A note on the switching adiabatic theorem
- 18 September 2012
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 53 (10) , 102202
Abstract
We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class Gα as a function of time, and we show that the error in adiabatic approximation remains small for running times of order g−2 |ln g |6α. Here g denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.Keywords
All Related Versions
Funding Information
- National Science Foundation (DMS-0907165, DMS-1210982)
This publication has 23 references indexed in Scilit:
- A Note on Exponential Estimates in Adiabatic TheoryCommunications in Partial Differential Equations, 2005
- Adiabatic charge transport and the Kubo formula for Landau‐type HamiltoniansCommunications on Pure and Applied Mathematics, 2004
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete ProblemScience, 2001
- Adiabatic theorems and applications to the quantum hall effectCommunications in Mathematical Physics, 1993
- Linear adiabatic theory. Exponential estimatesCommunications in Mathematical Physics, 1993
- Exponentially small adiabatic invariant for the Schrödinger equationCommunications in Mathematical Physics, 1991
- Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gapsCommunications in Mathematical Physics, 1991
- Adiabatic theorems and applications to the quantum hall effectCommunications in Mathematical Physics, 1987
- On the adiabatic theorem of quantum mechanicsJournal of Physics A: General Physics, 1980
- Adiabatic invariance to all ordersAnnals of Physics, 1959