Wave attenuation model for dephasing and measurement of conditional times

Inelastic scattering induces dephasing in mesoscopic systems. An analysis of previous models to simulate inelastic scattering in such systems is presented and a relatively new model based on wave attenuation is introduced. The problem of Aharonov-Bohm (AB) oscillations in conductance of a mesoscopic ring is studied. We show that the conductance is symmetric under flux reversal and the visibility of AB oscillations decays to zero as a function of the incoherence parameter, signaling dephasing. Further the wave attenuation model is applied to a fundamental problem in quantum mechanics, that of the conditional (reflection/transmission) times spent in a given region of space by a quantum particle before scattering off from that region.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

On-line sample concentration of organic anions in capillary zone electrophoresis by micelle to solvent stacking

Micelle to solvent stacking (MSS) is a new on-line sample concentration technique for charged analytes in capillary zone electrophoresis (CZE). Sample concentration in MSS mainly relies on the reversal in the effective electrophoretic mobility of the analyte at the boundary zone between the sample solution (S) and CZE background solution (BGS) inside the capillary. The basic condition for MSS is that the S is prepared in a matrix that contains an additive (i.e., micelles) which interacts with and has an opposite charge compared to the analytes. In addition, the BGS must contain a sufficient percentage of organic solvent. MSS was first reported for organic cations using anionic dodecyl sulfate micelles as additive in the S and methanol or acetonitrile as organic solvent in the BGS. Here, theoretical and experimental studies on MSS are described for organic anions using cationic cetyltrimethyl ammonium micelles as additive in the S and methanol as organic solvent in the BGS. Up to an order of magnitude improvement in concentration sensitivity was obtained for the test hypolipidaemic drugs using MSS in CZE with UV detection. The optimized method was also evaluated to the analysis of a spiked wastewater sample that was subjected to a simple extraction step.