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Mat. Zametki, 2011, Volume 89, Issue 4, Pages 614–634 (Mi mz9096)  

This article is cited in 4 scientific papers (total in 4 papers)

Squeezed States and Their Applications to Quantum Evolution

A. M. Chebotarev, T. V. Tlyachev, A. A. Radionov

M. V. Lomonosov Moscow State University

Abstract: 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, Bogolyubov formula, Campbell–Baker–Hausdorff formula, Schrödinger equation, carbon films in $(E,H)$-fields

DOI: https://doi.org/10.4213/mzm9096

Full text: PDF file (639 kB)
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English version:
Mathematical Notes, 2011, 89:4, 577–595

Bibliographic databases:

UDC: 517.958:530.145.6
Received: 17.10.2010
Revised: 18.11.2010

Citation: A. M. Chebotarev, T. V. Tlyachev, A. A. Radionov, “Squeezed States and Their Applications to Quantum Evolution”, Mat. Zametki, 89:4 (2011), 614–634; Math. Notes, 89:4 (2011), 577–595

Citation in format AMSBIB
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\paper Squeezed States and Their Applications to Quantum Evolution
\jour Mat. Zametki
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\vol 89
\issue 4
\pages 614--634
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\crossref{https://doi.org/10.4213/mzm9096}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2856753}
\transl
\jour Math. Notes
\yr 2011
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\issue 4
\pages 577--595
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Chebotarev, T. V. Tlyachev, A. A. Radionov, “Generalized Squeezed States and Multimode Factorization Formula”, Math. Notes, 92:5 (2012), 700–713  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Tlyachev T.V., Chebotarev A.M., Chirkin A.S., “A New Approach to Quantum Theory of Multimode Coupled Parametric Processes”, Phys. Scr., T153 (2013), 014060  crossref  mathscinet  adsnasa  isi  elib  scopus
    3. A. E. Teretenkov, “Quadratic Dissipative Evolution of Gaussian States”, Math. Notes, 100:4 (2016), 642–646  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. E. Teretenkov, “Dynamics of Moments for Quadratic GKSL Generators”, Math. Notes, 106:1 (2019), 151–155  mathnet  crossref  crossref  mathscinet  isi  elib
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