Instanton calculation of the density of states of disordered Peierls chains

We use the optimal fluctuation method to find the density of electron state s inside the pseudogap in disordered Peierls chains. The electrons are desc ribed by the one-dimensional Dirac Hamiltonian with randomly varying mass ( the Fluctuating Gap Model). We establish a relation between the disorder av erage in this model and the quantum-mechanical average for a certain double -well problem. We show that the optimal disorder fluctuation, which has the form of a soliton-antisoliton pair, corresponds to the instanton trajector y in the double-well problem. We use the instanton method developed for the double-well problem to find the contribution to the density of states from disorder realizations close to the optimal fluctuation.