Theoretical framework bridging classical and quantum mechanics for the dynamics of cryogenic liquid helium-4 using smoothed-particle hydrodynamics
Theoretical framework bridging classical and quantum mechanics for the dynamics of cryogenic liquid helium-4 using smoothed-particle hydrodynamics
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DOI：
10.1063/5.0122247
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发表时间：
2022-08
影响因子：
4.6
通讯作者：
Satori Tsuzuki
中科院分区：
文献类型：
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作者：
Satori Tsuzuki
我们最近的研究表明，基于光滑粒子流体动力学（SPH）的超流氦-4双流体模型的完全经典力学近似等价于在特定条件下求解多体量子力学方程。本研究进一步验证了这种等价性的存在。首先，我们推导了双流体模型中超流分量运动方程的SPH形式，即，由Gibbs-Duhem方程得到的化学势梯度驱动的运动方程。然后我们基于Gross-Pitaevskii理论推导了凝聚体运动方程的SPH形式，即，由相互作用玻色子的薛定谔方程得到的化学势梯度驱动的运动方程。在此之后，我们比较了两个离散方程。因此，我们发现，当量子压力可以忽略时，保持每个流体粒子的零内能的条件确保了方程的等价性。此外，即使当量子压力不可忽略时，如果量子压力梯度力等于相互摩擦力，它们的等价性也成立。零内能表示热力学基态，其包括基本激发态。因此，当流体粒子的速度不超过朗道临界速度时，就可以充分满足该条件，这对于在实验室系统中使用几个[公式：见正文]的特征速度进行模拟来说，并不是严格的条件。基于上述，我们对旋转的液氦-4进行了模拟，并成功地生成了具有量子化环流的涡旋晶格，称为量子晶格。
Our recent study suggested that a fully classical mechanical approximation of the two-fluid model of superfluid helium-4 based on smoothed-particle hydrodynamics (SPH) is equivalent to solving a many-body quantum mechanical equation under specific conditions. This study further verifies the existence of this equivalence. First, we derived the SPH form of the motion equation for the superfluid component of the two-fluid model, i.e., the motion equation driven by the chemical potential gradient obtained using the Gibbs–Duhem equation. We then derived the SPH form of the motion equation for condensates based on the Gross–Pitaevskii theory, i.e., the motion equation driven by the chemical potential gradient obtained from the Schrödinger equation of interacting bosons. Following this, we compared the two discretized equations. Consequently, we discovered that a condition maintaining zero internal energy for each fluid particle ensures the equivalence of the equations when the quantum pressure is negligible. Moreover, their equivalence holds even when the quantum pressure is non-negligible if the quantum pressure gradient force equals the mutual friction force. A zero internal energy indicates the thermodynamic ground state, which includes an elementary excitation state. Therefore, the condition can be sufficiently satisfied when the velocities of fluid particles do not exceed the Landau critical velocity, which is not a stringent condition for simulations with a characteristic velocity of a few [Formula: see text] in a laboratory system. Based on the above, we performed a simulation of rotating liquid helium-4 and succeeded in generating a vortex lattice with quantized circulation, known as a quantum lattice.