Pressure dependence of the boson peak for repulsive homogeneous potentials

Isotropic potentials used for studying glasses computationally are often positive homogeneous functions of the coordinates of the constituent particles or they reduce effectively to such forms at higher pressures. For such cases we show that the position and the intensity of the Boson peak, when it exists, scales asymptotically with pressure (P) as P-delta and P-3 delta, respectively, where delta = (2 + m)/[2(S + m)], (-m) is the degree of homogeneity, and S is the spatial dimension. In the same limit the shape of the entire vibrational spectrum saturates and the Boson peak frequency, the Debye frequency, and the average frequency become proportional to each other. Our numerical studies on single-component hyperquenched Lennard-Jones glass in three dimensions support the predicted scaling laws and are largely consistent with the predictions of one existing theory [W. Schirmacher et al., Phys. Rev. Lett. 98, 025501 (2007)] for the normalized boson peak intensity. However, the scaling exponent for the variation of the boson peak location and intensity with applied pressure is substantially different in this case from that found from laboratory experiments.