A note on the switching adiabatic theorem

作者：Elgart Alexander^*; Hagedorn George A

来源：Journal of Mathematical Physics, 2012, 53(10): 102202.

DOI：10.1063/1.4748968

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(alpha) as a function of time, and we show that the error in adiabatic approximation remains small for running times of order g(-2) vertical bar ln g vertical bar(6 alpha). Here g denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.

• 出版日期2012-10
• 单位Virginia Tech; 美国弗吉尼亚理工大学(Virginia Tech)