Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
| Autor: | Qureshi, Mumnuna A, Zhong, Johnny, Qureshi, Zihad, Mason, Peter, Betouras, Joseph J, Zagoskin, Alexandre M |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 97, 032117 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.97.032117 |
| Popis: | 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. Comment: 12 pages, 6 figures |
| Databáze: | arXiv |
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