Program
All lectures to take place in room ILC 150.
Monday 16 March
09:0009:30 

Registration & Welcome 
09:3010:30 
Jan Wehr 
Quantum Physics from Zero I 
10:4511:45 
Jan Wehr 
Quantum Physics from Zero II 

Lunch 

01:4502:45 
Robert Seiringer 
Inequalities for Schroedinger Operators and Applications I 
03:0004:00 
Robert Seiringer 
Inequalities for Schroedinger Operators and Applications II 
04:1505:15 
Volker Betz 
Superadiabatic transition histories in quantum molecular dynamics 
 
We are interested in the dynamics of a molecule's nuclear wave function near an avoided crossing of
two electronic energy levels. More precisely, we study the time development of the wave function's component
in an initially unoccupied energy subspace, when the wave packet crosses the transition region. In the optimal superadiabatic
representation, which we define, this component builds up monotonously, and has the approximate shape of an error function;
thus, its norm displays the same behaviour as observed by Michael Berry in a simplified, timeadiabtic model in 1990. Finally,
we give a simple, explicit formula for the transmitted wave packet in the scattering region, which is in excellent agreement with
high precision ab initio numerical computations. 
Tuesday 17 March
Wednesday 18 March
Thursday 19 March
09:3010:30 
Bruno Nachtergaele 
Quantum Entropy in Condensed Matter and Information Theory III 
10:4511:45 
Bruno Nachtergaele 
Quantum Entropy in Condensed Matter and Information Theory IV 
12:0001:00 
Mary Beth Ruskai 
A unified treatment of the convexity of relative entropy and certain trace functionals, with conditions for equality 
 
We introduce a generalization of relative entropy derived from the WignerYanaseDyson
entropy and give a simple, selfcontained proof that it is convex. Moreover, special cases
yield the joint convexity of relative entropy, and for the map (A,B) >
Tr K^* A^p K B^{1p} Lieb's joint concavity for 0 < p < 1 and Ando's joint convexity for
1 < p < 2. This approach allows us to obtain conditions for equality in these cases, as
well as conditions for equality in a number of inequalities which follow from them.
These include the monotonicity under partial traces, and some Minkowski type matrix
inequalities proved by Lieb and Carlen for mixed (p,q) norms. In all cases the equality
conditions are independent of p; for extensions to three spaces they are identical to
the conditions for equality in the strong subadditivity of relative entropy.
Here is the corresponding article. 

Lunch 


03:0004:00 
Christopher King 
Comments on Hastings' additivity counterexamples 
04:1505:15 
Ryoichi Kawai 
Entropy production and the arrow of time beyond the second law of thermodynamics 
 
We will show that the thermodynamic entropy production, upon
perturbing Hamiltonian system arbitrarily far out of equilibrium in a
transition between two equilibrium states, is exactly given by
relative entropy between a density operator in a timeforward process
at an arbitrary time and a density operator in the timereversed
process at the same instance. This result makes precise connection
between dissipation and irreversibility. The result also implies
various inequalities significantly more useful than the second law of
thermodynamics. 
06:30 
Buffet at Hotel Sheraton 

Friday 20 March
09:3010:30 
Eric Carlen 
Trace Inequalities and Quantum Entropy III 
10:4511:45 
Eric Carlen 
Trace Inequalities and Quantum Entropy IV 

Lunch 

01:4502:45 
Christian Hainzl 
Dynamical collapse of massive stars in the BogolubovHarteeFockapproximation 
 
I will talk about the finitetime blowup for relativistic (Bogolubov)HartreeFock equations
with radial initial data and negative energy. The corresponding (Bogolubov)HartreeFock
equations for gravitating particles serve as approximation for the
dynamical evolution of white dwarfs. 
03:0004:00 
Charles Newman 
Ising Euclidean (Quantum) Fields and Cluster Area Measures 
 
I will discuss a representation for the magnetization field of
the critical twodimensional Ising model in the scaling limit as a (conformal) random
field using renormalized area measures associated with SLE (SchrammLoewner Evolution)
clusters. The renormalized areas come from the scaling limit of critical FK
(FortuinKasteleyn) clusters and the random field is a convergent sum of the area
measures with random signs. The representation is based on the interpretation of the
lattice magnetization as the sum of the signed areas of clusters. If time permits,
potential extensions, including to three dimensions will also be discussed. The talk
will be based on joint work with F. Camia (arXiv:0812.4030; to appear in PNAS) and on
work in progress with F. Camia and C. Garban. 
