Program
All lectures to take place in room ILC 150.
Monday 16 March
09:00-09:30 |
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Registration & Welcome |
09:30-10:30 |
Jan Wehr |
Quantum Physics from Zero I |
10:45-11:45 |
Jan Wehr |
Quantum Physics from Zero II |
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Lunch |
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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 |
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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
Wednesday 18 March
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 |
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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. |
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Lunch |
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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 |
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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 |
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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 |
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Lunch |
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01:45-02:45 |
Christian Hainzl |
Dynamical collapse of massive stars in the Bogolubov-Hartee-Fock-approximation |
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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 |
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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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