论文标题
一种新颖的物质状态：$ d = 4-ε$扩展研究马尔萨斯羊群
A novel nonequilibrium state of matter: a $d=4-ε$ expansion study of Malthusian flocks
论文作者
论文摘要
我们表明，“马尔萨斯羊群”（即，在动作过程中都“出生”和“垂死”的自propelled实体（例如生物）的一致移动的集合属于空间维度$ d> 2 $。 We calculate the universal exponents and scaling laws of this new universality class to $O(ε)$ in a $d=4-ε$ expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2 < d \leq 4$.我们还获得了一个通用振幅比率，该比率与这些系统中横向和纵向速度和密度波动的阻尼有关。此外，我们在两个区域之间发现了一个均等（$ {\ bf r} $）空间中的通用分离质，其中相等的时间密度相关性$ \langleΔρ（{\ bf r}，t）Δρ（0，t）\ rangle $具有相反的符号。我们的扩展应在$ d = 3 $中非常准确，可以在我们的理论，模拟和实验之间进行精确的定量比较。
We show that "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O(ε)$ in a $d=4-ε$ expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2 < d \leq 4$. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real (${\bf r}$) space between two regions in which the equal time density correlation $\langleδρ({\bf r}, t)δρ(0, t)\rangle$ has opposite signs. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.
