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arXiv 1905.13670hep-phastro-ph.HEastro-ph.SR
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扩展中微子产生区对超新星集体振荡的影响

Effect of extended neutrino production region on collective oscillations in supernovae

Rasmus S. L. Hansen, Alexei Yu. Smirnov

摘要:

在超新星中,中微子是从宽度为$r_{\rm eff}$几公里的区域(而不是从无限小宽度的表面)发射出来的。我们研究了在这样一个扩展的发射区域上的集成(平均)对集体振荡的影响。平均导致通过因子$ \sim 1/r_{\rm eff} V_e \sim 10^{-10}$对相关性(密度矩阵的非对角元素)的附加抑制,其中$V_e$是物质势。这个因素进入进一步集体振荡的初始条件,因此,导致延迟的强烈的味道过渡。我们证明和量化这幅图片使用一个简单的例子,在两个相交的通量的集体效应。我们导出了在发射区积分的密度矩阵元的演化方程,并用数值和解析方法求解。对于解析解,我们使用了线性化方程。我们表明,延迟的发展的不稳定性和集体振荡依赖于抑制因子,由于平均(积分)的grammically。如果不稳定性发展的生产区域内,集成不仅会导致延迟,而且会修改的指数增长。

英文摘要:

In supernovae neutrinos are emitted from a region with a width $r_{\rm eff}$ of a few kilometers (rather than from a surface of infinitesimal width). We study the effect of integration (averaging) over such an extended emission region on collective oscillations. The averaging leads to additional suppression of the correlation (off-diagonal element of the density matrix) by a factor $ \sim 1/r_{\rm eff} V_e \sim 10^{-10}$, where $V_e$ is the matter potential. This factor enters the initial condition for further collective oscillations and, consequently, leads to a delay of the strong flavour transitions. We justify and quantify this picture using a simple example of collective effects in two intersecting fluxes. We have derived the evolution equation for the density matrix elements integrated over the emission region and solved it both numerically and analytically. For the analytic solution we have used linearized equations. We show that the delay of the development of the instability and the collective oscillations depends on the suppression factor due to the averaging (integration) logarithmically. If the instability develops inside the production region, the integration leads not only to a delay but also to a modification of the exponential grow.

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