Algebraic canonical quantization of lumped superconducting networks

We present a systematic canonical quantization procedure for lumped-element superconducting networks [1,2,3] by using a redundant configuration-space description. The algorithm is based on an original, explicit, and constructive implementation of the symplectic diagonalization of positive semidefinite Hamiltonian matrices, a particular instance of Williamson's theorem [4,5]. With it, we derive canonically quantized discrete-variable descriptions of passive causal systems. We exemplify the algorithm with representative singular electrical networks, a nonreciprocal extension for the black-box quantization method, as well as an archetypal Landau quantization problem. This viewpoint can be enriched using the techniques of quantization of constraint systems [5].

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