13 dec 1999

INTRODUCTION TO QUANTUM CHAOS
  

Next lecture

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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 Muratore-Ginanneschi, 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 three-body 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 point-like 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 point-like 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, 1-d
(optional: 16.4 average density of states, 2-d )
16.9 free particle motion
a) calculate R(q,q',t), 2-d
(optional: b) calculate R(q,q',t), 2-d const mag field )
(optional: c) calculate R(q,q',t), 1-d 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 + Hamilton-Jacobi 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 Muratore-Ginanneschi.
Exercises: e-mail description
Due Tuesday, 21 sep 99

Lecture 4           13:15 - 15:00 Thursday, 23 sep 99
Exercises: e-mail description

Lecture 5           13:15 - 15:00 Thursday, 30 sep 99
Exercises: e-mail 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 Muratore-Ginanneschi.
Exercises: e-mail 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 Muratore-Ginanneschi.
Exercises: e-mail 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 Muratore-Ginanneschi.
Exercises: e-mail 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 Muratore-Ginanneschi.
Exercises: e-mail 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, ... .

Term papers         due no later than 16:00 Wed 26 Jan 2000 - Dorte Glass office
 

predrag@nbi.dk