Italo Guarneri

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$Lectures on fractal geometry and dynamics$

”The world is full of interesting operators” Y. Avron (2004) , at the Cafe’
Table of contents Smilansky’s model. Dynamics Spectral theory Multi-oscillator model & wave packet reduction Band formalism.
Page 1: Inverted oscillators & collapse of
Page 5 and 6: Smilansky’s ”irreversible” mo
Page 7 and 8: Boxing the particle Let the particl
Page 9 and 10: Dynamics of Smilansky’s model II
Page 12 and 13: Band formalism, II (ψ, Hψ) = (ψ,
Page 14 and 15: BA&WL Theory Birkhoff (1911), Adams
Page 16 and 17: Application to the inverted oscilla
Page 18: Formal Eigenfunctions Sequences {u
Page 21 and 22: BA&WL again ’Exceptional’ energ
Page 23 and 24: Spectral Expansion Theorem For Ψ(E
Page 25 and 26: Collapse If α > ω then, for any
Page 27 and 28: Band formalism Born-Oppenheimer-lik
Page 29 and 30: ”Phase transition” α < ω α >

Italo Guarneri

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