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A symmetry trip from Caldirola to Bateman damped systems

A symmetry trip from Caldirola to Bateman damped systems,V. Aldaya,F. Coss' Dio,J. Guerrero,F. F. López-Ruiz

A symmetry trip from Caldirola to Bateman damped systems   (Citations: 1)
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For the Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg algebra can be found. The inclusion of the standard time evolution symmetry in this algebra for damped systems, in a unitary manner, requires a non-trivial extension of this basic algebra and hence the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman's dual system, which now includes a new particle acting as an energy reservoir. The group of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schr\"odinger equation. The usual second-order equation and the inclusion of the original Caldirola-Kanai model in Bateman's system are also discussed.
Published in 2011.
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