Coherent potential approximation for disordered bosons
Abstract
A family of random models for bosonic quasiparticle excitations, e.g. the vibrations of a disordered solid, is introduced. The generator of the linearized phase space dynamics of these models is the sum of a deterministic and a random part. The former may describe any model of N identical phonon bands, while the latter is a ddimensional generalization of the random matrix model of Lueck, Sommers, and Zirnbauer (LSZ). The models are constructed so as to exclude the unphysical occurrence of runaway solutions. By using the EfetovWegner supersymmetry method in combination with the new technique of superbosonization, the disordered boson model is cast in the form of a supermatrix field theory. A selfconsistent approximation of meanfield type arises from treating the field theory as a variational problem. The resulting scheme, referred to as a coherent potential approximation, becomes exact for large values of N. In the randommatrix limit, agreement with the results of LSZ is found. The selfconsistency equation for the full ddimensional problem is solved numerically.
 Publication:

arXiv eprints
 Pub Date:
 December 2010
 DOI:
 10.48550/arXiv.1012.5283
 arXiv:
 arXiv:1012.5283
 Bibcode:
 2010arXiv1012.5283S
 Keywords:

 Mathematical Physics
 EPrint:
 14 pages, 2 figures