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For an initial state $|\Psi\rangle_0$ as the ground state of a Hamiltonian $H(0)$, if it undergoes an adiabatic evolution $H(t)$ to reach the ground state $|\Psi\rangle_1$ of $H(1)$.
Then what's the evolution from the state $|\Psi\rangle_0$ and $|\Psi\rangle_1$?
Can the evolution be written in a form given by $H(t)$ something as $exp(-i\int H(t))dt$? If this is the case, then what's the difference between an adiabatic evolution and a non-adiabatic evolution?