On the Algebra of Fluctuation in Quantum Spin Chains

We present a proof of the central limit theorem for a pair of mutually non-commuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction of the time evolution of the algebra of normal fluctuation for Gibbs states of finite range interactions on a one-dimensional lattice. We show that the state of the algebra of normal fluctuation satisfies the $\beta$-KMS condition if the microscopic state is a $\beta$-KMS state

On Haag Duality for Pure States of Quantum Spin Chain

We consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals when the von Neumann algebras generated by observables localized in these intervals are not type I

Kakutani Dichotomy on Free States

Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.Comment: 12 page

Lymphocyte Responses to Chymotrypsin- or Trypsin V-Digested β-Lactoglobulin in Patients with Cow's Milk Allergy

<p/> <p>Chymotrypsin- or trypsin V- (a mixture of trypsin and chymotrypsin) digested β-lactoglobulin (BLG) peptides were prepared and were confirmed to have much less immunoglobulin (lg)G and lgE reactivity compared with intact BLG by IgG inhibition enzymelinked immunosorbent assay and IgE dot blotting. The lymphocyte responses to intact BLG and these peptides were examined using peripheral blood mononuclear cells (PBMCs) from 10 patients with cow's milk allergy. The PBMCs from most patients had lower lymphocyte responses to chymotrypsin- and trypsin V-digested BLG peptides than those to intact BLG. However, PBMCs from one and two patients retained significant proliferative responses to both peptides and to only the former peptide, respectively. Interferon-c production stimulated by chymotrypsin-digested peptides was still detectable in all five patients tested. Chymotrypsindigested BLG reduced lgE reactivity but still induced some lymphocyte responses.</p