Andreev-Lifshitz流体力学在压力作用下的应用
Andreev-Lifshitz Hydrodynamics Applied to an Ordinary Solid under Pressure
摘要：
我们已经把安德烈耶夫-李夫希茨超固体流体力学理论应用于普通固体。该理论包括内部压力$P$，其不同于所施加的压力$P_a$和应力张量$λ_{ik}$。在统一静态$P_{a}$下，我们有$λ_{ik} = (P-P_{a})δ_{ik}$。对于$P_{a} \ne 0$，麦克斯韦关系意味着$P \sim P_{a}^{2}$。该理论也允许空位扩散，但将空位视为守恒的。它给出了三组传播的弹性模式;它还给出了两个扩散模式，一个主要是熵密度，一个主要是空位密度（或者更一般地说，缺陷密度）。对于空位扩散模式（或等效地，晶格扩散模式），空位表现得像固体内的流体，其中与密度变化相关联的内部压力的偏差几乎抵消与应变相关联的应力的偏差。我们简要地考虑在固体$^4$ He在低温下的加压实验中，根据这种晶格扩散模式，其中小$P_{a}$的扩散常数$D_{L} \sim P_{a}^{2}$。该理论的一般原理--体积和应变都应该作为热力学变量包括在内，其结果是$P$和$λ_{ik}$都出现了--应该适用于所有受压固体，特别是接近固-液转变的固体。晶格扩散模式提供了额外的自由度，其可以允许具有不同表面处理的表面在本体中产生不同的响应。
英文摘要：
We have applied the Andreev-Lifshitz hydrodynamic theory of supersolids to an ordinary solid. This theory includes an internal pressure $P$, distinct from the applied pressure $P_a$ and the stress tensor $λ_{ik}$. Under uniform static $P_{a}$, we have $λ_{ik} = (P-P_{a})δ_{ik}$. For $P_{a} \ne 0$, Maxwell relations imply that $P \sim P_{a}^{2}$. The theory also permits vacancy diffusion but treats vacancies as conserved. It gives three sets of propagating elastic modes; it also gives two diffusive modes, one largely of entropy density and one largely of vacancy density (or, more generally, defect density). For the vacancy diffusion mode (or, equivalently, the lattice diffusion mode) the vacancies behave like a fluid within the solid, with the deviations of internal pressure associated with density changes nearly canceling the deviations of stress associated with strain. We briefly consider pressurization experiments in solid $^4$He at low temperatures in light of this lattice diffusion mode, which for small $P_{a}$ has diffusion constant $D_{L} \sim P_{a}^{2}$. The general principles of the theory -- that both volume and strain should be included as thermodynamic variables, with the result that both $P$ and $λ_{ik}$ appear -- should apply to all solids under pressure, especially near the solid-liquid transition. The lattice diffusion mode provides an additional degree of freedom that may permit surfaces with different surface treatments to generate different responses in the bulk.
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