Abstracts
Poster Abstracts | Talk Abstracts
Evolution-time dependence in near-adiabatic quantum evolutions
Presenting Author: Lucas Brady, University of California Santa Barbara
Contributing Author(s): Wim van Dam
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from H0 to H1 in a total evolution-time T, and our goal is to determine how the final state of the system depends on T. If the system is initially started in a non-degenerate ground state, the adiabatic theorem says that in the limit of large T, the system will stay in the ground state. We examine the near-adiabatic limit where the system evolves slowly enough that most but not all of the final state is in the ground state, and we find that the probability of leaving the ground state oscillates in T with a frequency determined by the integral of the spectral gap along the trajectory of the Hamiltonian, so long as the gap is big. If the gap becomes exceedingly small, the final probability is the sum of oscillatory behavior determined by the integrals of the gap before and after the small gap. We confirm these analytic predictions with numerical evidence from barrier tunneling problems in the context of quantum adiabatic optimization.
(Session 9c : Friday from 3:45pm-4:15pm)
- Home
- SQuInT
- Past SQuInT Meetings
- Lodging and Transportation
- Hotel Floor Maps (.pdf)
- Registration
- Submit Your Abstract
- Program
- Instructions for Presenters
SQuInT Chief Organizer
Akimasa Miyake, Assistant Professor
amiyake@unm.edu
SQuInT Co-Organizer
Mark M. Wilde, Assistant Professor LSU
mwilde@phys.lsu.edu
SQuInT Administrator
Gloria Cordova
gjcordo1@unm.edu
505 277-1850
SQuInT Founder
Ivan Deutsch, Regents' Professor
ideutsch@unm.edu