Quantum dynamics of circuits with memory capacitors and inductors

The quantum mechanical rate equations for a general class of circuits consisting of lossless memory elements embedded in a general lossless linear reciprocal circuit have been derived. The embedding circuit is described by a canonical Foster multiport circuit c. The approach is general since any lossless linear reciprocal embedding network can be formulated in this way. The presented circuit model is the framework for a general quantum circuit theory for lossless reciprocal circuits including also nonlinear elements. As an example two-state memreactances described by a spin model have been considered.