Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.     

Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum

Enhancement of entanglement is necessary for most quantum communication protocols many of which are defined in Hilbert spaces larger than 2. In this work we present the experimental realization of entanglement concentration of orbital angular momentum entangled photons. We investigate the specific case of three dimensions and the possibility of generating different entangled states out of an initial state. The results presented here are of importance for pure states as well as for mixed states.     

A Semigroup Approach to Boundary Feedback Systems

In this paper we convert a (linear abstract) initial boundary value problem into an abstract Cauchy problem on some product space and use semigroup methods to solve it. In particular, we apply spectral theory in order to discuss stability under boundary feedback.     

Bi-Invariant Domains in Semisimple Groups: Nonprincipal Orbits and Boundaries

Let G be a complex semisimple group with real form G . For the action of G × G on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits.     

A UNIFIED QUANTUM HALL CLOSE-PACKED COMPOSITE BOSON (CPCB) MODEL

Single-wavelength Landau cyclotron orbitals (SWOs) have been used as quantum Hall basis states to reproduce integer quantum Hall plateaus in a two-dimensional (2D) close-packing representation. But at the high magnetic fields B that correspond to fractional Hall plateaus, these SWOs are too small to give close packing. It is conventionally assumed that the fractional quantum Hall states are formed from collective electron excitations (CEEs). However, by invoking the use of multiple-wavelength Landau orbitals (MWOs), we can close-pack the fractional Hall plateaus in the same manner as the integer plateaus. Quantum Hall plateaus are characterized by the filling fractions n _e/n =k/m, where k=1, 2,... (all integers) and m=1, 3,... (all odd integers), and where n _e and n are the 2D electron e and magnetic flux =h/e densities, respectively. A composite particle (CP) is a bound state of an electron and m flux quanta . If m is even or odd, the CP is a composite fermion (CF) or composite boson (CB). In the CEE models, both CF and CB formalisms have been used. In the alternative MWO approach introduced here, the close-packed MWOs on a =k/m plateau each contain m de Broglie wavelengths . Each MWO traps m external flux quanta, produces m diamagnetic induced flux quanta, and carries the filling fraction , which accounts for the extreme accuracy (one part in 10⁸) of the Hall plateau conductance, _H= e ²/h. Since m is odd, these MWOs are CB states, and they form a boson condensate of close-packed composite boson (CPCB) states. The m=1 (m<1) CPCBs tile the integer (fractional) Hall plateaus. The filling fraction index k corresponds to k layers of CPCB orbitals. Plateau formation itself is due to the linear B dependence of the density of CPCB states. The CPCBs are decoupled from the semiconductor substrate, and hence may have large m* effective mass values. THE MWOs near the =1/2 non-plateau region are m=2 CF states.     

Safety first portfolio choice based on financial and sustainability returns

The aim of this paper is to expand the methodological spectrum of socially responsible investing by introducing stochastic sustainability returns into safety first models for portfolio choice. We provide a foundation of the notion of sustainability in portfolio theory and establish a general model for generalized safety first portfolio management with probabilistic constraints and three specifications of it. Moreover, we prove theorems about conditions for unique optimal solutions and for the constraints of one model being more restrictive than those of another. In an empirical part, we calculate the costs of investing according to our approach in terms of less financial return.     

MtsslWizard: In Silico Spin-Labeling and Generation of Distance Distributions in PyMOL

MtsslWizard is a computer program, which operates as a plugin for the PyMOL molecular graphics system. MtsslWizard estimates distances between spin labels on proteins quickly with user-configurable options through a simple graphical interface. In default mode, the program searches for ensembles of possible MTSSL conformations that do not clash with a static model of the protein. Once conformations are assigned, distance distributions between two or more ensembles are calculated, displayed, and can be exported to other software. The program’s use is evaluated in a number of challenging test cases and its strengths and weaknesses evaluated. The benefits of the program are its accuracy and simplicity.