The Monge-Kantorovich mass-transportation problem has been shown to be fundamental for various basic problems in analysis and geometry in recent years. Shen and Zheng (2010) proposed a probability method to transform the celebrated Monge-Kantorovich
problem in a bounded region of the Euclidean plane into a Dirichlet boundary problem associated to a nonlinear elliptic equation. Their results are original and sound, however, their arguments leading to the main results are skipped and difficult to follow. In the present paper, we adopt a different approach and give a short and easy-followed detailed proof for their main results.
We investigate the interplay between the edge and bulk states, induced by the Rashba spin-orbit coupling, in a zigzag silicene nanoribbon in the presence of an external electric field. The interplay can be divided into two kinds, one is the interplay
between the edge and bulk states with opposite velocities, and the other is that with the same velocity direction. The former can open small direct spin-dependent subgaps. A spin-polarized current can be generated in the nanoribbon as the Fermi energy is in the subgaps. While the later can give rise to the spin precession in the nanoribbon. Therefore, the zigzag silicene nanoribbon can be used as an efficient spin filter and spin modulation device.
We investigate the transport properties in a zigzag silicene nanoribbon in the presence of an external electric field. The staggered sublattice potential and two kinds of Rashba spin-orbit couplings can be induced by the external electric field due t
o the buckled structure of the silicene. A bulk gap is opened by the staggered potential and gapless edge states appear in the gap by tuning the two kinds of Rashba spin-orbit couplings properly. Furthermore, the gapless edge states are spin-filtered and are insensitive to the non-magnetic disorder. These results prove that the quantum spin Hall effect can be induced by an external electric field in silicene, which may have certain practical significance in applications for future spintronics device.
A mechanism to generate a spin-polarized current in a two-terminal zigzag silicene nanoribbon is predicted. As a weak local exchange field that is parallel to the surface of silicene is applied on one of edges of the silicene nanoribbon, a gap is ope
ned in the corresponding gapless edge states but another pair of gapless edge states with opposite spin are still protected by the time-reversal symmetry. Hence, a spin-polarized current can be induced in the gap opened by the local exchange field in this two-terminal system. What is important is that the spin-polarized current can be obtained even in the absence of Rashba spin-orbit coupling and in the case of the very weak exchange filed. That is to say, the mechanism to generate the spin-polarized currents can be easily realized experimentally.We also find that the spin-polarized current is insensitive to weak disorder.
We predict a mechanism to generate a pure spin current in a two-dimensional topological insulator. As the magnetic impurities exist on one of edges of the two-dimensional topological insulator, a gap is opened in the corresponding gapless edge states
but another pair of gapless edge states with opposite spin are still protected by the time-reversal symmetry. So the conductance plateaus with the half-integer values $e^2/h$ can be obtained in the gap induced by magnetic impurities, which means that the pure spin current can be induced in the sample. We also find that the pure spin current is insensitive to weak disorder. The mechanism to generate pure spin currents is generalized for two-dimensional topological insulators.
The absorption spectrum of the title compound in the spectral range of the Hydrogen-bonded OH-stretching vibration has been investigated using a five-dimensional gas phase model as well as a QM/MM classical molecular dynamics simulation in solution.
The gas phase model predicts a Fermi-resonance between the OH-stretching fundamental and the first OH-bending overtone transition with considerable oscillator strength redistribution. The anharmonic coupling to a low-frequency vibration of the Hydrogen bond leading to a vibrational progression is studied within a diabatic potential energy curve model. The condensed phase simulation of the dipole-dipole correlation function results in a broad band in the 3000 cm region in good agreement with experimental data. Further, weaker absorption features around 2600 cm have been identified as being due to motion of the Hydrogen within the Hydrogen bond.
A hybrid Car-Parrinello QM/MM molecular dynamics simulation has been carried out for the Watson-Crick base pair of 9-ethyl-8-phenyladenine and 1-cyclohexyluracil in deuterochloroform solution at room temperature. The resulting trajectory is analyzed
putting emphasis on the N-H$...$N Hydrogen bond geometry. Using an empirical correlation between the $NN$-distance and the fundamental NH-stretching frequency, the time-dependence of this energy gap along the trajectory is obtained. From the gap-correlation function we determine the infrared absorption spectrum using lineshape theory in combination with a multimode oscillator model. The obtained average transition frequency and the width of the spectrum is in reasonable agreement with recent experimental data.
