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It has been established that the low frequency quasi-localized modes ofamorphous solids at zero temperature exhibit universal density of states,depending on the frequencies as $D(\omega) \sim \omega^4$. It remains an openquestion whether this universal law extends to finite temperatures. In thisLetter we show that well quenched model glasses at temperatures as high as$T_g/3$ possess the same universal density of states. The only conditionrequired is that {\em average} particle positions stabilize before thermaldiffusion destroys the cage structure of the material. The universal density ofquasi-localized low frequency modes refers then to vibrations around thethermally averaged configuration of the material.

Universal Density of Low Frequency States in Amorphous Solids at Finite Temperatures