Optimal fluctuations and tail states of non-Hermitian operators

We develop a general variational approach to study the statistical properti es of the tail states of a wide class of non-Hermitian operators. The utili ty of the method, which is a refinement of the instanton approach introduce d by Zittartz and Langer [Phys. Rev. 148, 741 (1966)], is illustrated in de tail by reference to the problem of a quantum particle propagating in an im aginary scalar potential.