Parametric evolution of wavefunctions (2000-2006)
Developing a theory for the parametric evolution of the local density of
states (LDOS) is an important step in the studies of energy-spreading for
time dependent Hamiltonians H(Q,P;x(t)). The theory of Wigner regarding
line shapes refers to RMT model of banded matrices. My purpose was
to go beyond Wigner theory and to understand the parametric evolution of
the LDOS in case of real quantized Hamiltonians. The validity of the generic
theory is demonstrated by considering the deformation of an anharmonic
2D well (Collaboration with T. Kottos). Special considerations are
required in order to analyze cavities with 'moving walls' (Collaboration
with E.J. Heller), and the predictions are verified by numerical
work (Collaboration with A. Barnett). A related study concerns
wavepacket dynamics (Collaboration with F.M. Izrailev and T.
Kottos). An important issue that has been addressed is the clash between
RMT considerations and quantal-classical correspondence (QCC). An important
distinction is between detailed QCC and restricted QCC.
[1] D. Cohen and E.J. Heller, Phys. Rev. Lett. 84, 2841 (2000). [arXiv]
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[2] D. Cohen and T. Kottos, Phys. Rev. E 63, 36203 (2001). [arXiv]
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[3] D. Cohen, A. Barnett and E.J. Heller, Phys. Rev. E 63, 46207 (2001). [arXiv]
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[4] J.A. Mendez-Bermudez, T. Kottos and D. Cohen, PRE (2005). [arXiv]
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[5] J.A. Mendez-Bermudez, T. Kottos and D. Cohen, PRE (2006). [arXiv]
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