Algebraic canonical quantization of lumped superconducting networks
arXiv:2203.06167 · doi:10.1103/PhysRevB.106.024510
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.
arXiv comment24 pages. 6 Figures
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