Level dynamics approach to the large deviation statistical characteristic function

We propose a level dynamics approach to the large deviation statistical characteristic function phi(q) for temporal series of dynamical variable V, which is the largest eigenvalue of the generalized evolution operator H{q}(identical with H+qV). This is done first by deriving "equations of motion" for the eigenvalues and the eigenstates of H{q} with the initial conditions determined by those of H , the true evolution operator for the dynamical variable under consideration, and then by solving these equations. Furthermore, utilizing simple solvable models, it is shown that the eigenvalues and eigenstates satisfy the equations of motion derived in this paper.