Nikola P Petrov 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S89 doi:10.1088/1464-4266/7/3/013
Nikola P Petrov
Show affiliationsWe study the problem of the behaviour of a quantum massless scalar field in the space between two parallel infinite perfectly conducting plates, one of them stationary, the other moving periodically. We reformulate the physical problem into a problem about the asymptotic behaviour of the iterates of a map of the circle, and then apply results from the theory of dynamical systems to study the properties of the map. Many of the general mathematical properties of maps of the circle translate into properties of the field in the cavity. For example, we give a complete classification of the possible resonances in the system, and show that small enough perturbations do not destroy the resonances. We use some mathematical identities to give a transparent physical interpretation of the processes of creation and amplification of the quantum field due to the motion of the boundary and to elucidate the similarities of and the differences between the classical and quantum fields in domains with moving boundaries.
03.65.Ge Solutions of wave equations: bound states
03.50.De Classical electromagnetism, Maxwell equations
Optics, quantum optics and lasers
Issue 3 (March 2005)
Received 31 July 2004, accepted for publication 14 October 2004
Published 1 March 2005
Nikola P Petrov 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S89
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