Each year the AHP Prize founded by Birkhäuser is awarded for the most remarkable paper published in the journal Annales Henri Poincaré. The winner of the AHP Prize is selected by the Editorial Board.
Since 2008, the AHP Executive Board decided to award also 3 distinguished papers.
All papers are freely accessible online.
The AHP Prize 2010 was awarded to J.-M. Barbaroux, T. Chen, V. Vougalter and S. Vugalter for the paper "Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED"
The paper is devoted to the nonrelativistic QED Hamiltonian (sometimes called the Pauli-Fierz model) that attempts to capture Quantum Electrodynamics in the low energy regime. Charged particles, treated nonrelativistically, are minimally coupled to relativistic quantized photons. In this way one obtains a well-defined self-adjoint Hamiltonian depending on the fine structure constant α.
A formal (due to the presence of continuous spectrum) perturbative treatment of such a model leads to expressions for the ground state in terms of powers of α with logarithmic corrections. It was an observation of Hainzl and Hainzl and Seiringer that the results from the perturbation theory can be turned into rigorous upper and lower bounds (by adjusting constants). There has been a string of papers using this method. The prize-winning article is its high point, determining an exact expression for the hydrogen atom binding energy up to order α5
, with rigorous bounds for the o(α5
) reminder. This required fifty pages of hard estimates and a number of ingenious innovations.
Distinguished Paper Awards 2010
- "Entropy of Semiclassical Measures for Nonpositively Curved Surfaces" by Gabriel Rivière
- "Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction" by Wojciech De Roeck, Jürg Fröhlich and Alessandro Pizzo
The AHP Prize 2009 was awarded to D. Dolgopyat and B. Fayad for the paper "Unbounded Orbits for Semicircular Outer Billiard"
This paper concerns outer billiards, a dynamical system similar to the conventional (inner) billiards. Their study was put forward by J. Moser in the 1970s and provides an interesting example of an area preserving two- dimensional mapping with an explicit geometrical description. In particular, Moser posed the problem whether the orbits of the outer billiards can escape to infinity. The motivation for this question was that if the boundary of the outer billiard table is strictly convex and sufficiently smooth, then KAM-type arguments prove that all orbits stay bounded.
Surprisingly enough, the methods of this paper are essentially of the KAM type, although the authors prove an “anti-KAM” kind of result; these methods are likely to be applicable to similar problems, and their theorem opens the door for further study.
To summarize, this paper solves an old problem in an unexpected way, and its method can certainly be applicable to a bunch of new models, too.
Distinguished Paper Award 2009
"Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation" by Marcel Griesemer and David G. Hasler
The AHP Prize 2008 was awarded jointly to
P. Bálint and I. P. Tóth for the paper "Exponential Decay of Correlations in Multi-Dimensional Dispersing Billiards"
Billiards with some hyperbolicity have played a key role in the development of dynamical systems, since they represent a highly nontrivial natural example of chaotic dynamics. The nominated paper is very well-written and accessible to non billiard experts. It settles a long standing conjecture (modulo an additional assumption which is most likely generic) and clarifies our understanding of ergodicity and mixing properties of billiards.
L.Parnovski for the paper "Bethe-Sommerfeld Conjecture"
The Bethe-Sommerfeld conjecture concerns a basic property of an operator with wide application in physics and was considered a challenging problem in spectral theory in the last decades. In the case of rational lattices and in all dimensions the proof has achieved by Skriganov (1984) and Scrikanov & Sobolev (2006). The definitive result has been obtained by Parnowski in this paper, which proves the conjecture for any periodicity lattice, in all dimensions greater than two and with an arbitrary smooth potential.
Distinguished Paper Awards 2008
- "Resonances of the Confined Hydrogen Atom and the Lamb–Dicke Effect in Non-Relativistic QED" by Jérémy Faupin
- "Tunnel Effect for Kramers–Fokker–Planck Type Operators" by Frédéric Hérau, Michael Hitrik and Johannes Sjöstrand