The School
will be organized with the funds of the E.C. Project "The Mathematical
Aspects of Quantum Chaos" and also with local funds.
info@quantumchaos.net
LOCATION
click on the images to view the page with the close-up
Villa Gandolfi Pallavicini
Via Martelli 22/24, Bologna (Italy)
|
The Villa
|
The
villa is a beautiful restored Renaissance-style building in the
surrounding immediately outside Bologna to the east of the city
(about 30 minutes by bus from the historical center of Bologna,
see
map).
It's surrounded by a park, which will guarantee a quiet environment
for the school.
|
Villa
Pallavicini:
the Hall |
The
Villa was the domicile of a branch of the Conti Pallavicini's
family, one of the most powerful Italian noble family, whose origin
goes back to the middle age .
In particular, the Villa is famous for having given hospitality
to Wolfgang Amadeus Mozart in the 1770, while he was in Bologna
for taking the admission test to the famous "Accademia Filarmonica
Cittadina".
Today the Villa has been completed restored and it the location
of some important University structure, as such as the Alma Mater
Foundation, the school of Journalism and the Center for Islam
Studies.
|
Socrates
dependance |
Socrates dependance:
a room |
All
the participants will be located directly at the Villa and at the
"Socrates" dependance just behind the Villa.
Three daily meals and coffe-break will be served through a catering
service. |
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DIRECTIONS
See
the map or download the .PDF version of Bologna
Map (about 800k) offered by the official site of the University
of Bologna
by PLANE:
the airport is located just outside bologna, close to the
"tangenziale" of Bologna (the main arteria surronding the city).
From here you can take a taxi directly to the Villa (see instructions below)
by CAR:
Exit 11B on the "Tangenziale" of Bologna (the main arteria surronding
the city). Keep right and follow the directions to Castenaso. After
about 1 miles and two traffic light turn right on Via Pallavicini, the
Villa is at your right. On site there is plenty of private parking.
by Train:
Bologna
Train Station is one of the biggest in Italy and there are plenty
of trains arriving from all directions.
The station is located in the center of town.
From here you can either take a Taxi (see below) directly to the Villa or reach the Bus
stop in Via Rizzoli: from the main exit of the station, take Via Indipendenza and this street will bring you
to Piazza Maggiore (about 10 minutes walking).
From Via Rizzoli (near Piazza Maggiore) you can now take the bus to the Villa (see below)
by BUS:
Bus
number 14 runs from Piazza Maggiore to bus stop "Martelli"
which is right in front of the villa.
Tickets are L. 1,800 each or L. 12,000 for 8 rides. The service will
run until late at night.
by TAXI:
The full address is Villa Gandolfi Pallavicini, Via Martelli 22/24, Bologna (Italy) .
Taxi from the train station or airport will costs about L 20,000/30,000
(10/15 euro) (daytime weekly rate).
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SCHEDULE
From Saturday 1st to Monday 10th september 2001
THREE BASIC COURSES
Stephan De Bièvre
Université des Sciences et Technologies de Lille, UFR de
Mathématiques, Villeneuve d'Ascq, FRANCE
TITLE:
Quantum maps: a case study in quantum chaos
LECTURE
1: Hamiltonian maps on the two-torus.
Some
examples of Hamiltonian maps on the two-torus will be studied (translations,
the baker map, cat maps and their perturbations, skew products), and
their dynamical behaviour analysed in order to illustrate notions
such as integrability, ergodicity, (exponential) mixing, etc.
LECTURE
2: Quantization on the torus.
Both the
kinematical and dynamical aspects of quantization on the torus will
be discussed and several tools and estimates of semi-classical analysis
introduced: Weyl and anti-Wick quantization, the Egorov theorem.
LECTURE
3: The Schnirelman theorem
A
complete proof of the Schnirelman theorem for ergodic maps will be
given as well as an analysis of its limits, making a connection with
the lectures of Rudnick. Consequences of mixing on eigenfunction behaviour
will be further discussed as well as the behaviour of eigenfunction
zeros, if time permits.
