Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
Abstract
We consider the evolution of a quantum state of a Hamiltonian which is parametrically perturbed via a term proportional to the adiabatic parameter \lambda (t). Starting with the Pechukas-Yukawa mapping of the energy eigenvalues evolution on a generalised Calogero-Sutherland model of 1D classical gas, we consider the adiabatic approximation with two different expansions of the quantum state in powers of d\lambda/dt and compare them with a direct numerical simulation. We show that one of these expansions (Magnus series) is especially convenient for the description of non-adiabatic evolution of the system. Applying the expansion to the exact cover 3-satisfability problem, we obtain the occupation dynamics which provides insight on the population of states.
Keywords
Cite
@article{arxiv.1706.05243,
title = {Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system},
author = {Mumnuna A Qureshi and Johnny Zhong and Zihad Qureshi and Peter Mason and Joseph J Betouras and Alexandre M Zagoskin},
journal= {arXiv preprint arXiv:1706.05243},
year = {2018}
}
Comments
12 pages, 6 figures