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Classical Nonintegrability, Quantum Chaos (Paperback, 1997 ed.)
Loot Price: R1,684
Discovery Miles 16 840
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Classical Nonintegrability, Quantum Chaos (Paperback, 1997 ed.)
Series: Oberwolfach Seminars, 27
Expected to ship within 10 - 15 working days
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Total price: R1,704
Discovery Miles: 17 040
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Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos'
intended to introduce students and beginning researchers to the
techniques applied in nonin tegrable classical and quantum
dynamics. Several of these lectures are collected in this volume.
The basic phenomenon of nonlinear dynamics is mixing in phase
space, lead ing to a positive dynamical entropy and a loss of
information about the initial state. The nonlinear motion in phase
space gives rise to a linear action on phase space functions which
in the case of iterated maps is given by a so-called transfer
operator. Good mixing rates lead to a spectral gap for this
operator. Similar to the use made of the Riemann zeta function in
the investigation of the prime numbers, dynamical zeta functions
are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi
first introduces dynamical zeta functions and transfer operators,
illustrating and motivating these notions with a simple
one-dimensional dynamical system. Then she presents a commented
list of useful references, helping the newcomer to enter smoothly
into this fast-developing field of research. Chapter 3 on irregular
scattering and Chapter 4 on quantum chaos by A. Knauf deal with
solutions of the Hamilton and the Schr6dinger equation. Scatter ing
by a potential force tends to be irregular if three or more
scattering centres are present, and a typical phenomenon is the
occurrence of a Cantor set of bounded orbits. The presence of this
set influences those scattering orbits which come close."
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