LECTURE
4: Long time semi-classical estimates.
A
discussion of the Egorov theorem for logarithmic time scales and an
application to coherent state behaviour on such scales.
Andreas
Knauf
Department
of Mathematics at the University of Erlangen-Nuremburg,Germany
TITLE:
Introduction to Dynamical Systems
SUBJECTS:
1) Measure theoretic notions: v. Neumann ergodic theorem., ergodicity,
mixing and shifts
2) Hyperbolicity: Hyperbolic torus automorphisms, Lagrangian manifolds,
Anosov flows, negative curvature, billiards, topological obstructions
for Anosov property
3) Smooth ergodic theory,ergodicity for surfaces of negative curvature,
cone fields, non-smooth dynamical systems
4) Entropy: definitions, entropy and topology, entropy and periodic
orbits
5) Applications and questions: periodic potentials, classical gas,
transport, application of methods from statistical mechanics.
LITERATURE
W. Ballmann: Lectures on Spaces of Nonpositive Curvature
L.A. Bunimovich et al: Dynamical Systems, Ergodic Theory and Applications
K. Falconer: Techniques in Fractal Geometry
A. Katok, B. Hasselblatt: Introduction to the Modern Theory of Dynamical
Systems
C. Liverani, M.P. Wojtkowski: Ergodicity in Hamiltonian Systems
G. Paternain: Geodesic Flows
P. Walters: An Introduction to Ergodic Theory
Zeev
Rudnick
Tel Aviv University
TITLE:
Quantum Maps and their Arithmetic
SYLLABUS:
Below is a tentative syllabus for the course. Parts of it may overlap
with those of the other courses in the summer school and the final
syllabus will be determined at a later time to avoid too many repetitions
and/or omissions.
1. Quantum maps of the torus:
. Quantum mechanics on the torus
. Quantum ergodicity ("Schnirelman's theorem")
. Quantization of linear maps of the torus ("cat maps")
. Quantum symmetries and the desymmetrized cat map
. Quantum unique ergodicity
2. Number Theoretic background:
. basics . congruences
. Dirichlet characters
. L-functions
. exponential sums - an overview
3. The modular surface:
. classical and quantum mechanics in negative curvature
. Maass forms and Hecke operators
. a comparison with the quantized cat map
Summer School Schedule:
(preliminary version)
|
Saturday, September 1 2001 |
|
10:30-12:30 | Arrival |
| 12:30 |
Lunch |
| 14:00-18:30 |
Arrival |
| 18:30-19:30 |
Welcome |
| 19:30 |
Dinner |
| |
|
Sunday, September 2 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
A. Knauf: "Lecture 1" |
| 10:30-11:00 |
Coffee |
| 11:00-12:15 |
Z. Rudnick: "Lecture 1" |
| 12:30 |
Lunch |
| 15:30-16:45 |
A. Knauf: "Lecture 2" |
| 16:45-17:15 |
Coffee |
| 17:15-18:30 |
S. De Bièvre: "Lecture 1" |
| 19:30 |
Dinner |
| |
|
Monday, September 3 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
S. De Bièvre: "Lecture 2" |
| 10:30-11:00 |
Coffee |
| 11:00-12:15 |
Z. Rudnick: "Lecture 2" |
| 12:30 |
Lunch |
| 15:15-16:30 |
S. De Bièvre: "Lecture 3" |
| 16:30-17:00 |
Coffee |
| 17:00-17:50 |
F. Mezzadri: "Quantum cat maps and spin" |
| 17:50-18:40 |
A. Backer:
