Random walks with thermalizing collisions in bounded regions; physical applications valid from the ballistic to diffusive regimes

The behavior of a spin undergoing Larmor precession in the presence of fluctuating fields is of interest to workers in many fields. The fluctuating fields cause frequency shifts and relaxation which are related to their power spectrum, which can be determined by taking the Fourier transform of the auto-correlation functions of the field fluctuations. Recently we have shown how to calculate these correlation functions for all values of mean free path (ballistic to diffusive motion) in finite bounded regions, using the model of persistent continuous time random walks (CTRW) for particles subject to scattering by fixed (frozen) scattering centers so that the speed of the moving particles is not changed by the collisions. In this work we show how scattering with energy exchange from an ensemble of scatterers in thermal equilibrium can be incorporated into the CTRW. We present results for 1,2 and 3 dimensions. The results agree for all these cases contrary to the previously studied 'frozen' models. Our results for the velocity autocorrelation function show a long time tail $\left( \sim t^{-1/2}\right)$, which we also obtain from conventional diffusion theory, with the same power, independent of dimensionality. Our results are valid for any Markovian scattering kernel as well as any kernel based on a scattering cross section $\sim1/v.$Comment: 43 pages, 12 figure

Exciton states in monolayer MoSe2 and MoTe2 probed by upconversion spectroscopy

Transitions metal dichalcogenides (TMDs) are direct semiconductors in the atomic monolayer (ML) limit with fascinating optical and spin-valley properties. The strong optical absorption of up to 20 % for a single ML is governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited exciton states in MoSe$_2$ and MoTe$_2$ monolayers have so far been elusive due to their low oscillator strength and strong inhomogeneous broadening. Here we show that encapsulation in hexagonal boron nitride results in emission line width of the A:1$s$ exciton below 1.5 meV and 3 meV in our MoSe$_2$ and MoTe$_2$ monolayer samples, respectively. This allows us to investigate the excited exciton states by photoluminescence upconversion spectroscopy for both monolayer materials. The excitation laser is tuned into resonance with the A:1$s$ transition and we observe emission of excited exciton states up to 200 meV above the laser energy. We demonstrate bias control of the efficiency of this non-linear optical process. At the origin of upconversion our model calculations suggest an exciton-exciton (Auger) scattering mechanism specific to TMD MLs involving an excited conduction band thus generating high energy excitons with small wave-vectors. The optical transitions are further investigated by white light reflectivity, photoluminescence excitation and resonant Raman scattering confirming their origin as excited excitonic states in monolayer thin semiconductors.Comment: 14 pages, 7 figures, main text and appendi

The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds

We study the spectral flow of the hermitian Wilson-Dirac operator \ham(m) as a function of $m$ in smooth SU(2) instanton backgrounds on the lattice. For a single instanton background with Dirichlet boundary conditions on \ham(m), we find a level crossing in the spectral flow of \ham(m), and we find the shape of the crossing mode at the crossing point to be in good agreement with the zero mode associated with the single instanton background. With anti-periodic boundary conditions on \ham(m), we find that the instanton background in the singular gauge has the correct spectral flow but the one in regular gauge does not. We also investigate the spectral flows of two instanton and instanton-anti-instanton backgrounds.Comment: 18 pages, Latex file, 12 postscript figure

Temperature and Emission-Measure Profiles Along Long-Lived Solar Coronal Loops Observed with TRACE

We report an initial study of temperature and emission measure distributions along four steady loops observed with the Transition Region and Coronal Explorer (TRACE) at the limb of the Sun. The temperature diagnostic is the filter ratio of the extreme-ultraviolet 171-angstrom and 195-angstrom passbands. The emission measure diagnostic is the count rate in the 171-angstrom passband. We find essentially no temperature variation along the loops. We compare the observed loop structure with theoretical isothermal and nonisothermal static loop structure.Comment: 10 pages, 3 postscript figures (LaTeX, uses aaspp4.sty). Accepted by ApJ Letter

Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization

We describe a simple experimental implementation of the Malkus-Lorenz water wheel. We demonstrate that both chaotic and periodic behavior is found as wheel parameters are changed in agreement with predictions from the Lorenz model. We furthermore show that when the measured angular velocity of our water wheel is used as an input signal to a computer model implementing the Lorenz equations, high quality chaos synchronization of the model and the water wheel is achieved. This indicates that the Lorenz equations provide a good description of the water wheel dynamics.Comment: 12 pages, 7 figures. The following article has been accepted by the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp

Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system

In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take much longer time as compared to the time required to produce unitary transformations on the first qubit but much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup SU(2)xSU(2)xU(1), which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum information processing.Comment: 8 pages, 3 figure

Quantum Error Correction via Convex Optimization

We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to derive new codes that are locally optimal. We present examples of such codes that can handle errors which are too strong for codes derived by analogy to classical error correction techniques.Comment: 16 page

Interlayer exciton mediated second harmonic generation in bilayer MoS2

Second harmonic generation (SHG) is a non-linear optical process, where two photons coherently combine into one photon of twice their energy. Efficient SHG occurs for crystals with broken inversion symmetry, such as transition metal dichalcogenide monolayers. Here we show tuning of non-linear optical processes in an inversion symmetric crystal. This tunability is based on the unique properties of bilayer MoS2, that shows strong optical oscillator strength for the intra- but also inter-layer exciton resonances. As we tune the SHG signal onto these resonances by varying the laser energy, the SHG amplitude is enhanced by several orders of magnitude. In the resonant case the bilayer SHG signal reaches amplitudes comparable to the off-resonant signal from a monolayer. In applied electric fields the interlayer exciton energies can be tuned due to their in-built electric dipole via the Stark effect. As a result the interlayer exciton degeneracy is lifted and the bilayer SHG response is further enhanced by an additional two orders of magnitude, well reproduced by our model calculations.Comment: main paper and supplemen

Matrix Degradation in Human Immunodeficiency Virus Type 1-Associated Tuberculosis and Tuberculosis Immune Reconstitution Inflammatory Syndrome: A Prospective Observational Study.

Background: Extensive immunopathology occurs in human immunodeficiency virus (HIV)/tuberculosis (TB) coinfection, but the underlying molecular mechanisms are not well-defined. Excessive matrix metalloproteinase (MMP) activity is emerging as a key process but has not been systematically studied in HIV-associated TB. Methods: We performed a cross-sectional study of matrix turnover in HIV type 1 (HIV-1)-infected and -uninfected TB patients and controls, and a prospective cohort study of HIV-1-infected TB patients at risk of TB immune reconstitution inflammatory syndrome (TB-IRIS), in Cape Town, South Africa. Sputum and plasma MMP concentrations were quantified by Luminex, plasma procollagen III N-terminal propeptide (PIIINP) by enzyme-linked immunosorbent assay, and urinary lipoarabinomannan (LAM) by Alere Determine TB LAM assay. Peripheral blood mononuclear cells from healthy donors were cultured with Mycobacterium tuberculosis and extracellular matrix in a 3D model of TB granuloma formation. Results: MMP activity differed between HIV-1-infected and -uninfected TB patients and corresponded with specific TB clinical phenotypes. HIV-1-infected TB patients had reduced pulmonary MMP concentrations, associated with reduced cavitation, but increased plasma PIIINP, compared to HIV-1-uninfected TB patients. Elevated extrapulmonary extracellular matrix turnover was associated with TB-IRIS, both before and during TB-IRIS onset. The predominant collagenase was MMP-8, which was likely neutrophil derived and M. tuberculosis-antigen driven. Mycobacterium tuberculosis-induced matrix degradation was suppressed by the MMP inhibitor doxycycline in vitro. Conclusions: MMP activity in TB differs by HIV-1 status and compartment, and releases matrix degradation products. Matrix turnover in HIV-1-infected patients is increased before and during TB-IRIS, informing novel diagnostic strategies. MMP inhibition is a potential host-directed therapy strategy for prevention and treatment of TB-IRIS

Loop Evolution Observed with AIA and Hi-C

In the past decade, the evolution of EUV loops has been used to infer the loop substructure. With the recent launch of High Resolution Coronal Imager (Hi-C), this inference can be validated. In this presentation we discuss the first results of loop analysis comparing AIA and Hi-C data. In the past decade, the evolution of EUV loops has been used to infer the loop substructure. With the recent launch of High Resolution Coronal Imager (Hi-C), this inference can be validated. In this presentation we discuss the first results of loop analysis comparing AIA and Hi-C data