1 research outputs found
Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
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 figure