Mason_Numerical Pechukas_35.pdf (642.74 kB)
Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
journal contribution
posted on 2018-04-13, 10:26 authored by Mumu Qureshi, Johnny Zhong, Zihad Qureshi, Peter Mason, Joseph BetourasJoseph Betouras, Alexandre ZagoskinAlexandre Zagoskin© 2018 American Physical Society. We consider the evolution of the quantum states of a Hamiltonian that is parametrically perturbed via a term proportional to the adiabatic parameter λ(t). Starting with the Pechukas-Yukawa mapping of the energy eigenvalue evolution in a generalized Calogero-Sutherland model of a one-dimensional classical gas, we consider the adiabatic approximation with two different expansions of the quantum state in powers of dλ/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 nonadiabatic evolution of the system. Applying the expansion to the exact cover 3-satisfiability problem, we obtain the occupation dynamics, which provides insight into the population of states and sources of decoherence in a quantum system.
Funding
This work was supported by EPSRC through Grant No. EP/M006581/1.
History
School
- Science
Department
- Physics
Published in
Physical Review AVolume
97Issue
3Citation
QUERESHI, M.A. ...et al., 2018. Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system. Physical Review A, 97: 032117.Publisher
© American Physical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2018Notes
This paper was accepted for publication in the journal Physical Review A and the definitive published version is available at https://doi.org/10.1103/PhysRevA.97.032117ISSN
2469-9926eISSN
2469-9934Publisher version
Language
- en