Size dependence of second-order hyperpolarizability of finite periodic chain under Su-Schrieffer-Heeger model

The second hyperpolarizability $\gamma_N(-3\omega\omega,\omega,\omega)$ of $N$ double-bond finite chain of trans-polyactylene is analyzed using the Su-Schrieffer-Heeger model to explain qualitative features of the size-dependence behavior of $\gamma_N$. Our study shows that $\gamma_N/N$ is {\it nonmonotonic} with $N$ and that the nonmonotonicity is caused by the dominant contribution of the intraband transition to $\gamma_N$ in polyenes. Several important physical effects are discussed to reduce quantitative discrepancies between experimental and our resultsComment: 3 figures, 1 tabl

Uniqueness of Bessel models: the archimedean case

In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.Comment: 22 page

Some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems

We study theoretically some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems. Based on a scattering wave function approach, we show rigorously that in the equilibrium state no finite spin polarizations can exist in a multi-terminal mesoscopic spin-orbit coupled system (both in the leads and in the spin-orbit coupled region) and also no finite equilibrium terminal spin currents can exist. By use of a typical two-terminal mesoscopic spin-orbit coupled system as the example, we show explicitly that the nonequilibrium terminal spin currents in a multi-terminal mesoscopic spin-orbit coupled system are non-conservative in general. This non-conservation of terminal spin currents is not caused by the use of an improper definition of spin current but is intrinsic to spin-dependent transports in mesoscopic spin-orbit coupled systems. We also show that the nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in a thin strip of \textit{finite} length of a two-dimensional electronic system with intrinsic spin-orbit coupling may be non-antisymmetric in general, which implies that some cautions may need to be taken when attributing the occurrence of nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in such a system to an intrinsic spin Hall effect.Comment: 11 pages, 6 figure

Time Dependent Theory for Random Lasers

A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate $P_{r}^{c}$ exists for the appearance of the lasing peaks. The number of lasing modes increase with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length $\xi$ and average mode length $L_m$.Comment: 8 pages. Send to PR

Non-equilibrium spin polarization effects in spin-orbit coupling system and contacting metallic leads

We study theoretically the current-induced spin polarization effect in a two-terminal mesoscopic structure which is composed of a semiconductor two-dimensional electron gas (2DEG) bar with Rashba spin-orbit (SO) interaction and two attached ideal leads. The nonequilibrium spin density is calculated by solving the scattering wave functions explicitly within the ballistic transport regime. We found that for a Rashba SO system the electrical current can induce spin polarization in the SO system as well as in the ideal leads. The induced polarization in the 2DEG shows some qualitative features of the intrinsic spin Hall effect. On the other hand, the nonequilibrium spin density in the ideal leads, after being averaged in the transversal direction, is independent of the distance measured from the lead/SO system interface, except in the vicinity of the interface. Such a lead polarization effect can even be enhanced by the presence of weak impurity scattering in the SO system and may be detectable in real experiments.Comment: 6 pages,5 figure