- 04-240 Nikola P. Petrov
- Dynamical Casimir effect in a periodically changing domain:
A dynamical systems approach
Aug 2, 04
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Abstract. We study the problem of the behavior 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 behavior
of the iterates of a map of the circle,
and then apply results from 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 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 and the differences
between the classical and quantum fields
in domains with moving boundaries.