Electrical Resonance Circuits as Analogs to Quantum Mechanical Billiards

Resonance in electrical circuits pdf

Fast-tunable resonators and quantum electrical circuits

In this thesis, measurements on superconducting electrical circuits that exhibit quantum mechanical effects are presented. Nonlinear superconducting circuits can be regarded as artificial atoms with energy spectra that can be engineered. The artificial atoms can be used as quantum bits for quantum computation. By coupling the artificial atoms to the electromagnetic field inside a transmission l...

Quantum Billiards

Quantum mushroom billiards.

We report the first large-scale statistical study of very high-lying eigenmodes (quantum states) of the mushroom billiard proposed by L. A. Bunimovich [Chaos 11, 802 (2001)]. The phase space of this mixed system is unusual in that it has a single regular region and a single chaotic region, and no KAM hierarchy. We verify Percival's conjecture to high accuracy (1.7%). We propose a model for dyna...

Random Quantum Billiards

We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach is formally distinct from that of the familiar Gaussian orthogonal ensemble, there is remarkable agreement in the resulting distributions of level spacings ...