Geodesic
Squeezed States and Their Applications to Quantum Evolution
Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 614-634

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In this paper, we consider quantum multidimensional problems solvable by using the second quantization method. A multidimensional generalization of the Bogolyubov factorization formula, which is an important particular case of the Campbell–Baker–Hausdorff formula, is established. The inner product of multidimensional squeezed states is calculated explicitly; this relationship justifies a general construction of orthonormal systems generated by linear combinations of squeezed states. A correctly defined path integral representation is derived for solutions of the Cauchy problem for the Schrödinger equation describing the dynamics of a charged particle in the superposition of orthogonal constant $(E,H)$-fields and a periodic electric field. We show that the evolution of squeezed states runs over compact one-dimensional matrix-valued orbits of squeezed components of the solution, and the evolution of coherent shifts is a random Markov jump process which depends on the periodic component of the potential.
Keywords: squeezed state, Campbell–Baker–Hausdorff formula, Schrödinger equation, carbon films in $(E,H)$-fields.
Mots-clés : Bogolyubov formula 
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     title = {Squeezed {States} and {Their} {Applications} to {Quantum} {Evolution}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a13/}
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A. M. Chebotarev; T. V. Tlyachev; A. A. Radionov. Squeezed States and Their Applications to Quantum Evolution. Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 614-634. http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a13/