TY - JOUR
T1 - A random matrix definition of the boson peak
AU - Manning, M. L.
AU - Liu, A. J.
N1 - Publisher Copyright:
Copyright © EPLA, 2015.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency ω∗. We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling ω∗ ∼ p-1/2. We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of ω∗ with coordination number that is observed near the jamming transition.
AB - The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency ω∗. We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling ω∗ ∼ p-1/2. We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of ω∗ with coordination number that is observed near the jamming transition.
UR - http://www.scopus.com/inward/record.url?scp=84923366911&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84923366911&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/109/36002
DO - 10.1209/0295-5075/109/36002
M3 - Article
AN - SCOPUS:84923366911
SN - 0295-5075
VL - 109
JO - EPL
JF - EPL
IS - 3
M1 - 36002
ER -