EXPECTATIONS FOR NEW STATES OF MATTER

Gordon Baym

Quantization Operators, Alberto Lanconelli

The aim of this paper is to investigate whether a fundamental property of conditional expectations holds true for second quantization oper- ators. We provide necessary and su-cient conditions for that and we show how they reduce for speciflc choices of operators. Our proofs are based on two crucial formulas which relates Wick and ordinary products. New proofs for these two formulas are also given.

RODNEY M. J. COTTERILL

Volkmar Liebscher, Michael Skeide

Abstract. We propose a definition of markovian systems of transition expec-tation as a generalization of Liebscher’s continuous time version of Accardi’s quantum Markov chains and we show in a reconstruction theorem that the transition expectations may be recovered with the help product systems of Hilbert modules and units for them in the sense of Bhat and Skeide. 1.

Christian Gross, Immanuel Bloch

Ultracold atoms in optical lattices have proven to provide an extremely clean and controlled setting to explore quantum many-body phases of matter. Now, imaging of atoms in such lattice structures has reached the level of single-atom sensitive detection combined with the highest resolution down to the level of individual lattice sites. This has opened up fundamentally new opportunities for the characterization and the control of quantum many-body systems. Here we give a brief overview of this field and explore the opportunities offered for future research.