Spin filtering implemented through Rashba and weak magnetic modulations

We present two theoretical schemes for spin filters in one-dimensional semiconductor quantum wires with spatially modulated Rashba spin-orbit coupling (SOC) as well as weak magnetic potential. For case I, the SOC is periodic and the weak magnetic potential is applied uniformly along the wire. Full spin polarizations with opposite signs are obtained within two separated energy intervals. For case II, the weak magnetic potential is periodic while the SOC is uniform. An ideal negative/positive switching effect for spin polarization is realized by tuning the strength of SOC. The roles of SOC, magnetic potential, and their coupling on the spin filtering are analyzed.Comment: 4 pages, 4 figure

The Sorting Index and Permutation Codes

In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced a new Mahonian statistic $sor$, called the sorting index. Petersen proved that the pairs of statistics $(sor,cyc)$ and $(inv,rl\textrm{-}min)$ have the same joint distribution over the symmetric group, and asked for a combinatorial proof of this fact. In answer to the question of Petersen, we observe a connection between the sorting index and the B-code of a permutation defined by Foata and Han, and we show that the bijection of Foata and Han serves the purpose of mapping $(inv,rl\textrm{-}min)$ to $(sor,cyc)$. We also give a type $B$ analogue of the Foata-Han bijection, and we derive the quidistribution of $(inv_B,{\rm Lmap_B},{\rm Rmil_B})$ and $(sor_B,{\rm Lmap_B},{\rm Cyc_B})$ over signed permutations. So we get a combinatorial interpretation of Petersen's equidistribution of $(inv_B,nmin_B)$ and $(sor_B,l_B')$. Moreover, we show that the six pairs of set-valued statistics $\rm (Cyc_B,Rmil_B)$, $\rm(Cyc_B,Lmap_B)$, $\rm(Rmil_B,Lmap_B)$, $\rm(Lmap_B,Rmil_B)$, $\rm(Lmap_B,Cyc_B)$ and $\rm(Rmil_B,Cyc_B)$ are equidistributed over signed permutations. For Coxeter groups of type $D$, Petersen showed that the two statistics $inv_D$ and $sor_D$ are equidistributed. We introduce two statistics $nmin_D$ and $\tilde{l}_D'$ for elements of $D_n$ and we prove that the two pairs of statistics $(inv_D,nmin_D)$ and $(sor_D,\tilde{l}_D')$ are equidistributed.Comment: 25 page

Energy Spectra of Anti-nucleons in Finite Nuclei

The quantum vacuum in a many-body system of finite nuclei has been investigated within the relativistic Hartree approach which describes the bound states of nucleons and anti-nucleons consistently. The contributions of the Dirac sea to the source terms of the meson-field equations are taken into account up to the one-nucleon loop and one-meson loop. The tensor couplings for the $\omega$- and $\rho$-meson are included in the model. The overall nucleon spectra of shell-model states are in agreement with the data. The calculated anti-nucleon spectra in the vacuum differ about 20 -- 30 MeV with and without the tensor-coupling effects.Comment: 4 pages, to appear in the Proceedings of MENU 2004 (Beijing, Aug. 29 -- Sept. 4, 2004

Ideal switching effect in periodic spin-orbit coupling structures

An ideal switching effect is discovered in a semiconductor nanowire with a spatially-periodic Rashba structure. Bistable `ON' and `OFF' states can be realized by tuning the gate voltage applied on the Rashba regions. The energy range and position of `OFF' states can be manipulated effectively by varying the strength of the spin-orbit coupling (SOC) and the unit length of the periodic structure, respectively. The switching effect of the nanowire is found to be tolerant of small random fluctuations of SOC strength in the periodic structure. This ideal switching effect might be applicable in future spintronic devices.Comment: 4 pages and 4 figure

P‐64: UV‐Light‐Modified Polyimide Films for Liquid‐Crystal Alignment

Infrared, UV‐visible and X‐ray photoelectron spectroscopy measurements indicate that bond‐breaking and oxidation occur during broadband UV‐illumination of the polyimide film in the air. Surface tension and polarity are increased based on the measurements of contact angles. No obvious morphology change has been observed through atomic force microscopy analysis. While the polarized UV‐light generates a relatively small pretilt angle on a nonrubbed surface, it reduces the pretilt angle to some degree on a rubbed surface, depending upon the UV‐light polarization direction relative to the rubbing direction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/92039/1/1.1833863.pd

Preprint arXiv: arXiv:2209.08871 Submitted on 19 Sep 2022

We provide further analytical insights into the newly established noninteracting (free-fermion) Page curve, focusing on both the kinematic and dynamical aspects. First, we unveil the underlying canonical typicality and atypicality for random free-fermion states. The former appears for a small subsystem and is exponentially weaker than the well-known result in the interacting case. The latter explains why the free-fermion Page curve differs remarkably from the interacting one when the subsystem is macroscopically large, i.e., comparable with the entire system. Second, we find that the free-fermion Page curve emerges with unexpectedly high accuracy in some simple tight binding models in long-time quench dynamics. This contributes a rare analytical result concerning quantum thermalization on a macroscopic scale, where conventional paradigms such as the generalized Gibbs ensemble and quasi-particle picture are not applicable