Classical Analogue of the Quantum Theory of Perturbations

José Martínez-Carranza, Francisco Soto, H. M. Moya-Cessa

Wolfgang Scherer

A complete analogue of Kolmogorov's perturbation algorithm in classical mechanics is presented for perturbations of self-adjoint operators. The resulting perturbation theory is different from the usual Rayleigh - Schrödinger (or Kato - Rellich) perturbation theory.

İlhami Ünal, Brian Malone, Andrii Semenov +2 more

Spin-photon interactions are commonly described using quantum-mechanical Hamiltonian models, whereas the influence of local EM-field overlap on the coupling response is less explored.This study presents a dipole-based fullwave EM analogue for investigating resonator perturbations inspired by spin-qubit systems.An effective oscillating electric dipole is introduced as an EM analogue of qubit-induced polarization within a superconducting coplanar waveguide (CPW) resonator.The effects of dipole resonance frequency, orientation, and spatial position on the transmission response are systematically investigated.The results show that the magnitude of the resonator perturbation is governed by the local dipole-field overlap and decreases as the dipole is displaced from the high-field region or rotated away from the dominant electric-field direction.A coupled-resonator configuration is furthermore used as a consistency test and exhibits hybridized resonant modes and avoided-crossing behaviour in agreement with classical coupled-mode theory.The proposed framework is an electromagnetic analogue rather than a quantum-state model, and is intended to provide physical and geometryaware insight for future integration with quantitative cQED parameter-extraction methods.

S. M. McRae

Susmita Kar, Pratim Kumar Chattaraj

The behavior of a driven symmetric triple well potential has been studied by developing an algorithm where the well‐established Bohmian mechanics and time‐dependent Fourier Grid Hamiltonian method are incorporated and the quantum theory of motion (QTM) phase space structures of the particle are constructed, both in “nonclassical” and “classical” limits. Comparison of QTM phase space structures with their classical analogues shows both similarity as well as dissimilarities. The temporal nature and the spatial symmetry of applied perturbation play crucial roles in having similar phase space structures. © 2016 Wiley Periodicals, Inc.

Luigi E. Picasso, L. Bracci, Emilio d’Emilio