"Numerical aspects of eigenfunctions and eigenvalues 1" |
| 19:30 |
Dinner |
| |
|
Tuesday, September 4 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
S. De Bièvre: "Lecture 4" |
| 10:30-11:00 |
Coffee |
| 11:15-12:30 |
Z. Rudnick: "Lecture 3" |
| 12:30 |
Lunch |
| 15:15-16:30 |
Z. Rudnick: "Lecture 4" |
| 16:30-17:00 |
Coffee |
| 17:00-17:50 |
F. Benatti: "The classical limit of quantum dynamical entropies" |
| 17:50-18:40 |
A. Backer:
"Numerical aspects of eigenfunctions and eigenvalues 2" |
| 19:30 |
Dinner |
| |
|
Wednesday, September 5 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
S. De Bièvre: "Lecture 5" |
| 10:30-11:00 |
Coffee |
| 11:15-12:30 |
Z. Rudnick: "Lecture 5" |
| 12:30 |
Lunch |
| 13:30-19:30 |
Free |
| 19:30 |
Dinner |
| |
|
Thursday, September 6 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
S. De Bièvre: "Lecture 6" |
| 10:30-11:00 |
Coffee |
| 11:15-12:30 |
Z. Rudnick: "Lecture 6" |
| 12:30 |
Lunch |
| 15:15-16:30 |
A. Knauf: "Lecture 3" |
| 16:30-17:00 |
Coffee |
| 17:00-17:30 |
S. Fuerstberger: "Semiclassical properties of billiard boundary functions" |
| 17:30-18:00 |
C. Hughes: "Random matrix theory and the Riemann zeta function" |
| 18:15-18:45 |
R. Glaser: "Quantum ergodicity for non-relativistic particles with spin" |
| 19:30 |
Dinner |
| |
|
Friday, September 7 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
A. Knauf: "Lecture 4" |
| 10:30-11:00 |
Coffee |
| 11:15-12:30 |
A. Knauf: "Lecture 5" |
| 12:30 |
Lunch |
| 15:15-16:30 |
U. Smilansky: "Quantum Graphs 1" |
| 16:30-17:00 |
Coffee |
| 17:00-18:00 |
R. Artuso: "From normal to anomalous deterministic diffusion 1" |
| 18:00-18:50 |
P.M. Kurlberg: "Value distribution for eigenfunctions of quantized cat maps" |
| 19:30 |
Dinner |
| |
|
Saturday, September 8 2001 |
| 08:00-09:15 |
Breakfast |
| 09:15-10:30 |
A. Knauf: "Lecture 6" |
| 10:30-11:00 |
Coffee |
| 11:00-12:00 |
R. Artuso: "From normal to anomalous deterministic diffusion 2" |
| 12:30 |
Lunch |
| 15:15-16:10 |
S. Nonnenmacher: "Spectrum of classical vs. quantum Perron-Frobenius operators for maps" |
| 16:10-17:00 |
S. Isola: "On the spectrum of Farey and Gauss maps" |
| 17:00-17:30 |
Coffee |
| 17:30-18:00 |
A. Rampioni: "Return Time Statistics" |
| 18:00-18:50 |
T. Prosen: "On general relation between quantum ergodicity and fidelity of quantum dynamics" |
| 19:30 |
Dinner |
| |
|
Sunday, September 9 2001 |
| 08:00-09:45 |
Breakfast |
| 09:45-10:45 |
U. Smilansky: "Quantum Graphs 2" |
| 10:45-11:00 |
Coffee |
| 11:00-12:00 |
U. Smilansky: "Quantum Graphs 3" |
| 12:30 |
Lunch |
| 15:30-16:20 |
G. Berkolaiko:
"Looking for chaos in quantum graphs" |
| 16:20-17:10 |
R. Schubert: "Seminar Title" |
| 17:10-17:40 |
Coffee |
| 17:40-18:30 |
J. Bolte: "Semiclassics for particles with spin" |
| 18:30-19:30 |
Closing |
| 19:30 |
Dinner |
| |
|
Monday, September 10 2001 |
| 08:00-10:00 |
Breakfast |
| 10:00-12:30 |
Departure |
| 12:30 |
Lunch |
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