Steady-state quantum analysis of linear systems

A rigorous basis for the quantum analysis of the steady state of linear distributed systems is established. The analysis of a distributed system of finite length requires, for self-consistency, that excitations be stated at the boundaries of the system even in the absence of externally applied excitations. The commutators of the amplitudes at the boundaries are stated and a useful analogy with thermal noise of classical systems is established. The use of these boundary conditions enables one to formulate the theory of the steady state for distributed quantum systems. When the system under consideration is coupled to a dissipation mechanism, operator-noise sources have to be assigned to the dissipative elements. The commutation relations that must be obeyed by these noise sources are derived. This formalism enables one to analyze the steady-state operation of an attenuator and of a maser amplifier. Finally, properties of multiterminal-pair networks are discussed using the steady-state quantum approach.