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.     

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.     

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.     

Vocalizations produced by humpback whale (Megaptera novaeangliae) calves recorded in Hawaii

Although humpback whale (Megaptera novaeangliae) calves are reported to vocalize, this has not been measurably verified. During March 2006, an underwater video camera and two-element hydrophone array were used to record nonsong vocalizations from a mother-calf escort off Hawaii. Acoustic data were analyzed; measured time delays between hydrophones provided bearings to 21 distinct vocalizations produced by the male calf. Signals were pulsed (71%), frequency modulated (19%), or amplitude modulated (10%). They were of simple structure, low frequency (mean=220 Hz), brief duration (mean=170 ms), and relatively narrow bandwidth (mean=2 kHz). The calf produced three series of "grunts" when approaching the diver. During winters of the years 2001-2005 in Hawaii, nonsong vocalizations were recorded in 109 (65%) of 169 groups with a calf using an underwater video and single (omnidirectional) hydrophone. Nonsong vocalizations were most common (34 of 39) in lone mother-calf pairs. A subsample from this dataset of 60 signals assessed to be vocalizations provided strong evidence that 10 male and 18 female calves vocalized based on statistical similarity to the 21 verified calf signals, proximity to an isolated calf (27 of 28 calves), strong signal-to-noise ratio, and/or bubble emissions coincident to sound.