: "Mean field quantum systems and large deviations", Lectures in the Mark Kac Seminar, Summer 1993; Written version in preparation as "Quantum lattice systems with infinite range interactions"  Home/Search   Document Not in Database   Summary   Related Articles

....separate subsection of the introduction. In Section 2 and Section 3 we describe the basic notions of our approach. It is based on a set of comparison maps j hh 0 which relate observables at different values of h. This framework was originally designed for applications in statistical mechanics [We3] and has many further conceivable applications. In Section 2 it is shown that this furnishes a language in which the convergence of sequences of observables, and the theorems of the desired type can be adequately expressed. The definition of the comparison maps j hh 0 requires some additional ....

....A h 00 , the norm (3:16) goes to zero as h 0 0, uniformly in h. An important Corollary of Theorem 9 is the following construction of j convergent sequences and j convergent states. The sequences described in (1) are called basic sequences in the theory of generalized inductive limits [We3,GW,DW] Their convergence is equivalent to the asymptotic transitivity j hh 00 j hh 0 j h 0 h 00 of the comparison. 10 Corollary. 1) Fix h 0 0 and X 2 A h 0 . Then X h = j hh 0 X is j convergent, and j lim h j hh 0 X = j 0h 0 X : 2) Let : A 0 C be a state, and ....

: "Mean field quantum systems and large deviations", Lectures in the Mark Kac Seminar, Summer 1993; Written version in preparation as "Quantum lattice systems with infinite range interactions"

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC