Improved Calculation of Vibrational Mode Lifetimes in Anharmonic Solids - Part I: Theory

We propose here a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. From this we derive the lifetime of a vibrational mode in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. These insights should lead to significantly shorter calculations compared to current methods. A companion piece presents numerical results.Comment: 18 pages, 3 figure

Augmented space recursion for partially disordered systems

Off-stoichiometric alloys exhibit partial disorder, in the sense that only some of the sublattices of the stoichiometric ordered alloy become disordered. This paper puts forward a generalization of the augmented space recursion (ASR) (introduced earlier by one of us (Mookerjee et al 1997(*))) for systems with many atoms per unit cell. In order to justify the convergence properties of ASR we have studied the convergence of various moments of local density of states and other physical quantities like Fermi energy and band energy. We have also looked at the convergence of the magnetic moment of Ni, which is very sensitive to numerical approximations towards the k-space value 0.6 $\mu_{B}$ with the number of recursion steps prior to termination.Comment: Latex 2e, 21 Pages, 13 Figures, iopb style file attache

Phase Diagram for Anderson Disorder: beyond Single-Parameter Scaling

The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams in all physical dimensions, a plethora of additional, weaker Anderson transitions are found, characterized by the long-distance behavior of states. Critical disorders are found for Anderson transitions at which the asymptotically dominant sector of augmented space changes for all states at the same disorder. At fixed disorder, critical energies are also found at which the localization properties of states are singular. Under the approximation of single-parameter scaling, this phase diagram reduces to the widely-accepted one in 1, 2 and 3 dimensions. In two dimensions, in addition to the Anderson transition at infinitesimal disorder, there is a transition between two localized states, characterized by a change in the nature of wave function decay.Comment: 51 pages including 4 figures, revised 30 November 200