Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres

Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedIn quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrodinger equation can be mapped to solutions of the Schrodinger equation for harmonic potentials, both the trapping oscillator and the inverted `oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environmentPeer reviewe

Robotic ubiquitous cognitive ecology for smart homes

Robotic ecologies are networks of heterogeneous robotic devices pervasively embedded in everyday environments, where they cooperate to perform complex tasks. While their potential makes them increasingly popular, one fundamental problem is how to make them both autonomous and adaptive, so as to reduce the amount of preparation, pre-programming and human supervision that they require in real world applications. The project RUBICON develops learning solutions which yield cheaper, adaptive and efficient coordination of robotic ecologies. The approach we pursue builds upon a unique combination of methods from cognitive robotics, machine learning, planning and agent- based control, and wireless sensor networks. This paper illustrates the innovations advanced by RUBICON in each of these fronts before describing how the resulting techniques have been integrated and applied to a smart home scenario. The resulting system is able to provide useful services and pro-actively assist the users in their activities. RUBICON learns through an incremental and progressive approach driven by the feed- back received from its own activities and from the user, while also self-organizing the manner in which it uses available sensors, actuators and other functional components in the process. This paper summarises some of the lessons learned by adopting such an approach and outlines promising directions for future work

Extended Hauser-Feshbach Method for Statistical Binary-Decay of Light-Mass Systems

An Extended Hauser-Feshbach Method (EHFM) is developed for light heavy-ion fusion reactions in order to provide a detailed analysis of all the possible decay channels by including explicitly the fusion-fission phase-space in the description of the cascade chain. The mass-asymmetric fission component is considered as a complex-fragment binary-decay which can be treated in the same way as the light-particle evaporation from the compound nucleus in statistical-model calculations. The method of the phase-space integrations for the binary-decay is an extension of the usual Hauser-Feshbach formalism to be applied to the mass-symmetric fission part. The EHFM calculations include ground-state binding energies and discrete levels in the low excitation-energy regions which are essential for an accurate evaluation of the phase-space integrations of the complex-fragment emission (fission). In the present calculations, EHFM is applied to the first-chance binary-decay by assuming that the second-chance fission decay is negligible. In a similar manner to the description of the fusion-evaporation process, the usual cascade calculation of light-particle emission from the highly excited complex fragments is applied. This complete calculation is then defined as EHFM+CASCADE. Calculated quantities such as charge-, mass- and kinetic-energy distributions are compared with inclusive and/or exclusive data for the $^{32}$S+$^{24}$Mg and $^{35}$Cl+$^{12}$C reactions which have been selected as typical examples. Finally, the missing charge distributions extracted from exclusive measurements are also successfully compared with the EHFM+CASCADE predictions.Comment: 34 pages, 6 Figures available upon request, Phys. Rev. C (to be published

Mitochondrial phylogeography and demographic history of the Vicuña: implications for conservation

The vicuña (Vicugna vicugna; Miller, 1924) is a conservation success story, having recovered from near extinction in the 1960s to current population levels estimated at 275 000. However, lack of information about its demographic history and genetic diversity has limited both our understanding of its recovery and the development of science-based conservation measures. To examine the evolution and recent demographic history of the vicuña across its current range and to assess its genetic variation and population structure, we sequenced mitochondrial DNA from the control region (CR) for 261 individuals from 29 populations across Peru, Chile and Argentina. Our results suggest that populations currently designated as Vicugna vicugna vicugna and Vicugna vicugna mensalis comprise separate mitochondrial lineages. The current population distribution appears to be the result of a recent demographic expansion associated with the last major glacial event of the Pleistocene in the northern (18 to 22°S) dry Andes 14–12 000 years ago and the establishment of an extremely arid belt known as the 'Dry Diagonal' to 29°S. Within the Dry Diagonal, small populations of V. v. vicugna appear to have survived showing the genetic signature of demographic isolation, whereas to the north V. v. mensalis populations underwent a rapid demographic expansion before recent anthropogenic impacts

Steiner t-designs for large t

One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner t-designs for large values of t. Although in his classical 1987 paper, L. Teirlinck has shown that non-trivial t-designs exist for all values of t, no non-trivial Steiner t-design with t > 5 has been constructed until now. Understandingly, the case t = 6 has received considerable attention. There has been recent progress concerning the existence of highly symmetric Steiner 6-designs: It is shown in [M. Huber, J. Algebr. Comb. 26 (2007), pp. 453-476] that no non-trivial flag-transitive Steiner 6-design can exist. In this paper, we announce that essentially also no block-transitive Steiner 6-design can exist.Comment: 9 pages; to appear in: Mathematical Methods in Computer Science 2008, ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in Computer Scienc

Parity Violating Measurements of Neutron Densities

Parity violating electron nucleus scattering is a clean and powerful tool for measuring the spatial distributions of neutrons in nuclei with unprecedented accuracy. Parity violation arises from the interference of electromagnetic and weak neutral amplitudes, and the $Z^0$ of the Standard Model couples primarily to neutrons at low $Q^2$. The data can be interpreted with as much confidence as electromagnetic scattering. After briefly reviewing the present theoretical and experimental knowledge of neutron densities, we discuss possible parity violation measurements, their theoretical interpretation, and applications. The experiments are feasible at existing facilities. We show that theoretical corrections are either small or well understood, which makes the interpretation clean. The quantitative relationship to atomic parity nonconservation observables is examined, and we show that the electron scattering asymmetries can be directly applied to atomic PNC because the observables have approximately the same dependence on nuclear shape.Comment: 38 pages, 7 ps figures, very minor changes, submitted to Phys. Rev.

Up-Down Quark Mass Difference Effect in Nuclear Many-Body Systems

A charge-symmetry-breaking nucleon-nucleon force due to the up-down quark mass difference is evaluated in the quark cluster model. It is applied to the shell-model calculation for the isovector mass shifts of isospin multiplets and the isospin-mixing matrix elements in 1s0d-shell nuclei. We find that the contribution of the quark mass difference effect is large and agrees with experiment. This contribution may explain the Okamoto-Nolen-Schiffer anomaly, alternatively to the meson-mixing contribution, which is recently predicted to be reduced by the large off-shell correction

Microscopic calculations of medium effects for 200-MeV (p,p') reactions

We examine the quality of a G-matrix calculation of the effective nucleon-nucleon (NN) interaction for the prediction of the cross section and analyzing power for 200-MeV (p,p') reactions that populate natural parity states in $^{16}$O, $^{28}$Si, and $^{40}$Ca. This calculation is based on a one-boson-exchange model of the free NN force that reproduces NN observables well. The G-matrix includes the effects of Pauli blocking, nuclear binding, and strong relativistic mean-field potentials. The implications of adjustments to the effective mass ansatz to improve the quality of the approximation at momenta above the Fermi level will be discussed, along with the general quality of agreement to a variety of (p,p') transitions.Comment: 36 pages, TeX, 18 figure