Geometrical description and Faddeev-Jackiw quantization of electrical
networks
- URL: http://arxiv.org/abs/2304.12252v2
- Date: Thu, 7 Dec 2023 11:58:55 GMT
- Title: Geometrical description and Faddeev-Jackiw quantization of electrical
networks
- Authors: A. Parra-Rodriguez and I. L. Egusquiza
- Abstract summary: We develop a new description of the dynamics of general lumped-element electrical circuits.
We identify and classify the singularities that arise in the search for Hamiltonian descriptions of general networks.
This work will prove useful, for instance, to automatize the computation of exact Hamiltonian descriptions of superconducting quantum chips.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In lumped-element electrical circuit theory, the problem of solving Maxwell's
equations in the presence of media is reduced to two sets of equations, the
constitutive equations encapsulating local geometry and dynamics of a confined
energy density, and the Kirchhoff equations enforcing conservation of charge
and energy in a larger, topological, scale. We develop a new geometric and
systematic description of the dynamics of general lumped-element electrical
circuits as first order differential equations, derivable from a Lagrangian and
a Rayleigh dissipation function. Through the Faddeev-Jackiw method we identify
and classify the singularities that arise in the search for Hamiltonian
descriptions of general networks. The core of our solution relies on the
correct identification of the reduced manifold in which the circuit state is
expressible, e.g., a mix of flux and charge degrees of freedom, including the
presence of compact ones. We apply our fully programmable method to obtain
(canonically quantizable) Hamiltonian descriptions of nonlinear and
nonreciprocal circuits which would be cumbersome/singular if pure node-flux or
loop-charge variables were used as a starting configuration space. This work
unifies diverse existent geometrical pictures of electrical network theory, and
will prove useful, for instance, to automatize the computation of exact
Hamiltonian descriptions of superconducting quantum chips.
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