A strong operator topology adiabatic theorem

Abstract

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

15 pages, no figures

References in corpus (3)

• Adiabatic Theorem without a Gap Condition
• Exponential Estimates in Adiabatic Quantum Evolution
• Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

Cited by in corpus (2)

• Minimal work principle: proof and counterexamples
• On the efficiency of Hamiltonian-based quantum computation for low-rank matrices