Schrödinger-Poisson–Vlasov-Poisson correspondence
Schrödinger-Poisson–Vlasov-Poisson correspondence
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DOI：
10.1103/physrevd.97.083519
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发表时间：
2018-01
影响因子：
5
通讯作者：
P. Mocz;Lachlan Lancaster;A. Fialkov;F. Becerra;Pierre-Henri Chavanis Princeton;Harvard;U. Sabatier;Toulouse
中科院分区：
文献类型：
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作者：
P. Mocz;Lachlan Lancaster;A. Fialkov;F. Becerra;Pierre-Henri Chavanis Princeton;Harvard;U. Sabatier;Toulouse
薛定谔-泊松方程描述了超流玻色-爱因斯坦凝聚体在自引力作用下的三维波函数行为。当λ/m→0，m为玻色子质量时，方程被假设为近似无碰撞的弗拉索夫-泊松方程，也称为无碰撞的玻尔兹曼-泊松方程。后者用6D经典分布函数描述无碰撞物质。我们调查的性质，这种对应关系的一套数值测试问题，在1D，2D和3D沿着与分析处理时，可能的。我们证明了，由于干涉和测不准原理，超流的密度场总是在π/m→0时出现单位阶振荡，而势场则在（π/m）2时收敛到经典解.因此，任何与超流势耦合的动力学都有望在λ/m→0时恢复到经典的无碰撞极限。量子超流体能够捕捉到丰富的现象，如多重相片，壳层交叉和温暖的分布。此外，量子压力张量在经典解中充当焦散线和奇点的正则化子。这表明了令人兴奋的前景使用薛定谔-泊松方程作为一个低记忆的方法来近似的高维演化的Vlasov-Poisson方程。作为一个特殊的例子，我们考虑由超轻轴子组成的暗物质，在经典极限（λ/m→0）下，它被认为是无碰撞的冷暗物质。
The Schrodinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As ℏ/m→0, m being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as ℏ/m→0 due to interference and the uncertainty principle, the potential field converges to the classical answer as (ℏ/m)2. Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as ℏ/m→0. The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schrodinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultralight axions, which in the classical limit (ℏ/m→0) is expected to manifest itself as collisionless cold dark matter.