Geodesic
The Relation and Evolution of Squeezing and Instability for Systems with Quadratic Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 3, pp. 477-490

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We propose a method that allows relating the quantum squeezing effect to the classical instability by establishing evolution equations for elements of the dispersion matrix directly in terms of elements of the stability matrix. The solution of these equations is written in terms of the evolution operator. Knowing this operator, we can analyze the system instability at finite times. Based on the developed formalism, we investigate two physical systems: the degenerate and nondegenerate parametric amplifiers with external $\delta$-shaped pulses. We show that we can either amplify or, on the contrary, weaken both the squeezing effect and the system instability using $\delta$-pulses.
Keywords: squeezing, instability, stability matrix, evolution operator, Lyapunov exponent.
Mots-clés : dispersion matrix 
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     author = {V. I. Kuvshinov and V. V. Marmysh and V. A. Shaporov},
     title = {The {Relation} and {Evolution} of {Squeezing} and {Instability} for {Systems} with {Quadratic} {Hamiltonians}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {477--490},
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     volume = {139},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a8/}
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V. I. Kuvshinov; V. V. Marmysh; V. A. Shaporov. The Relation and Evolution of Squeezing and Instability for Systems with Quadratic Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 3, pp. 477-490. http://geodesic.mathdoc.fr/item/TMF_2004_139_3_a8/