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The thermal noise of DC Josephson current in the superconducting leads coupled with a quantum dot system is investigated, and the general thermal current noise formula is derived in the presence of Zeeman field. The resonant structure versus gate voltage and Zeeman energy are displayed. Novel structures associated with the bound state and normal energy state are obtained. As the temperature is low, the Andreev reflection plays an important role in thermal noise and this provides new channels for electron to tunnel. However, if the temperature is high enough, the thermal noise due to Andreev reflection is trivial compared with the normal transport one. The thermal noise versus phase difference is also given to exhibit the temperature dependence. The Fano factor versus phase is much larger than 1 if the temperature is nonzero.

Maxwell equations are not logical consistent. This problem is caused by the implication that the divergence and the curl of a vector are not related. Based on Chen's S-R decomposition of a rank-two tensor, this logical un-consistency is discarded and, as a consequence, the classical Maxwell equations are reformulated to deduce London equations. From boundary field point, the relations between Josephson current and outside magnetic field are established, which shows that the Josephson current is produced by vortices of boundary magnetic field. From local field point, the first London equation corresponds to the local average rotation of electric field and the second London equation corresponds to the local average rotation of magnetic field. The relation between the Josephson effects and vortices of electromagnetic fields is discussed.

Effect of proximity-induced unconventional p-wave superconductivity in a three-dimensional topological insulator-based S/F/S structure on the Andreev bound states (ABSs) and Josephson supercurrent is studied. We investigate, in detail, the suppression of Andreev reflection and helical ABSs in the presence of three types of triplet superconducting gap. The magnetization of ferromagnetic section is perpendicular to the surface of junction. The influence of such features on the supercurrent flow on the surface of the topological insulator is studied. We carry out our goal by introducing a relevant form of Dirac spinors for gapless renormalized by chemical potential μ excitation states. Therefore, it enables us to consider the virtual Andreev process, simultaneously, and we propose to investigate it in a tunneling conductance junction. It is shown that the results obtained in this case are completely different from those in conventional superconductivity, as s- or d-waves, for example, the magnetization is found to decrease the gap for p_x and p_x+ip_y case, whereas increase it for p_y order. Strongly suppressed Andreev reflection is demonstrated.

We present the bosonic operator Hamiltonian models of two Josephson junctions which are connected in series and in parallel, respectively. By introducing the entangled state representations (|η〉 representation and Cooper pairs representation) and projecting the operator Hamiltonian onto the |η〉 representation we obtain the correct Josephson current and phase equations consistent with the classical Hamiltonian cases.

The dynamics of the coexisting ultracold atomic and molecular condensates in the presence of Feshbach resonance, atom–atom, molecule–molecule and atom–molecule interactions is described in terms of coupled Gross–Pitaevskii equation. We show that the appearence of oscillation or the existence of Josephson-like currents in the condensates is the natural consequence of the Gross–Pitaevskii equation under a suitable approximation regarding the nature of the condensate wave function.

By taking into account the interface scattering effect in a d-wave superconductor (S)/insulator layer (I)/d-wave superconductor (S) junction, the temperature dependence of the critical current and the current-phase relation are studied theoretically. It is found that both the barrier scattering and the roughness scattering at the interface always suppress the Andreev reflection and the current-phase relation is almost sinusoidal in the junction. The Josephson current strongly depends on the crystalline axis orientation of the d-wave superconductor in the junction. Some different phenomena appear depending on whether the crystal orientations of the superconductors on the two sides are the same or not, and this is mainly presented in the influence of the zero-energy states formation at the interface on the critical current which changes with temperature and phase.

Maxwell equations are not logical consistent. This problem is caused by the implication that the divergence and the curl of a vector are not related. Based on Chen's S-R decomposition of a rank-two tensor, this logical un-consistency is discarded and, as a consequence, the classical Maxwell equations are reformulated to deduce London equations. From boundary field point, the relations between Josephson current and outside magnetic field are established, which shows that the Josephson current is produced by vortices of boundary magnetic field. From local field point, the first London equation corresponds to the local average rotation of electric field and the second London equation corresponds to the local average rotation of magnetic field. The relation between the Josephson effects and vortices of electromagnetic fields is discussed.