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@ARTICLE{Riwar:916848,
      author       = {Riwar, Roman-Pascal and DiVincenzo, David},
      title        = {{C}ircuit quantization with time-dependent magnetic fields
                      for realistic geometries},
      reportid     = {FZJ-2023-00142, arXiv:2103.03577},
      year         = {2022},
      note         = {21 pages, 4 figures},
      abstract     = {Quantum circuit theory has become a powerful and
                      indispensable tool to predict the dynamics of
                      superconducting circuits. Surprisingly however, the question
                      of how to properly account for a time-dependent driving via
                      external magnetic fields has hardly been addressed so far.
                      Here, we derive a general recipe to construct a low-energy
                      Hamiltonian, taking as input only the circuit geometry and
                      the solution of the external magnetic fields. A gauge fixing
                      procedure for the scalar and vector potentials is given
                      which assures that time-varying magnetic fluxes make
                      contributions only to the potential function in the
                      $Schr\'odinger$ equation. Our proposed procedure is valid
                      for continuum geometries and thus significantly generalizes
                      previous efforts, which were based on discrete circuits. We
                      study some implications of our results for the concrete
                      example of a parallel-plate SQUID circuit. We show that if
                      we insist on representing the response of this SQUID with
                      individual, discrete capacitances associated with each
                      individual Josephson junction, this is only possible if we
                      permit the individual capacitance values to be negative,
                      time-dependent or even momentarily singular. Finally, we
                      provide some experimentally testable predictions, such as a
                      strong enhancement of the qubit relaxation rates arising
                      from the effective negative capacitances, and the emergence
                      of a Berry phase due to time dependence of these
                      capacitances.},
      cin          = {PGI-11 / PGI-2},
      cid          = {I:(DE-Juel1)PGI-11-20170113 / I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5224 - Quantum Networking (POF4-522) / 5221 - Advanced
                      Solid-State Qubits and Qubit Systems (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5224 / G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2103.03577},
      howpublished = {arXiv:2103.03577},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2103.03577;\%\%$},
      url          = {https://juser.fz-juelich.de/record/916848},
}