Within condensed matter physics, wave propagation and localization in disordered media form the foundation for understanding thermal and electrical transport in amorphous solids. When solid aerogel backbones exhibit disordered amorphous networks characterized by random fluctuations in bond lengths and spatial densities, extended lattice vibrational waves (phonons)—which propagate freely in ideal crystals—encounter local potential field disturbances. Analyzing local thermal distortion and phonon localization Anderson transition dynamics in disordered amorphous frameworks reveals the micro-origin of ultralow thermal conductivity from a quantum statistical physics perspective.

Within thermally excited disordered amorphous aerogel networks, local thermal distortions induce spatial fluctuations in local elastic constants. When high-frequency thermal phonon wavelengths approach spatial correlation lengths of disorder, phonon wavepackets undergo coherent backscattering. This interference effect halts phonon wavepacket propagation, trapping energy within localized spatial domains—a physical process known as phonon Anderson localization.

As phonon frequencies increase or structural disorder rises, the system undergoes an Anderson phase transition from extended phonon states to localized phonon states. Within localized regimes, thermal energy cannot propagate via long-range lattice waves, relying on anharmonic hopping between local vibrations. This phonon localization deprives the disordered skeleton of long-range thermal transport capabilities, explaining its ultralow thermal conductivity.