Quantum circuit theory

In RF nanoelectronics and mesoscopic electronics quantum effects play a role on the circuit and system level. In this work a quantum electrodynamics based circuit theory is introduced that allows to establish quantum mechanical models of distributed circuits. Based on the Hamiltonian description of the Foster equivalent circuits a quantization of the equivalent circuits is performed. The quantum mechanical interaction of the modes via nonlinear elements is discussed. A DC-pumped Josephson parametric amplifier is treated quantum mechanically.