2,257 research outputs found
The resonance spectrum of the cusp map in the space of analytic functions
We prove that the Frobenius--Perron operator of the cusp map
, (which is an approximation of the
Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions
corresponding to eigenvalues different from 0 and 1. We also prove that for any
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment and some finite or
countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy
spaces is adde
Quantum Zeno and anti-Zeno effects in the Friedrichs model
We analyze the short-time behavior of the survival probability in the frame
of the Friedrichs model for different formfactors. We have shown that this
probability is not necessary analytic at the time origin. The time when the
quantum Zeno effect could be observed is found to be much smaller than usually
estimated. We have also studied the anti-Zeno era and have estimated its
duration.Comment: References added. Appendix B shortened. Discussions extende
Resonances of the cusp family
We study a family of chaotic maps with limit cases the tent map and the cusp
map (the cusp family). We discuss the spectral properties of the corresponding
Frobenius--Perron operator in different function spaces including spaces of
analytic functions. A numerical study of the eigenvalues and eigenfunctions is
performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.
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