We consider two Hamiltonians that are close to each other, H 1 ≈ H 2 , and analyze the time decay of the corresponding Loschmidt echo M ( t ) : = | ⟨ ψ 0 , e i t H 2 e - i t H 1 ψ 0 ⟩ | 2 that expresses the effect of an ... ...