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The phase dynamics of the coupled Josephson junctions in the framework of CCJJ and CCJJ+DC models is studied. The current voltage characteristics (CVC) are numerically calculated for the stacks with different number of junctions at different model parameters. We manifest the difference of these models for the branching at I = Ic and in the hysteretic region. The essential difference is observed in the breakpoint region, where the longitudinal plasma wave is created. We discuss the main features of both models, related with the role of the diffusion current between the superconducting layers.

We study quantum phase fluctuations in planar junctions between high-Tc superconductors for a range of relative orientations of the a-b crystal axes. Specifically, attention is directed towards the fermionic subspace of low energy Andreev bound states, midgap states (MGS). This subspace, being responsible for most of the Josephson current, strongly couples to the phase degree of freedom. Low frequency phase fluctuations may introduce intrinsic dynamics in this subspace, which would lead to a strong dynamical modulation of the Josephson current, and thus affect the phase quantum dynamics. In this article it is found that transitions between pairs of MGS induced by the phase fluctuations are forbidden due to specific symmetry properties of the MGS, and the macroscopic quantum Hamiltonian remains essentially adiabatic within the assumption of a specular interface.

Concerning the spontaneous THz electromagnetic wave emission from intrinsic Josephson junctions, we revisit the theory for intrinsic Josephson effects from standpoints of the couplings between stacked junctions and consequent superconducting phase dynamics. After reviewing the previous simulation works based on the theory, we present recent multi-physics simulation studies suggested by authors to systematically reproduce the emission experiments. Some typical simulation results are exhibited and the future perspective of the simulation is also given.

To model the IV-characteristics of shunted intrinsic Josephson junctions we calculated phase dynamics of a chain of two identical junctions covered by a resistive shunt and with a resistive crosspiece between the shunt and the junctions. The coherent solution of dynamic equations for this system is unstable at some bias currents above critical currents of junctions. We have shown that this instability leads to the multibranch structure of IV-curves in the hysteretic region. The multibranch structure appears due to the random switching of junctions to the superconducting state above their critical currents. We found that the resistance of the interface between a covering shunt and the junctions can regulate the multibranch behaviour.

We study a phase dynamics induced by a spin dynamics in a ferromagnetic Josephson junction, in which two superconductors (SC's) are separated by a ferromagnetic layer. A new phenomenological model for the phase variable is proposed by including the spin dynamics excited by the ferromagnetic resonance (FMR) in the gauge invariant phase of s-wave SC's. We found that the current-voltage characteristics show step structures by tuning the microwave frequency to FMR. The result originats from the coupling between the spin and the phase dynamics, and provides a new route to observe the spin wave excitation by using the Josephson effect.

We study the phase dynamics and the resonance features of coupled Josephson junctions in layered superconductors and their manifestations in the current- voltage characteristics and temporal dependence of the electric charge in the superconducting layers. Results on the effect of the external radiation and shunting of the stack of Josephson junctions by LC-elements are presented. We discuss the ideas concerning the experimental observation of these resonances.

Within the last years many groups have realized and investigated different types of intrinsic Josephson junction (IJJ) arrays out of high-temperature superconducting single crystals or thin films. We tried to improve the synchronization between the junctions by external shunts. Mesa structures as well as microbridges on vicinal cut substrates showed multi-branch behaviour in their IV characteristics and random switching between branches. Theoretical modelling was done investigating phase dynamics and stability numerically as well as analytically. Branch structure in current voltage characteristics of IJJ is studied in the framework of different models, particularly, in capacitevely coupled Josephson junctions (CCJJ) model and CCJJ model with diffusion current. Results of modelling of return current in IV characteristics for stacks with different number of IJJ are presented. We discussed the possible mechanisms of synchronization and the ranges of stability. Conclusions with respect to application of such arrays such as radiation sources were given.