A note on the switching adiabatic theorem
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 G^{α} 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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 October 2012
 DOI:
 10.1063/1.4748968
 arXiv:
 arXiv:1204.2318
 Bibcode:
 2012JMP....53j2202E
 Keywords:

 approximation theory;
 eigenvalues and eigenfunctions;
 quantum theory;
 03.65.Ta;
 03.65.Fd;
 02.10.Ud;
 02.60.Gf;
 Foundations of quantum mechanics;
 measurement theory;
 Algebraic methods;
 Linear algebra;
 Algorithms for functional approximation;
 Mathematical Physics;
 Quantum Physics;
 35Q41;
 81P68;
 81Q05
 EPrint:
 20 pages, no figures, to appear in JMP