Quantum transport properties of ultrathin silver nanowires

The quantum transport properties of the ultrathin silver nanowires are investigated. For a perfect crystalline nanowire with four atoms per unit cell, three conduction channels are found, corresponding to three $s$ bands crossing the Fermi level. One conductance channel is disrupted by a single-atom defect, either adding or removing one atom. Quantum interference effect leads to oscillation of conductance versus the inter-defect distance. In the presence of multiple-atom defect, one conduction channel remains robust at Fermi level regardless the details of defect configuration. The histogram of conductance calculated for a finite nanowire (seven atoms per cross section) with a large number of random defect configurations agrees well with recent experiment.Comment: 4 pages, 6 figure

Calibrating the effective magnitudes of type Ia supernovae with a model-independent method

This research explores the correlation between the absolute magnitude and the redshift of Type Ia supernovae (SNe Ia) with a model-independent approach. The Pantheon sample of SNe Ia and strong gravitational lensing systems (SGLS) are used. With the cosmic distance-duality relation (CDDR), the evolution parameter of the magnitude, the light curve parameters of SNe Ia, and the parameters of the SGLS geometric model are constrained simultaneously. Considering the consistency of the redshifts, we selected a subsample of SNe Ia in which the redshift of each SNe Ia is close to the corresponding redshift of the SGLS sample. Two parametric models are used to describe this evolution, which can be written as $\delta_M=\varepsilon z$ and $\delta_M=\varepsilon\log(1+z)$, respectively. Our analysis reveals that $\varepsilon=-0.036^{+0.357}_{-0.339}$ in the first parametric model and $\varepsilon=-0.014^{+0.588}_{-0.630}$ in the second model, indicating that no significant evolution ($\varepsilon=0$) is supported at the 1$\sigma$ confidence level in this study. These results represent a significant advancement in our understanding of the intrinsic properties of SNe Ia and provide important constraints for future SNe Ia study.Comment: 8 pages, 2 figures, Accepted by Physical Review

The upper and lower solution method for nonlinear third-order three-point boundary value problem

This paper is concerned with the following nonlinear third-order three-point boundary value problem \left\{ \begin{array}{l} u^{\prime \prime \prime }(t)+f\left( t,u\left( t\right) ,u^{\prime}\left(t\right) \right) =0,\, t\in \left[ 0,1\right], \\ u\left( 0\right) =u^{\prime }\left( 0\right) =0,\, u^{\prime}\left( 1\right) =\alpha u^{\prime }\left( \eta \right),\label{1.1} \end{array} \right. where $0<\eta <1$ and $0\leq \alpha <1.$ A new maximum principle is established and some existence criteria are obtained for the above problem by using the upper and lower solution method

Building quantum neural networks based on swap test

Artificial neural network, consisting of many neurons in different layers, is an important method to simulate humain brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of quantum neural network in which the weights between neurons are all quantum states. We also construct a quantum circuit to realize this quantum neural network model. A learning algorithm is proposed meanwhile. We show the validity of learning algorithm theoretically and demonstrate the potential of the quantum neural network numerically.Comment: 10 pages, 13 figure