Quantum-mechanical representations of canonical transformations and adiabatic invariance

A representation of the canonical transformation to action-angle variables is obtained using the (classical) adiabatic invariance of the actions. It is shown that in one dimension this is in fact the exact quantum-mechanical formula for this representation and hence provides a formally exact expression for the eigenfunctions. For higher dimensions some interesting limitations of the method are also discussed and shown to be related to the adiabatic theorem in quantum mechanics. They cause the representation and thus the eigen-functions of integrable systems in more than one dimension to be given correctly to all orders of .     

The defect character of interface junction lines

Junction lines, where three or more interfaces meet in polycrystalline materials, are analysed from a topological point of view. Using circuit mapping methods, it is shown that, in contiguous polyerystals, the dislocations constituting the interfaces always react at junctions according to topological conservation principles. This conclusion is at variance with recent suggestions in the literature. In addition, it is shown that, in certain circumstances, junction lines can themselves exhibit defect character, i.e., dislocation and/or disclination character. Such defects arise in order to accommodate the coexistence of the abutting crystals. Simple examples are illustrated.     

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of ...     

Analyticity and ergodicity in the maximum-entropy approach to statistical nuclear reactions

In the maximum-entropy approach to statistical nuclear reactions one imposes naturally the constraints of unitarity and symmetry of theS-matrix, and of a fixed expectation value ofS. We show that the analytical structure of theS-matrix and the requirement that the problem be ergodic (so that energy averages can be replaced by ensemble averages) impose certain restrictions on the distribution of statisticalS-matrices. Some of these additional constraints are then imposed numerically in a two-channel calculation, and are shown to improve the results for the fluctuation cross sections, the elastic enhancement factor, etc.     

Anomalous slow fidelity decay for symmetry-breaking perturbations

Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.     

Microwave emulations and tight-binding calculations of transport in polyacetylene

A novel approach to investigate the electron transport of cis- and trans-polyacetylene chains in the single-electron approximation is presented by using microwave emulation measurements and tight-binding calculations. In the emulation we take into account the different electronic couplings due to the double bonds leading to coupled dimer chains. The relative coupling constants are adjusted by DFT calculations. For sufficiently long chains a transport band gap is observed if the double bonds are present, whereas for identical couplings no band gap opens. The band gap can be observed also in relatively short chains, if additional edge atoms are absent, which cause strong resonance peaks within the band gap. The experimental results are in agreement with our tight-binding calculations using the nonequilibrium Green's function method. The tight-binding calculations show that it is crucial to include third nearest neighbor couplings to obtain the gap in the cis-polyacetylene.     

Thermodynamic,structural and morphological studies on liquid-crystalline blue phases

Abstract

This article describes the progress in experimental studies of liquid-crystalline blue phases during the past 5 years. Additionally, these results are compared critically with the predictions of theories of the blue phases. Areas considered in this review include (i) the thermodynamic stability of the three polymorphic blue phases and the influence of the cholesteric pitch on this; (ii) the phase diagrams of blue phases; (iii) electric field effects on the blue phase structure and stability; (iv) the morphology and growth of liquid single crystals of blue phases; (v) the symmetry and structural properties of the blue phases.