-70. http://geodesic.mathdoc.fr/item/JSFU_2020_13_1_a4/