Local theory of disordered systems

Abstract

Th e mos t s trikin g c ha rac te ri s ti c of c rysta llin e so lid s is th e ir pe ri odi city. As a res ult of thi s fe ature, theore ti ca l desc ri pti o ns of ph ysica l phe nome na in s uc h syste ms a re us ua ll y give n in wave num ber or mom.entum s pace. The rec iproca l la tti ce of a c rystal a nd th e Fe rmi s urface of a meta l a re exa mples. In a di so rde re d sys te m , on th e oth e r han d , the re is no s uc h pe ri odi cit y a nd mome ntum space desc ri pti ons a re mu c h less na tural. Howe ve r, in s uc h sys te ms, phys ica l co nd iti ons nea r a point r , in coo rdinate s pace, beco me ind e pen de nt of th e co nditi ons a t a di sta nt po int ,. ', provi de d th at I r ' -d is :a rge compa re d to e ith e r a c ha rac te ri st ic mea n free path or so me othe r app rop ri ate le ngt h. This s ugges ts th at one can a na lyze a mac roscop ic di so rd e re d sys te m by averaging ove r th e pro pe rti es of mi c ros copic ne ighbo rhoods.