Title: Breathers in Quantum Lattices.

Speaker: F Palmero (pdf slides 600 Kb)
with JC Eilbeck

Abstract: The phenomenon of localization of energy by nonlinearity in classical lattices (discrete breathers) has been much studied in last years and it is possible to say that, at present, it is relatively well understood. On the other hand, the understanding of its quantum equivalence is very limited. There exist some theoretical results and some experimental observations of these states in different quantum systems, but the amount of results related to this area is not large. It is also interesting to mention the study of quantum breathers can be very important to some applications in areas as quantum dots and quantum computing developments, and Bose--Einstein condensates in periodical optics traps. One of the mains problems in the framework of quantum breathers is the determination of the matrix representation of the Hamiltonian operator and its spectrum, at least partially. In general, the problem involves, firstly, the determination by means of symbolics mathematics programs of a matrix and, as a following step, a total or partial numerical spectrum must be calculated, a hard problem when the metrics becomes large. In some cases, where some symmetries exist, the matrix can be further diagonalized into smaller blocks but, in general, it is not possible and it is in this kind of problems where supercomputers and parallel computing can play a very important role.

TAM Worksop 2005, HPC-Europa, Transnational Acces Meeting.
HLRS , High Performance Computing Center Stuttgart, Germany, September 21-24, 2005. Talk by F Palmero.