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.     

Synthesis and Reaction of the First 1,2‐Oxaphosphetane Complexes

While P^V 1,2‐oxaphosphetanes are well known from the Wittig reaction, their P^III analogues are still unexplored. Herein, the synthesis and reactions of the first 1,2‐oxaphosphetane complexes are presented, which were achieved by reaction of the phosphinidenoid complex [Li(12‐crown‐4)(solv)][(OC)₅W{(Me₃Si)₂HCPCl}] with different epoxides. The title compounds appeared to be stable in toluene up to 100 °C, before unselective decomposition started. Acid‐induced ring expansion with benzonitrile resulted in selective formation of the first complex bearing a 1,3,4‐oxazaphosphacyclohex‐2‐ene ligand.     

Pulsed EPR Dipolar Spectroscopy under the Breakdown of the High-Field Approximation: The High-Spin Iron(III) Case

Pulsed EPR dipolar spectroscopy (PDS) offers several methods for measuring dipolar coupling and thus the distance between electron-spin centers. To date, PDS measurements to metal centers were limited to ions that adhere to the high-field approximation. Here, the PDS methodology is extended to cases where the high-field approximation breaks down on the example of the high-spin Fe³⁺/nitroxide spin-pair. First, the theory developed by Maryasov et al. (Appl. Magn. Reson. 2006 , 30, 683–702) was adapted to derive equations for the dipolar coupling constant, which revealed that the dipolar spectrum does not only depend on the length and orientation of the interspin distance vector with respect to the applied magnetic field but also on its orientation to the effective g-tensor of the Fe³⁺ ion. Then, it is shown on a model system and a heme protein that a PDS method called relaxation-induced dipolar modulation enhancement (RIDME) is well-suited to measuring such spectra and that the experimentally obtained dipolar spectra are in full agreement with the derived equations. Finally, a RIDME data analysis procedure was developed, which facilitates the determination of distance and angular distributions from the RIDME data. Thus, this study enables the application of PDS to for example, the highly relevant class of high-spin Fe³⁺ heme proteins.     

Solid State NMR and TG/MS Study on the Transformation of Methyl Groups During Pyrolysis of Preceramic Precursors to SiOC Glasses

The sol-gel method was used to prepare two different starting gels containing SiCH₃-groups for the preparation of SiOC ceramics. To understand the role of Si—H bonds in the incorporation of carbon into the SiOC network, gels prepared from a 1:2 mixture of triethoxysilane and methyldiethoxysilane (T^HD^H2) and solely methyltriethoxysilane (T^Me) were investigated. Thermogravimetric analysis coupled with mass spectroscopy (TG-MS) in inert atmosphere was performed to attain an insight into the decomposition reactions involved during gel-glass transformation. Samples calcined at different temperatures up to 1000°C were characterized by ²⁹Si and ¹³C magic angle spinning nuclear magnetic resonance (MAS-NMR) spectroscopy. The presence of SiH groups in the starting gel allows an efficient conversion of Si—CH₃ groups into CSi₄ sites at lower temperatures. As a result, despite a much lower amount of carbon in the starting T^HD^H2 gel (C/Si = 0.33) compared to the T^Me gel (C/Si = 1), the amount of carbon inserted into the SiOC network of both glasses is equivalent, but the T^Me sample contains the 10 fold amount of free carbon.