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arXiv · 1706.05243

Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system

Mumnuna A Qureshi·Johnny Zhong·Zihad Qureshi·Peter Mason·Joseph J Betouras·Alexandre M Zagoskin
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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.

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Mumnuna A Qureshi, Johnny Zhong, Zihad Qureshi, Peter Mason, Joseph J Betouras, Alexandre M Zagoskin. 2017-06-16. Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system. https://doi.org/10.1103/physreva.97.032117

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