Symmetry and Structural Properties of Condensed Matter

Abstract

This volume comprises the proceedings of the Ninth Summer School on Theoretical Physics under the leading title `Symmetry and Structural Properties of Condensed Matter' (SSPCM 2007). The school, organised by Rzeszów University of Technology, Poland, together with AGH University of Science and Technology, Cracow, Poland, in 5–12 September 2007 in Myczkowce. The meeting aimed to continue the series of biannual SSPCM schools (since 1990), and focused on the promotion of some advanced mathematical methods within the physics of condensed matter, with an emphasis on quantum information aspects.The main topics of the SSPCM07 school were the following: Quantum information and computing Finite dimensional Hilbert spaces Generating functions and exactly soluble models The Proceedings are divided into three parts accordingly. These topics can be seen as a natural continuation of the previous SSPCM05 school, aimed at studying interrelations between solid state physics and quantum informatics, as well as an extension of earlier SSPCM meetings, devoted to mathematical tools of condensed matter theory.The school gathered together more than 60 participants from 11 countries and 7 scientific centres in Poland. Some of them were there for the first time, and some had attended nearly all previous meetings. We had advanced researchers as well as their young collaborators and students. AcknowledgementsThe Organizing Committee wishes to express our gratitude to all participants for several their activities at the school and for creating so friendly and inspiring an atmosphere that one can talk about the term: `SSPCM society'. Special thanks are due to all lecturers, for preparing and presenting their talks, and for several valuable discussions. We also give thanks to all those who prepared manuscripts, giving us thus an opportunity to share their ideas, to all referees who improved significantly the quality of this volume, to all members of our International Advisory Committee, and to chairmen for their polite but efficient leading of sessions.It is our sad duty to inform the whole SSPCM society that one of us, Professor Jan Mozrzymas from The Institute of Theoretical Physics, Wrocław University, died on 8 January 2006. He was a lecturer and a very active participant of our first four SSPCM meetings in Zajaczkowo near Poznań. Some of us remember his lectures on crystallography, solitons and motions of electric charges, nicely intertwined with differential geometry, theta functions, knots or Rieman surfaces. We shall keep his attitude towards physics and mathematics in our minds. As the Organizing Committee, we would like to express our special gratitude to The Nicholas C Metropolis Mathematics Foundation (USA) for substantial financial support of our two last SSPCM schools. We direct this gratitude to Professor James D Louck, The President of this Foundation, and also one of the most regular lecturers of our series of SSPCM schools. He was so kind to introduce us, in his impressive address at the ceremonial dinner, into the history and aims of the Foundation which we like to sketch here briefly. The Founder, Professor Nicholas C Metropolis, was a famous researcher who started his work in Chicago in 1942 within the Fermi group that was building the first nuclear reactor, in 1943 he joined the group of Bethe in Los Alamos, taking part in the construction of the atomic bomb. He was in scientific contact with many well known mathematicians and physicists of those times, Feynman, von Neumann, Ulam, Szilard, Teller, and Wigner. Before he died in 1999, he created The Mathematics Foundation with the purpose of supporting science, with a special emphasis on mathematical orientation. We wish to thank the Nicholas C Metropolis Foundation, not only as benefactors (in fact, this support has allowed us to initiate the last two SSPCM schools), but also for giving us the honour of being seen as proper members in the perspective of such an important tradition.We would also like to acknowledge the support of European Physical Society. On behalf of the organizers of SSPCM 2007 Tadeusz Lulek, Andrzej Wal and Barbara Lulek Editors