Algebraic canonical quantization of lumped superconducting networks

• URL: http://arxiv.org/abs/2203.06167v3
• Date: Mon, 12 Sep 2022 13:13:53 GMT
• Title: Algebraic canonical quantization of lumped superconducting networks
• Authors: I. L. Egusquiza and A. Parra-Rodriguez
• Abstract summary: We present a systematic canonical quantization procedure for lumped-element superconducting networks. The algorithm is based on an original, explicit, and constructive implementation of the symplectic diagonalization of positive semidefinite Hamiltonian matrices.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of 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. 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.

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