声在一维量子液体中的传播与衰减
Propagation and attenuation of sound in one-dimensional quantum liquids
摘要：
在低温下，一维量子液体的元激发形成气体，该气体可以相对于系统的质心整体移动。这种内部运动在指数级的长时间尺度上衰减。因此，在很宽的频率范围内，液体由双流体流体动力学描述，并且系统支持两种声音模式。这两种声音的物理性质取决于形成量子液体的粒子是否具有自旋自由度。对于具有自旋的粒子，这些模式类似于超流体$^4$ He中的第一和第二声音模式，它们分别是密度波和熵波。当考虑耗散过程时，我们发现，在低频率下，第二种声音被转化为热扩散，而第一种声音模式保持弱阻尼，成为普通的声音。在无自旋液体中，熵和密度振荡强烈耦合，并且所产生的声音模式是第一和第二声音的混合。随着频率降低和耗散过程变得重要，到单流体状态的交叉分两步发生。首先，混合模式转变为主要的密度波和熵波，类似于第一和第二声音，然后密度波转变为普通声音，熵波变成热扩散模式。最后，我们考虑了由于粘性和固有的热传导性的气体的激发，控制在高频率的声音模式的衰减的耗散。
英文摘要：
At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid $^4$He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid the entropy and density oscillations are strongly coupled, and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.
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