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A resonator together with a resistive shunting cover over the microbridge was applied to synchronize intrinsic Josephson junctions. We made both numerical and experimental investigations of the electrical properties of such microbridges: the multibranch behaviour above critical currents and switching between branches. The stability analyses revealed that in-phase states are sensitive to noise. Optimal parameters for synchronization of the system of two junctions up to 26-27% spread of critical currents are calculated.

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We investigated numerically synchronization of Josephson junctions inside the transmission line. We have found that due to the resonance behavior of the system there appear the self-induced resonance steps, strong synchronization of junctions on these steps and the inhomogeneous distribution of the Joule heat extraction (the selfheating) along the line which can lead to the formation of "hot spots" in the line. The developed model can be applied to explain recent experiments in which these effects were obtained.

Recent experiments on synchronized radiation from intrinsic Josephson junctions in high‐temperature superconductors showed that the difference of temperatures of the junctions can influence synchronization. We investigated numerically the mechainsm of this influence on the example of two overdamped Josephson junctions loaded by a shunt consisting of the resistance and the inductance. We showed that strong synchronization of radiation was obtained by means of external separate heating/cooling of junctions. Due to the change of critical currents in the process of heating or cooling, the current–voltage (I–V) characteristics of the junctions cross each other and junctions are synchronized by the ac current in the load in the vicinity of this crossing. The maximal tolerant spread of critical currents for this mechanism of synchronization is 15–20% that is twice larger than the maximal tolerant spread for this system without the separate heating. I–V characteristics of two separately heated junctions. Phase locking in this system is impossible without heating for such large spreads of critical currents.

We have shown that thermoelastic losses give the significant contribution to the total mechanical damping in the low loss quartz even for the bulk samples if the thickness of the sample is smaller than other dimensions. We have developed a model that describes experimental data of mechanical losses in a round quartz plate with the diameter 7.48 cm and the thickness 1.2 cm at temperatures 5–25 K in the range of eigenfrequencies 11–300 kHz. The model takes into account both the contribution of thermoelastic losses and the contribution due to the interaction of the acoustic wave with thermal phonons (Akhieser damping). Thermoelastic processes determine losses below 120 kHz. At larger eigenfrequencies, the Akhieser damping dominates.

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