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Construction of Complex Invariants for Classical Dynamical Systems

โœ Scribed by R.S. Kaushal; Shweta Singh

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
144 KB
Volume
288
Category
Article
ISSN
0003-4916

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โœฆ Synopsis

With a view to extracting some further insight into the features of a dynamical system, we investigate here the possibility of its admitting complex dynamical invariants. For this purpose, both the rationalization and the Lie algebraic methods are employed to study the one-dimensional Hamiltonian systems on the extended complex phase plane characterized by x = x 1 + i p 2 , p = p 1 + i x 2 . Several systems (including the PT -symmetric ones) are found to admit complex invariants. These invariants are expected to play an important role in the analysis of complex trajectories in both the classical and quantum mechanics of the system concerned.

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