ИСТИНА

Superconducting elements with embedded Josephson junctions (SQUIDs) are widely used in quantum electronics and computer engineering. One of the modern applications of SQUIDs is to create quantum neurons elements which may be considered as basic elements of neural networks. Recently, an inertialess model of a neuron consisting of a superconducting circuit interrupted by a single Josephson junction. Currently, there is no mathematical neuron model that takes into account both the contact capacity (“inertia”) and the intrinsic dissipative processes. Despite the quantum nature of the SQUID, there is a range of parameters where it is possible to describe the operation of a neuron in a classical way. In this paper, we study the switching process of the rf-SQUID taking into account the capacity of the junction and dissipation in it. The dynamics of the junction is described by the Josephson equations for phase and current. We are interested in the presence of bistable SQUID states and transfers between them under the action of an external magnetic flux. Numerical simulation of the SQUID dynamics in the framework of a resistive model has been performed. To account for thermodynamic equilibrium with the medium, an ensemble of the junction copies was introduced, and the switching process at finite temperatures was modeled using the Monte Carlo method. As a result of modeling, we obtained a change in the distribution function of the phase difference for each time moment depending on the external magnetic flux and system parameters. The features of dynamics at critical values of the switching time for the non-dissipative case were established. During of modeling the dissipative process, some nontrivial results for energy dependence over time were found.