States of physical systems

States of physical systems may be represented by states onB*-algebras, satisfying certain requirements of physical origin. We discuss such requirements as are associated with the presence of unbounded observables or invariance under a group. It is possible in certain cases to obtain a unique decomposition of states invariant under a group into extremal invariant states. Our main results is such a decomposition theorem when the group is the translation group in dimensions and theB*-algebra satisfies a certain locality condition. An application of this theorem is made to representations of the canonical anticommutation relations.     

Studies in the Helicene Series NMR. Evidence of ‘Helicene-like’ Conformations in the cis 1,2-Diarylethylenes. Part XVII

The cis and trans isomers of eight 1,2-diarylethylenes, precursors of helicenes, have been studied by NMR. spectroscopy. The observed differences in chemical shifts, specific solvent effects and steric effects (bromo derivatives) can be explained by the contribution of ‘helicenelike’ conformers in the cis isomers.     

W-algebras for generalized Toda theories

The generalized Toda theories obtained in a previous paper by the conformal reduction of WZNW theories possess a new class ofW-algebras, namely the algebras of gauge-invariant polynomials of the reduced theories. An algorithm for the construction of base-elements for theW-algebras of all such generalized Toda theories is found, and theW-algebras for the maximalSL(N,R) generalized Toda theories are constructed explicitly, the primary field basis being identified.     

Sharp determinants

We introduce a sharp trace Tr ^# ℳ and a sharp determinant Det ^# (1−z ℳ) for an algebra of operators ℳ acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the discrete spectrum of ℳ. The relationship with weighted zeta functions of interval maps and Milnor–Thurston kneading determinants is explained. This yields a result on convergence of the discrete spectrum of approximated operators. Oblatum 8-V-1995 & IX-1995     

Electrostatic potential around halogenated anesthetics. Acidic hydrogen; chlorine vs. fluorine

Maps of electrostatic potential around a number of halocarbon anethetics have been obtained through Gaussian ab initio calculations. Information is obtained on the mode of association of these compounds with possible receptors. The positive potential found along the extension of the C? H bonds substantiates the role of the “acidic hydrogen.” The presence of fluorines on the carbon atom to which it is bound restricts the access to this positive site through the repulsive action of the fluorine lone pairs, an observation that explains the very different behavior of chloroform and fluoroform, for example, with respect to their anesthetic potencies and hydrogen bonding abilities. In the absence of an acidic hydrogen the chlorine atoms can serve as associative sites.     

Some remarks on the ground state of infinite systems in statistical mechanics

We investigate the ground states of infinite quantum lattice systems. It is shown in particular that a positive energy operator is associated with these states.     

Do turbulent crystals exist?

We discuss the possibility that, besides periodic and quasiperiodic crystals, there exist turbulent crystals as thermodynamic equilibrium states at non-zero temperature. Turbulent crystals would not be invariant under translation, but would differ from other crystals by the fuzziness of some diffraction peaks. Turbulent crystals could appear by breakdown of long range order in quasiperiodic crystals with two independent modulations.     

Structure and <Emphasis Type="Italic">f</Emphasis> -Dependence of the A.C.I.M. for a Unimodal Map <Emphasis Type="Italic">f</Emphasis> of Misiurewicz Type

By using a suitable Banach space on which we let the transfer operator act, we make a detailed study of the ergodic theory of a unimodal map f of the interval in the Misiurewicz case. We show in particular that the absolutely continuous invariant measure ρ can be written as the sum of 1/square root spikes along the critical orbit, plus a continuous background. We conclude by a discussion of the sense in which the map may be differentiable.     

Graph-Counting Polynomials for Oriented Graphs

If \(\mathcal{F}\) is a set of subgraphs F of a finite graph E we define a graph-counting polynomial \(p_\mathcal{F}(z)=\sum _{F\in \mathcal{F}}z^{|F|}\) In the present note we consider oriented graphs and discuss some cases where \(\mathcal{F}\) consists of unbranched subgraphs E. We find several situations where something can be said about the location of the zeros of \(p_\mathcal{F}\).