 Quantum quench

A quantum quench changes a quantum system's control parameters rapidly and studies the subsequent unitary time evolution. In the ideal sudden limit, write an initial energy eigenstate $|m_i⟩$ using a complete final orthonormal eigenbasis:The Born rule probabilities for a nondegenerate final energy measurement are $|c_n{|}^2$, with ${\sum }_n|c_n{|}^2=1$. For a degenerate energy eigenvalue, sum the probabilities over its orthonormal energy eigenstates. Subsequent relative quantum phases can alter other measurement probabilities even though these final energy populations stay fixed. A quench need not begin in an energy eigenstate; the same expansion applies to any initial pure state.