Entropy and the Quantum - Tucson, Arizona, March 16-20, 2009

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Program


All lectures to take place in room ILC 150.

Monday 16 March

09:00-09:30 Registration & Welcome
09:30-10:30 Jan Wehr Quantum Physics from Zero I
10:45-11:45 Jan Wehr Quantum Physics from Zero II
Lunch
01:45-02:45 Robert Seiringer Inequalities for Schroedinger Operators and Applications I
03:00-04:00 Robert Seiringer Inequalities for Schroedinger Operators and Applications II
04:15-05:15 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, time-adiabtic 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

09:30-10:30 Jan Wehr Quantum Physics from Zero III
10:45-11:45 Bruno Nachtergaele Quantum Entropy in Condensed Matter and Information Theory I
12:00-01:00 Bruno Nachtergaele Quantum Entropy in Condensed Matter and Information Theory II
Lunch
03:00-04:00 Eric Carlen Trace Inequalities and Quantum Entropy I
04:15-05:15 Eric Carlen Trace Inequalities and Quantum Entropy II


Wednesday 18 March

09:30-10:30 Robert Seiringer Inequalities for Schroedinger Operators and Applications III
10:45-11:45 Robert Seiringer Inequalities for Schroedinger Operators and Applications IV
12:00-01:00 Luc Rey-Bellet Quantum large deviations and entropy
In classical statistical mechanics entropies and relative entropies are rate functions which characterize the rate at which (large) fluctuations occur. We discuss a number of similar results obtained recently for quantum mechanical systems. The problem here is only partially understood and we will also discuss a number of open problems. This talk is based on joint works with Marco Lenci and Yoshiko Ogata respectively.

01:30-05:30

Excursion

Vans to take us to the Arizona-Sonora Desert Museum.


Thursday 19 March

09:30-10:30 Bruno Nachtergaele Quantum Entropy in Condensed Matter and Information Theory III
10:45-11:45 Bruno Nachtergaele Quantum Entropy in Condensed Matter and Information Theory IV
12:00-01:00 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 Wigner-Yanase-Dyson entropy and give a simple, self-contained 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^{1-p} 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
03:00-04:00 Christopher King Comments on Hastings' additivity counterexamples
04:15-05:15 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 time-forward process at an arbitrary time and a density operator in the time-reversed 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

09:30-10:30 Eric Carlen Trace Inequalities and Quantum Entropy III
10:45-11:45 Eric Carlen Trace Inequalities and Quantum Entropy IV
Lunch
01:45-02:45 Christian Hainzl Dynamical collapse of massive stars in the Bogolubov-Hartee-Fock-approximation
I will talk about the finite-time blow-up for relativistic (Bogolubov)-Hartree-Fock equations with radial initial data and negative energy. The corresponding (Bogolubov)-Hartree-Fock equations for gravitating particles serve as approximation for the dynamical evolution of white dwarfs.
03:00-04:00 Charles Newman Ising Euclidean (Quantum) Fields and Cluster Area Measures
I will discuss a representation for the magnetization field of the critical two-dimensional Ising model in the scaling limit as a (conformal) random field using renormalized area measures associated with SLE (Schramm-Loewner Evolution) clusters. The renormalized areas come from the scaling limit of critical FK (Fortuin-Kasteleyn) 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.


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