Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength, as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid-Mott insulator crossover and its analog for attractive interactions is recognized.

Does speed matter? : the impact of the EU membership incentive on rule adoption in minority language rights protection

Denna avhandling tar sin utgångspunkt i ett ifrågasättande av effektiviteten i EU:s konditionalitetspolitik avseende minoritetsrättigheter. Baserat på den rationalistiska teoretiska modellen, External Incentives Model of Governance, syftar denna hypotesprövande avhandling till att förklara om tidsavståndet på det potentiella EU medlemskapet påverkar lagstiftningsnivån avseende minoritetsspråksrättigheter. Mätningen av nivån på lagstiftningen avseende minoritetsspråksrättigheter begränsas till att omfatta icke-diskriminering, användning av minoritetsspråk i officiella sammanhang samt minoriteters språkliga rättigheter i utbildningen. Metodologiskt används ett jämförande angreppssätt både avseende tidsramen för studien, som sträcker sig mellan 2003 och 2010, men även avseende urvalet av stater. På basis av det \"mest lika systemet\" kategoriseras staterna i tre grupper efter deras olika tidsavstånd från det potentiella EU medlemskapet. Hypotesen som prövas är följande: ju kortare tidsavstånd till det potentiella EU medlemskapet desto större sannolikhet att staternas lagstiftningsnivå inom de tre områden som studeras har utvecklats till en hög nivå. Studien visar att hypotesen endast bekräftas delvis. Resultaten avseende icke-diskriminering visar att sambandet mellan tidsavståndet och nivån på lagstiftningen har ökat markant under den undersökta tidsperioden. Detta samband har endast stärkts mellan kategorin av stater som ligger tidsmässigt längst bort ett potentiellt EU medlemskap och de två kategorier som ligger närmare respektive närmast ett potentiellt EU medlemskap. Resultaten avseende användning av minoritetsspråk i officiella sammanhang och minoriteters språkliga rättigheter i utbildningen visar inget respektive nästan inget samband mellan tidsavståndet och utvecklingen på lagstiftningen mellan 2003 och 2010.

Reflection of matter waves in potential structures

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

Single-mode acceleration of matter waves in circular waveguides

Ultracold gases in ring geometries hold promise for significant improvements of gyroscopic sensitivity. Recent experiments have realized atomic and molecular storage rings with radii in the centimeter range, sizes whose practical use in inertial sensors requires velocities significantly in excess of typical recoil velocities. We use a combination of analytical and numerical techniques to study the coherent acceleration of matter waves in circular waveguides, with particular emphasis on its impact on single-mode propagation. In the simplest case we find that single-mode propagation is best maintained by the application of time-dependent acceleration force with the temporal profile of a Blackmann pulse. We also assess the impact of classical noise on the acceleration process.

Does road network density matter in optimally locating facilities?

Optimal location on the transport infrastructure is the preferable requirement for many decision making processes. Most studies have focused on evaluating performances of optimally locate p facilities by minimizing their distances to a geographically distributed demand (n) when p and n vary. The optimal locations are also sensitive to geographical context such as road network, especially when they are asymmetrically distributed in the plane. The influence of alternating road network density is however not a very well-studied problem especially when it is applied in a real world context. This paper aims to investigate how the density level of the road network affects finding optimal location by solving the specific case of p-median location problem. A denser network is found needed when a higher number of facilities are to locate. The best solution will not always be obtained in the most detailed network but in a middle density level. The solutions do not further improve or improve insignificantly as the density exceeds 12,000 nodes, some solutions even deteriorate. The hierarchy of the different densities of network can be used according to location and transportation purposes and increase the efficiency of heuristic methods. The method in this study can be applied to other location-allocation problem in transportation analysis where the road network density can be differentiated.