We show that blow up of solutions with arbitrary positive initial energy of the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u) (*)$ in a Hilbert space, where $P,A$ are positive linear operators and $F(cdot)$ is a continuo
usly differentiable gradient operator can be obtained from the result of H.A. Levine on the growth of solutions of the Cauchy problem for (*). This result is applied to the study of inital boundary value problems for nonlinear Klein-Gordon equations, generalized Boussinesq equations and nonlinear plate equations. A result on blow up of solutions with positive initial energy of the initial boundary value problem for wave equation under nonlinear boundary condition is also obtained.
Valleytronics is rapidly emerging as an exciting area of basic and applied research. In two dimensional systems, valley polarisation can dramatically modify physical properties through electron-electron interactions as demonstrated by such phenomena
as the fractional quantum Hall effect and the metal-insulator transition. Here, we address the electrons spin alignment in a magnetic field in silicon-on-insulator quantum wells under valley polarisation. In stark contrast to expectations from a non-interacting model, we show experimentally that less magnetic field can be required to fully spin polarise a valley-polarised system than a valley-degenerate one. Furthermore, we show that these observations are quantitatively described by parameter free ab initio quantum Monte Carlo simulations. We interpret the results as a manifestation of the greater stability of the spin and valley degenerate system against ferromagnetic instability and Wigner crystalisation which in turn suggests the existence of a new strongly correlated electron liquid at low electron densities.
We calculate the full one-loop electroweak radiative corrections, of ${cal O}(alpha^2alpha_s)$, to the cross section of single $Z$-boson inclusive hadroproduction at finite transverse momentum ($p_T$). This includes the ${cal O}(alpha)$ corrections t
o $Z+j$ production, the ${cal O}(alpha_s)$ corrections to $Z+gamma$ production, and certain QCD-electroweak interference contributions involving a single quark trace. We recover the QCD and purely weak corrections and study the QED corrections and the QCD-electroweak interference contributions for the first time. We also consider direct and resolved photoproduction in elastic and inelastic scattering. We present $p_T$ and rapidity distributions for the experimental conditions at the Fermilab Tevatron and the CERN LHC and assess the significance of the various contributions.
We report on magneto-optical studies of Bi2Se3, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parame
ters: the fundamental bandgap and the band velocity. In a magnetic field, this model implies a unique property - spin splitting equal to twice the cyclotron energy: Es = 2Ec. This explains the extensive magneto-transport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The Es = 2Ec match differentiates the massive Dirac electrons in bulk Bi2Se3 from those in quantum electrodynamics, for which Es = Ec always holds.
For certain measurements, the Corbino geometry has a distinct advantage over the Hall and van der Pauw geometries, in that it provides a direct probe of the bulk 2DEG without complications due to edge effects. This may be important in enabling detect
ion of the non-Abelian entropy of the 5/2 fractional quantum Hall state via bulk thermodynamic measurements. We report the successful fabrication and measurement of a Corbino-geometry sample in an ultra-high mobility GaAs heterostructure, with a focus on transport in the second and higher Landau levels. In particular, we report activation energy gaps of fractional quantum Hall states, with all edge effects ruled out, and extrapolate the conductivity prefactor from the Arrhenius fits. Our results show that activated transport in the second Landau level remains poorly understood. The development of this Corbino device opens the possibility to study the bulk of the 5/2 state using techniques not possible in other geometries.
Electrostatic gates are of paramount importance for the physics of devices based on high-mobility two-dimensional electron gas (2DEG) since they allow depletion of electrons in selected areas. This field-effect gating enables the fabrication of a wid
e range of devices such as, for example, quantum point contacts (QPC), electron interferometers and quantum dots. To fabricate these gates, processing is usually performed on the 2DEG material, which is in many cases detrimental to its electron mobility. Here we propose an alternative process which does not require any processing of the 2DEG material other than for the ohmic contacts. This approach relies on processing a separate wafer that is then mechanically mounted on the 2DEG material in a flip-chip fashion. This technique proved successful to fabricate quantum point contacts on both GaAs/AlGaAs materials with both moderate and ultra-high electron mobility.
The introduction of a strong Rashba spin orbit coupling (SOC) had been predicted to enhance the spin motive force (SMF) [see Phys. Rev. Lett. {bf 108}, 217202 (2012)]. In this work, we predict further enhancement of the SMF by time modulation of the
Rashba coupling $alpha_R$, which induces an additional electric field $E^R_d={dot alpha_R} m_e/ehbar({hat z}times {mathbf m})$. When the modulation frequency is higher than the magnetization precessing frequency, the amplitude of this field is significantly larger than previously predicted results. Correspondingly, the spin torque on the magnetization is also effectively enhanced. Additionally, the nature of SOC induced spin torque in the system can be transformed from damping to antidamping-like by modulating ${dot alpha_R}$. We also suggest a biasing scheme to achieve rectification of SMF, {it i.e.}, by application of a square wave voltage at the resonant frequency. Finally, we numerically estimate the resulting spin torque field arising from a Gaussian pulse time modulation of $alpha_R$.
We describe the current state and future plans for a set of tools for scientific data management (SDM) designed to support scientific transparency and reproducible research. SDM has been in active use at our MRI Center for more than two years. We des
igned the system to be used from the beginning of a research project, which contrasts with conventional end-state databases that accept data as a project concludes. A number of benefits accrue from using scientific data management tools early and throughout the project, including data integrity as well as reuse of the data and of computational methods.
We calculate the cross section for the inclusive production of B mesons in pp and ppbar collisions at next-to-leading order in the general-mass variable-flavor-number scheme and show that a suitable choice of factorization scales leads to a smooth tr
ansition to the fixed-flavor-number scheme. Our numerical results are in good agreement with data from the Tevatron and LHC experiments at small and at large transverse momenta.
We develop a theoretical description of electro-magnon solitons in a coupled ferroelectric-ferromagnetic heterostructure. The solitons are considered in the weakly nonlinear limit as a modulation of plane waves corresponding to two, electric- and mag
netic-like branches in the spectrum. Emphasis is put on magnetic-like envelope solitons that can be created by an alternating electric field. It is shown also that the magnetic pulses can be amplified by an electric field with a frequency close to the band edge of the magnetic branch.
