Geometry of the adiabatic theorem

DOI10.1088/0143-0807/33/5/1063zbMATH Open1266.81071arXiv1112.4442OpenAlexW2059701928WikidataQ99713240 ScholiaQ99713240MaRDI QIDQ4919740

Pedro Ruas Dieguez, Clyffe De Assis Ribeiro, Rafael Antunes Ribeiro, Augusto César Lobo

Publication date: 15 May 2013

Published in: European Journal of Physics (Search for Journal in Brave)

Abstract: We present a simple and pedagogical derivation of the quantum adiabatic theorem for two level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for an understanding of the adiabatic theorem for this case.

Full work available at URL: https://arxiv.org/abs/1112.4442

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (3)

Weak values and modular variables from a quantum phase-space perspective ⋮ The Hannay angles: Geometry, adiabaticity, and an example ⋮ Geometry of adiabatic Hamiltonians for two-level quantum systems

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