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@ARTICLE{Rymarz:1007153,
      author       = {Rymarz, Martin and DiVincenzo, David P.},
      title        = {{C}onsistent {Q}uantization of {N}early {S}ingular
                      {S}uperconducting {C}ircuits},
      journal      = {Physical review / X},
      volume       = {13},
      number       = {2},
      issn         = {2160-3308},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2023-01970},
      pages        = {021017},
      year         = {2023},
      abstract     = {The theory of circuit quantum electrodynamics has
                      successfully analyzed superconducting circuits on the basis
                      of the classical Lagrangian, and the corresponding quantized
                      Hamiltonian describing these circuits. In many simplified
                      versions of these networks, the modeling involves a singular
                      Lagrangian that employs Kirchhoff’s laws to eliminate
                      inherent constraints of the system. In this work, we
                      demonstrate the failure of such singular theories for the
                      quantization of realistic, nearly singular superconducting
                      circuits. Instead, we rigorously prove the validity of a
                      perturbative analysis within the Born-Oppenheimer
                      approximation. In particular, we find that the limiting
                      behavior of the low-energy dynamics obtained from the
                      regularized approach exhibits a fixed-point structure
                      flowing to one of a few universal fixed points as parasitic
                      capacitance values go to zero. This singular limit of the
                      regularized analysis is, in many cases, completely unlike
                      the singular theory. Consequently, we conclude that
                      classical network synthesis techniques which build on
                      Kirchhoff’s laws must be critically examined prior to
                      applying circuit quantization.},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5224 - Quantum Networking (POF4-522) / DFG project
                      390534769 - EXC 2004: Materie und Licht für
                      Quanteninformation (ML4Q) (390534769)},
      pid          = {G:(DE-HGF)POF4-5224 / G:(GEPRIS)390534769},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000985618900001},
      doi          = {10.1103/PhysRevX.13.021017},
      url          = {https://juser.fz-juelich.de/record/1007153},
}