Canonical quantization of superconducting circuits

226 p.Los circuitos superconductores han surgido como una de las implementaciones físicas más prometedorasen tecnologías cuánticas, fusionando la física, la ingeniería y las matemáticas. Esta tesis expone modeloshamiltonianos matemáticamente consistentes y precisos para describir redes superconductoras idealesformadas por un número arbitrario de elementos concentrados y distribuidos como condensadores,inductores, uniones de Josephson, giradores, y líneas de transmisión. Aunque son ideales, hemosdemostrado que estos modelos que están basados en las leyes de Kirchhoff, son finitos y no presentanproblemas de divergencias, disipando malentendidos de la literatura previa. Finalmente se describe unaextensión de la teoría estándar para cuantizar circuitos que incluyen elementos ideales no recíprocos deforma sistemática, y se allana el camino para su extensión a giradores y circuladores dependientes defrecuencia

Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem

Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show that the SIC existence problem is equivalent to three other, on the face of it quite different problems. Although it is still not clear whether these reformulations of the problem will make it more tractable, we believe that the fact that SICs have these connections to other areas of mathematics is of some intrinsic interest. Specifically, we reformulate the SIC problem in terms of (1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result being a greatly strengthened version of one previously obtained by Appleby, Flammia and Fuchs). The connection between these three reformulations is non-trivial: It is not easy to demonstrate their equivalence directly, without appealing to their common equivalence to SIC existence. In the course of our analysis we obtain a number of other results which may be of some independent interest.Comment: 36 pages, to appear in Quantum Inf. Compu

Performances of passive electric networks and piezoelectric transducers for beam vibration control

This thesis is focused on beam vibration control using piezoelectric transducers and passive electric networks. The first part of this study deals with the modeling and the analysis of stepped piezoelectric beams. A refined one-dimensional model is derived and experimentally validated. The modal properties are determined with four numerical methods. A homogenized model of stepped periodic piezoelectric beams is derived by using two-scale convergence. The second part deals with the performance analysis of three passive circuits in damping structural vibrations: the piezoelectric shunting, the second order transmission line and the fourth order transmission line. The effects of uncertainties of the electric parameters on the system performances are analyzed. Theoretical predictions are validated through different experimental setup

An intrinsic Hamiltonian formulation of the dynamics of LC-circuits

First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduce