We present an elementary proof that the quantum adiabatic approximation is correct up to exponentially small errors for Hamiltonians that depend analytically on the time variable. Our proof uses optimal truncation of a straightforward asymptotic expansion. We estimate the terms of the expansion with
โฆ LIBER โฆ
Error estimates for Krylov subspace approximations of matrix exponentials
โ Scribed by D.E. Stewart; T.S. Leyk
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 402 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0377-0427
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## Abstract This paper studies mixed finite element approximations to the solution of the viscoelasticity wave equation. Two new transformations are introduced and a corresponding system of firstโorder differentialโintegral equations is derived. The semiโdiscrete and fullโdiscrete mixed finite elem