Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-10-07
Physics
Condensed Matter
Disordered Systems and Neural Networks
20 pages and 6 figures (including supplementary notes)
Scientific paper
The vast majority of solids in Nature are strongly disordered or amorphous. Many of these materials show "universality" in their low-temperature elastic properties, despite enormous differences in their microscopic structure\cite{HR86,pohl02}. Discovered 40 years ago\cite{zellerP}, this universality has emerged as one of the outstanding unsolved mysteries in condensed matter physics\cite{AJL88}. Here we show that the mere presence of strong disorder and tunneling states symmetric under spatial inversion necessarily gives universality. Such tunneling states interact weakly with phonons, yet gap the non-symmetric tunneling states above a crossover energy. Thus neither glassiness nor any amorphous structure are required for universality, only strong disorder - a result concordant with recent experiments\cite{pohl02}.
Schechter Moshe
Stamp Philip C. E.
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