Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals

In this paper, a non-Hermitian Aubry-Andr\'e-Harper model with power-law hoppings ($1/s^{a}$) and quasiperiodic parameter $\beta$ is studied, where $a$ is the power-law index, $s$ is the hopping distance, and $\beta$ is a member of the metallic mean family. We find that under the weak non-Hermitian effect, there preserves $P_{\ell=1,2,3,4}$ regimes where the fraction of ergodic eigenstates is $\beta$-dependent as $\beta^{\ell}$L ($L$ is the system size) similar to those in the Hermitian case. However, $P_{\ell}$ regimes are ruined by the strong non-Hermitian effect. Moreover, by analyzing the fractal dimension, we find that there are two types of edges aroused by the power-law index $a$ in the single-particle spectrum, i.e., an ergodic-to-multifractal edge for the long-range hopping case ($a<1$), and an ergodic-to-localized edge for the short-range hopping case ($a>1$). Meanwhile, the existence of these two types of edges is found to be robust against the non-Hermitian effect. By employing the Simon-Spence theory, we analyzed the absence of the localized states for $a<1$. For the short-range hopping case, with the Avila's global theory and the Sarnak method, we consider a specific example with $a=2$ to reveal the presence of the intermediate phase and to analytically locate the intermediate regime and the ergodic-to-multifractal edge, which are self-consistent with the numerically results.Comment: 8 pages, 8 figure

Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model

We investigate the transition from PT-symmetry to PT-symmetry breaking and vice versa in the non-Hermitian Landau-Zener (LZ) models. The energy is generally complex, so the relaxation rate of the system is set by the absolute value of the gap. To illustrate the dynamics of phase transitions, the relative population is introduced to calculate the defect density in nonequilibrium phase transitions instead of the excitations in the Hermitian systems. The result shows that the adiabatic-impulse (AI) approximation, which is the key concept of the Kibble-Zurek (KZ) mechanism in the Hermitian systems, can be generalized to the PT-symmetric non-Hermitian LZ models to study the dynamics in the vicinity of a critical point. Therefore, the KZ mechanism in the simplest non-Hermitian two-level models is presented. Finally, an exact solution to the non-Hermitian LZ-like problem is also shown.Comment: 11 pages, 3 figure

Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states

The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work, we introduce compass-like states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that, when a significant quantity of photons is added (or subtracted), the Wigner function of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.Comment: PHYSICAL REVIEW A 107, 052614 (2023), 15 Figures, 20 page

Different Magnitudes of Tensile Strain Induce Human Osteoblasts Differentiation Associated with the Activation of ERK1/2 Phosphorylation

Mechanical factors are related to periprosthetic osseointegration following total hip arthroplasty. However, osteoblast response to strain in implanted femurs is unclear because of the absence of accurate stress-measuring methods. In our study, finite element analysis was performed to calculate strain distribution in implanted femurs. 0.8-3.2% tensile strain was then applied to human osteoblasts. Higher magnitudes of strain enhanced the expression of osteocalcin, type I collagen, and Cbfa1/Runx2. Lower magnitudes significantly increased ALP activity. Among these, type I collagen expression increased with the activation of ERK1/2 phosphorylation in a strain-magnitude-dependent manner. Our study marks the first investigation of osteoblast response at different magnitudes of periprosthetic strain. The results indicate that the functional status of human osteoblasts is determined by strain magnitude. The strain distribution in the proximal region of implanted femur should be improved for osseointegration

Regulatory controls of duplicated gene expression during fiber development in allotetraploid cotton.

Polyploidy complicates transcriptional regulation and increases phenotypic diversity in organisms. The dynamics of genetic regulation of gene expression between coresident subgenomes in polyploids remains to be understood. Here we document the genetic regulation of fiber development in allotetraploid cotton Gossypium hirsutum by sequencing 376 genomes and 2,215 time-series transcriptomes. We characterize 1,258 genes comprising 36 genetic modules that control staged fiber development and uncover genetic components governing their partitioned expression relative to subgenomic duplicated genes (homoeologs). Only about 30% of fiber quality-related homoeologs show phenotypically favorable allele aggregation in cultivars, highlighting the potential for subgenome additivity in fiber improvement. We envision a genome-enabled breeding strategy, with particular attention to 48 favorable alleles related to fiber phenotypes that have been subjected to purifying selection during domestication. Our work delineates the dynamics of gene regulation during fiber development and highlights the potential of subgenomic coordination underpinning phenotypes in polyploid plants. [Abstract copyright: © 2023. The Author(s).

Study on Torque Distribution of Torque Split Transmission System of Face Gear

In order to research the influence of installation errors and support deformations on load distribution in the torque split transmission system of face gear,a calculating method for load distribution of torque split transmission system of face gear is proposed. At first,the model of load sharing for torque split transmission system of face gear is established by torque balance equation and deformation compatibility condition,and the deformation compatibility condition directly relate to time- vary meshing stiffness of gear pair. Secondly,the force on the face gear is analyzed,and the form that the deformation of support system is described,the support deformation is translated to errors of gear. Thirdly,the meshing stiffness of gear pair is fit as function of load by tooth contact analysis（ TCA） and loaded tooth contact analysis（ LTCA）. At last,the calculation method for coefficients of load sharing is proposed. Numerical example demonstrates that the coefficients of two path in the system is respectively 0. 65 and 1. 35 under the combined effects of installation errors and support deformation,while the radial support deformation ax1 of the pinion is- 692. 3 μm,the coefficients of the two path is respectively 0. 987 0 and 1. 013. Hence,the radial elastic support ax1 of the pinion,to some extent,is able to offset the influence of unequal torque splitting caused by installation errors and support deformation

Electron emission from a two-dimensional crystal with atomic thickness

Electron emission from a two-dimensional (2D) crystal with atomic thickness is theoretically studied with all the features associated with the low dimensionality and the atomic thickness being well considered. It is shown that, the atomic thickness results in quantum confinement of electrons in the crystal along thickness direction, and consequently two different ways of electron emission from it without and with quantum confinement of electrons normal to emission boundary: edge emission and surface emission. While electron emission from the edge of a 2D crystal can be described by the existing model, electron emission from the surface goes beyond its reach. Here, to describe the latter electron emission, a model based on the energy band theory with the quantum confinement along thickness direction being considered is proposed. It is shown that, the proposed model is a general one capable of describing not only electron emission with quantum confinement normal to an emission boundary but also electron emission without the regarded quantum confinement. The model is expected to advance the understanding and description of electron emission from a solid

INFLUENCE OF ACTIVE MODIFICATION PARAMETERS ON BEARING CHARACTERISTICS OF OPPOSITE GEAR PAIRS (MT)

Active gear design is a method that can pre-control gear meshing performance directly. In order to study the influence of active gear design on the bearing characteristics of tooth surface, the relationship between active modification parameters of the face gear and bearing characteristics of tooth surface is studied. Firstly, the contact model of the gear pair is established by the finite element method, and then different groups of active modification parameters are designed for simulation analysis. The results show that the geometric transmission error greatly influences gear transmission stability and contact strength, and controlling its amplitude can control bearing transmission error amplitude. Pre-designed contact path inclination angle within 30° neighborhood, bearing contact characteristics are better. The contact ellipse length mainly affects the contact strength of tooth surface and bending strength of tooth root. According to the simulation results, when it takes 0.5～0.75 times of tooth width, face gear pair has better bearing contact characteristics