Effective theory for the propagation of a wave-packet in a disordered and nonlinear medium

The propagation of a wave-packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schr\"odinger equation (Gross-Pitaevskii equation). This problem is directly connected to experiments on expanding Bose gases and to studies of transverse localization in nonlinear optical media. In a nonlinear medium the energy of the wave-packet is stored both in the kinetic and potential parts, and details of its propagation are to a large extent determined by the transfer from one form of energy to the other. A theory describing the evolution of the wave-packet has been formulated in [G. Schwiete and A. Finkelstein, Phys. Rev. Lett. 104, 103904 (2010)] in terms of a nonlinear kinetic equation. In this paper, we present details of the derivation of the kinetic equation and of its analysis. As an important new ingredient we study interparticle-collisions induced by the nonlinearity and derive the corresponding collision integral. We restrict ourselves to the weakly nonlinear limit, for which disorder scattering is the dominant scattering mechanism. We find that in the special case of a white noise impurity potential the mean squared radius in a two-dimensional system scales linearly with t. This result has previously been obtained in the collisionless limit, but it also holds in the presence of collisions. Finally, we mention different mechanisms through which the nonlinearity may influence localization of the expanding wave-packet.Comment: 21 pages, 10 figure

Mapping service components to EJB business objects

The emerging trends for e-business engineering revolve around specialisation and cooperation. Successful companies focus on their core competencies and rely on a network of business partners for the support services required to compose a comprehensive offer for their customers. Modularity is crucial for a flexible e-business infrastructure, but related requirements seldom reflect on the design and operational models of business information systems. Software components are widely used for the implementation of e-business applications, with proven benefits in terms of system development and maintenance. We propose a service-oriented componentisation of e-business systems as a way to close the gap with the business models they support. Blurring the distinction between external services and internal capabilities, we propose a homogeneous model for the definition of e-business applications components and present a process-based technique for component modelling. We finally present an Enterprise Java Beans extension that implements the model

Stakeholder identification in the requirements engineering process

Adequate, timely and effective consultation of relevant stakeholders is of paramount importance in the requirements engineering process. However, the thorny issue of making sure that all relevant stakeholders are consulted has received less attention than other areas which depend on it, such as scenario-based requirements, involving users in development, negotiating between different viewpoints and so on. The literature suggests examples of stakeholders, and categories of stakeholder, but does not provide help in identifying stakeholders for a specific system. In this paper, we discuss current work in stakeholder identification, propose an approach to identifying relevant stakeholders for a specific system, and propose future directions for the work

Persistent Orbital Degeneracy in Carbon Nanotubes

The quantum-mechanical orbitals in carbon nanotubes are doubly degenerate over a large number of states in the Coulomb blockade regime. We argue that this experimental observation indicates that electrons are reflected without mode mixing at the nanotube-metal contacts. Two electrons occupying a pair of degenerate orbitals (a ``shell'') are found to form a triplet state starting from zero magnetic field. Finally, we observe unexpected low-energy excitations at complete filling of a four-electron shell.Comment: 6 pages, 4 figure

Topographic Mapping of the Quantum Hall Liquid using a Few-Electron Bubble

A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded two-dimensional electron gas. Under quantum Hall effect conditions, applying a positive voltage to the tip locally enhanced the 2D electron density and created a ``bubble'' of electrons in an otherwise unoccupied Landau level. As the tip scanned along the sample surface, the bubble followed underneath. The tip sensed the motions of single electrons entering or leaving the bubble in response to changes in the local 2D electrostatic potential.Comment: 4 pages, 3 JPG figures, Revtex. For additional info and AVI movies, visit http://electron.mit.edu/st

Consistency analysis of Kaluza-Klein geometric sigma models

Geometric sigma models are purely geometric theories of scalar fields coupled to gravity. Geometrically, these scalars represent the very coordinates of space-time, and, as such, can be gauged away. A particular theory is built over a given metric field configuration which becomes the vacuum of the theory. Kaluza-Klein theories of the kind have been shown to be free of the classical cosmological constant problem, and to give massless gauge fields after dimensional reduction. In this paper, the consistency of dimensional reduction, as well as the stability of the internal excitations, are analyzed. Choosing the internal space in the form of a group manifold, one meets no inconsistencies in the dimensional reduction procedure. As an example, the SO(n) groups are analyzed, with the result that the mass matrix of the internal excitations necessarily possesses negative modes. In the case of coset spaces, the consistency of dimensional reduction rules out all but the stable mode, although the full vacuum stability remains an open problem.Comment: 13 pages, RevTe

Interaction effects at the magnetic-field induced metal-insulator transition in Si/SiGe superlattices

A metal-insulator transition was induced by in-plane magnetic fields up to 27 T in homogeneously Sb-doped Si/SiGe superlattice structures. The localisation is not observed for perpendicular magnetic fields. A comparison with magnetoconductivity investigations in the weakly localised regime shows that the delocalising effect originates from the interaction-induced spin-triplet term in the particle-hole diffusion channel. It is expected that this term, possibly together with the singlet particle-particle contribution, is of general importance in disordered n-type Si bulk and heterostructures.Comment: 5 pages, 3 figures, Solid State Communications, in prin

Cliffordons

At higher energies the present complex quantum theory with its unitary group might expand into a real quantum theory with an orthogonal group, broken by an approximate $i$ operator at lower energies. Implementing this possibility requires a real quantum double-valued statistics. A Clifford statistics, representing a swap (12) by a difference $\gamma_1-\gamma_2$ of Clifford units, is uniquely appropriate. Unlike the Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein, and para- statistics, which are tensorial and single-valued, and unlike anyons, which are confined to two dimensions, Clifford statistics are multivalued and work for any dimensionality. Nayak and Wilczek proposed a Clifford statistics for the fractional quantum Hall effect. We apply them to toy quanta here. A complex-Clifford example has the energy spectrum of a system of spin-1/2 particles in an external magnetic field. This supports the proposal that the double-valued rotations --- spin --- seen at current energies might arise from double-valued permutations --- swap --- to be seen at higher energies. Another toy with real Clifford statistics illustrates how an effective imaginary unit $i$ can arise naturally within a real quantum theory.Comment: 15 pages, no figures; original title ("Clifford statistics") changed; to appear in J. Math. Phys., 42, 2001. Key words: Clifford statistics, cliffordons, double-valued representations of permutation groups, spin, swap, imaginary unit $i$, applications to quantum space-time and the Standard Model. Some of these results were presented at the American Physical Society Centennial Meeting, Atlanta, March 25, 199