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arXiv · 2203.06167

Algebraic canonical quantization of lumped superconducting networks

I. L. Egusquiza·A. Parra-Rodriguez
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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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I. L. Egusquiza, A. Parra-Rodriguez. 2022-03-11. Algebraic canonical quantization of lumped superconducting networks. https://doi.org/10.1103/physrevb.106.024510

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