Narrow Results

Using the equivalent single-particle multi-channel network and the Landauer formula, we theoretically study anti-resonances in conductance of a normal metal–superconductor junction with a side-coupled quantum dot. The transport properties depend on the interplay between the Coulomb blockade effect and the Andreev reflection. It is found that the calculated dependence of the conductance on the gate voltage of dot exhibits two anti-resonant conductance dips. This behavior is caused by the destructive interference of the wave directly transmitted through the normal metal–superconductor junction and the wave reflected from the dot. Moreover, we find that the shape of two anti-resonance profile is symmetric, due to the Andreev reflection, depending on the strength of coupling between the quantum dot and normal metal.

An asymmetric system consisting of two coupled radio frequency superconducting quantum interference devices (RF-SQUIDs) with general geometry as nonlinear macroscopic system with mutual inductance under the influence of a time-dependent external field has been investigated numerically. Due to the importance of mutual induction in the construction of such nonlinear asymmetric systems, the dependence of coupling coefficient on the frequency changes, the primary and secondary resonance amplitudes and also the anti-resonances in both squids have been investigated. By changing the geometry of the arrangement of squids, the dynamic behavior parameters of the system have been studied. The eigenvalues of this system have been found and by changing frequency, the stable and unstable states have been studied.

Based on the finite element method (FEM), characteristics of the local resonance band gap and the Bragg scattering band gap of two periodically-distributed vibrator structures are studied. Conditions of original anti-resonance generation are theoretically derived. The original anti-resonance effect leads to localization of vibration. Factors which influence original anti-resonance band gap are analyzed. The band gap width and the mass ratio between two vibrators are closely correlated to each other. Results show that the original anti-resonance band gap has few influencing factors. In the locally resonant structure, the Bragg scattering band gap is found. The mass density of the elastic medium and the elasticity modulus have an important impact on the Bragg band gap. The coexistence of the two mechanisms makes the band gap larger. The band gap covered 90% of the low frequencies below 2000 Hz. All in all, the research could provide references for studying the low-frequency and broad band gap of phononic crystal.

A hybrid phononic crystal has been investigated. The characteristic frequency of XY mode, transmission loss and displacement vector have been calculated by the finite element method. There are Bragg scattering band gap and local resonance band gap in the band structures. We studied the influence factors of band gap. There are many flat bands in the eigenfrequencies curve. There are many flat bands in the curve. The band gap covers a large range in low frequency. The band gaps cover more than 95% below 3000 Hz.