In an insulator, thermal transport at high temperature is expected to be dominated by entirely classical phonon dynamics. In apparent tension with this expectation, recent experimental observations have led to the conjecture that the transport lifetime, τ, is subject to a Planckian bound from below, namely, τ ≳ τ_Pl ≡ ℏ ∕ (k_BT). Here, we argue that this Planckian bound is due to a quantum-mechanical bound on the sound velocity: v_s < v_M. The ‘melting velocity’ v_M is defined in terms of the melting temperature of the crystal, the interatomic spacing and Planck’s constant. We show that for several classes of insulating crystals, both simple and complex, τ ∕ τ_Pl ≈ v_M ∕ v_s at high temperatures. The velocity bound therefore implies the Planckian bound.

在绝缘体中，高温下的热传输预计将完全由经典的声子动力学主导。与这种预期明显矛盾的是，最近的实验观察导致了这样一种猜想，即传输寿命τ受制于下面的普朗克界限，即τ ≳ τ _Pl ≡ ℏ ∕ ( k _B T )。在这里，我们认为这个普朗克界是由于声速上的量子力学界：v _s < v _M。'熔化速度' v _M是根据晶体的熔化温度、原子间距和普朗克常数定义的。我们表明，对于几类绝缘晶体，无论是简单的还是复杂的，τ ∕ τ _Pl ≈ v _M ∕ v _s在高温下。因此，速度界意味着普朗克界。