Quantum-Mechanical Model of Neural Network Elements

Abstract

A model of a neural-network-like quantum-mechanical system is considered. The role of neurons is played by quantum-mechanical particles which evolve under the action of an external double-well potential. An instanton is used as a spike. Neurons are connected by the interaction potential ${{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})$. The connection is directional owing to asymmetry of the interaction potential. Therefore, the complete Hamiltonian of the system is $\hat {H} = \sum\nolimits_i \left( {\frac{1}{2}\hat {p}_{i}^{2} + {{V}_{0}}({{{\hat {q}}}_{i}})} \right) + \sum\nolimits_{i > j} \,{{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})$. The system is investigated by the path integral Monte Carlo (PIMC) method. It is shown that with a certain choice of parameters in this system it is possible to transfer activity in long chains of neurons.