13 dec 1999
INTRODUCTION TO QUANTUM CHAOS
Fysik711B  Fall semester 1999 
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PLACE AND TIMES:
Lecture: 13:15  15:00 thu,
Aud. C  NBI Blegdamsvej
Øvelser: 11:30  12:15 tue,
Aud. C  NBI Blegdamsvej
TEACHING ASSISTANTS 
unsung heros volunteering:
Paolo
MuratoreGinanneschi,
Kristian Schaadt,
Niels Søndergaard,
Yueheng Lan,
?.
PROBLEM SETS:
Please deliver solutions to problem sets by Thursday, at the
lecture, or place them in Predrag's mailbox/CATS mailbox.
Lecture 1
13:15  15:00 Thursday, 2 sep 99 in Aud. C  NBI Blegdamsvej
Introduction
Reading:
Chapter 1:
An overview of the main themes of the course.
Recommended reading before you decide to download anything else.
Appendix A
 A brief history of chaos.
Classical mechanics has not stood still since Newton. The formalism that
we use today was developed by Euler and Lagrange. By the end of the 1800's the
three problems that would lead to the notion of chaotic dynamics were
already known: the threebody problem, the ergodic hypothesis,
and nonlinear oscillators.
Chapter 16
Semiclassical quantum mechanics:
sect. 16.1 only, review of quantum mechanics.
Lecture 2
13:15  15:00 Thursday, 9 sep 99
Semiclassical approximation
In semiclassical applications of quantum
mechanics the particle is a
pointlike object bouncing from potential walls
the same way it does in the classical mechanics. The real
novelty of quantum mechanics is
the interference of the
pointlike particle with its own other versions
traveling along different classical trajectories,
which is simply impossible in classical mechanics.
Combination of
classical dynamics and wave interference
leads to the semiclassical approximations.
Reading:
Chapter 16
Semiclassical quantum mechanics:
sect. 16.2 only, derivation of Hamilton's equations
as short wavelength approximation to wave mechanics.
Chapter 2 Dynamics.
We recapitulate the basic notions of dynamics.
If you are familiar with the dynamics on the level of an
introductory graduate nonlinear dynamics course
you might be bored.
Problem set session
11:15  13:00 Tuesday, 14 sep 99 in Aud. C  NBI Blegdamsvej
Discussion led by
Kristian Schaadt
Exercises

Complex Gaussians and deltas, density of states:
16.1 Dirac delta function
16.15 complex phase \pi/4
Read section 16.1.1 Average density of states
16.3 average density of states, 1d
(optional: 16.4 average density of states, 2d )
16.9 free particle motion
a) calculate R(q,q',t), 2d
(optional: b) calculate R(q,q',t), 2d const mag field )
(optional: c) calculate R(q,q',t), 1d harmonic osc. )
Numerical simulation of dynamical systems:
Exercise
5.10 Integrate numerically R\"ossler system
(Poincare section is discussed in sect. 2.2)
Due Tuesday, 14 sep 99
Lecture 3
13:15  15:00 Thursday, 16 sep 99
Semiclassical approximation
We use Madelung fluid picture + HamiltonJacobi theory to
piece together a semiclassical wave function
Reading:
sect. 16.2.3 Density evolution
sect. 16.2.4 Semiclassical wave function
sect. 16.3 Semiclassical propagator
Problem set session
11:15  13:00 Tuesday, 21 sep 99 in Aud. C  NBI Blegdamsvej
Discussion led by Paolo
MuratoreGinanneschi.
Exercises:
email description
Due Tuesday, 21 sep 99
Lecture 4
13:15  15:00 Thursday, 23 sep 99
Exercises:
email description
Lecture 5
13:15  15:00 Thursday, 30 sep 99
Exercises:
email description
Lecture 6 A. Jackson
13:15  15:00 Thursday, 7 oct 99
Random Matrix Theory I
Reading:
Lecture notes
Lecture 7 A. Jackson
13:15  15:00 Thursday, 14 oct 99
Random Matrix Theory II
Reading:
Lecture notes
18 24 oct 99: kartofler!
Lecture 8 A. Jackson
13:15  15:00 Thursday, 28 0ct 99
Random Matrix Theory III
Reading:
Lecture notes
Problem set session
11:30  12:15 Tuesday, 2 nov 99 in Aud. C  NBI Blegdamsvej
Discussion led by Paolo
MuratoreGinanneschi.
Exercises:
email description
Lecture 9
13:15  15:00 Thursday, 4 nov 99
Dynamics, local and global
Problem set session
11:30  12:15 Tuesday, 9 nov 99 in Aud. C  NBI Blegdamsvej
Discussion led by Paolo
MuratoreGinanneschi.
Exercises:
email description
Lecture 10
13:15  15:00 Thursday, 11 nov 99
Trace formulas, spectral determinants
Problem set session
11:30  12:15 Tuesday, 16 nov 99 in Aud. C  NBI Blegdamsvej
Discussion led by Paolo
MuratoreGinanneschi.
Exercises:
email description
Lecture 11
H. Bruus
13:15  15:00 Thursday, 18 nov 99
Mesoscopics I
Reading:
Lecture notes
Lecture 12
H. Bruus
13:15  15:00 Thursday, 25 nov 99
Mesoscopics II
Reading:
Lecture notes
Lecture 13
13:15  15:00 Thursday, 2 dec 99
Dynamical zeta functions, cycle expansions
Problem set session
10:30  12:15 Tuesday, 7 dec 99 in Aud. C  NBI Blegdamsvej
Discussion led by Paolo
MuratoreGinanneschi.
Exercises:
email description
Lecture 14
13:15  15:00 Thursday, 9 Dec 99
Helium
Term papers will take 2 weeks from start to finish. I am still formulating
the projects and am open to suggestions.
Lecture 15 (the last of the course)
13:15  15:00 Thursday, 16 dec 99
What went wrong with this course?
Intermittency, mixed systems, border of order, ... .