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Physical Review A

Dynamics of SU(1,1) coherent states for the damped harmonic oscillator

Jeong Ryeol Choi, Kyu Hwang Yeon

Published May 29, 2009• 5 citations
Publisher

Abstract

Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.

DOI
10.1103/physreva.79.054103

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Publisher's Note: Dynamics of SU(1,1) coherent states for the damped harmonic oscillator [Phys. Rev. A79, 054103 (2009)]

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with production errors on pages 2 and 3. On page 2, the last line in the right-hand column should read as "played in Fig. 2͑dЈ͒, it is clear…."On page 3, the fourth line of the caption to Fig. 2

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Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.
We study the time evolution of SU(1,1) coherent states driven by a damped harmonic oscillator as described by the Kanai-Caldirola Hamiltonian. The coherence of these states is preserved and their time evolution is described by nonlinear ``classical'' equations. The trajectories of all SU(1,1) coherent states in phase space asymptotically approach a common point as t\ensuremath{\rightarrow}\ensuremath{\infty}. In all cases, this approach is accompanied by a damping of the associated energy expectation value to zero.