Particle abundance in a thermal plasma: Quantum kinetics versus Boltzmann equation
Particle abundance in a thermal plasma: Quantum kinetics versus Boltzmann equation
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热等离子体中的粒子丰度：量子动力学与玻尔兹曼方程
DOI：
10.1103/physrevd.71.023523
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发表时间：
2004
影响因子：
5
通讯作者：
C. Ho
中科院分区：
文献类型：
--
作者：
D. Boyanovsky;K. Davey;C. Ho
我们通过引入基于非平衡有效作用的量子动力学描述来研究热化等离子体中粒子种类的丰度。用朗之万方程对量子动力学进行随机解释就自然而然地出现了。我们考虑一种在真空中稳定的粒子种类，并与构成平衡热浴的较重粒子相互作用。渐近理论提出了完全重整化单粒子分布函数的定义。它的实时动态完全由非平衡有效作用决定，该作用提供了微扰膨胀的戴森式恢复。分布函数在时间尺度 $\ensuremath{\sim}1/2{\ensuremath{\Gamma}}_{k}(T)$ 上达到热平衡，其中 ${\ensuremath{\Gamma}}_{k}(T)$ 是准粒子弛豫率。平衡分布函数取决于全谱密度，因此存在涨落-耗散关系。这种依赖性导致壳外对粒子丰度的贡献。研究了玻色子场 $\ensuremath{\Phi}$ 与两个较重玻色子场 ${\ensuremath{\chi}}_{1,2}$ 相互作用的特定模型。最重粒子的衰变及其重组导致粒子 $\ensuremath{\Phi}$ 的谱函数宽度，并对丰度进行离壳修正。我们发现在高温和低温但高动量区域都与玻色-爱因斯坦结果有很大的偏差。后者的丰度呈指数级抑制，但大于玻色-爱因斯坦结果。我们得到了重正化微扰理论中的玻尔兹曼方程，并强调了差异的根源。讨论了宇宙学后果：我们认为，对候选冷暗物质丰度的修正在观测上可以忽略不计，并且重组消除了宇宙微波背景（CMB）任何可能的光谱畸变。然而，我们预计高温下的增强可能对重子发生很重要。
We study the abundance of a particle species in a thermalized plasma by introducing a quantum kinetic description based on the nonequilibrium effective action. A stochastic interpretation of quantum kinetics in terms of a Langevin equation emerges naturally. We consider a particle species that is stable in the vacuum and interacts with heavier particles that constitute a thermal bath in equilibrium. Asymptotic theory suggests a definition of a fully renormalized single particle distribution function. Its real time dynamics is completely determined by the nonequilibrium effective action which furnishes a Dyson-like resummation of the perturbative expansion. The distribution function reaches thermal equilibrium on a time scale $\ensuremath{\sim}1/2{\ensuremath{\Gamma}}_{k}(T)$ with ${\ensuremath{\Gamma}}_{k}(T)$ being the quasiparticle relaxation rate. The equilibrium distribution function depends on the full spectral density as a consequence the fluctuation-dissipation relation. Such dependence leads to off shell contributions to the particle abundance. A specific model of a bosonic field $\ensuremath{\Phi}$ in interaction with two heavier bosonic fields ${\ensuremath{\chi}}_{1,2}$ is studied. The decay of the heaviest particle and its recombination lead to a width of the spectral function for the particle $\ensuremath{\Phi}$ and to off shell corrections to the abundance. We find substantial departures from the Bose-Einstein result both in the high temperature and the low temperature but high momentum region. In the latter the abundance is exponentially suppressed but larger than the Bose-Einstein result. We obtain the Boltzmann equation in renormalized perturbation theory and highlight the origin of the differences. Cosmological consequences are discussed: we argue that the corrections to the abundance of cold dark matter candidates are observationally negligible and that recombination erases any possible spectral distortions of the cosmic microwave background (CMB). However we expect that the enhancement at high temperature may be important for baryogenesis.