论文标题
大规范合奏，Boltzmann，Fermi-Dirac和Bose-Einstein分布之间的关系：玻色子的量子原理和Bosonic真空状态，这是黑暗能量和暗物质的候选者
Relation between grand canonical ensemble, Boltzmann, Fermi-Dirac, and Bose-Einstein distribution: Quantum principle for bosons and bosonic vacuum state, a candidate for dark energy and dark matter
论文作者
论文摘要
我们获得构成两个能级之间的热平衡的条件：（i）在两个水平上总能量相等； （ii）所有颗粒的温度相等。利用这些条件，我们得出了适用于所有颗粒的热平衡的微分方程。集成提供了Boltzmann分布，这表明它是热平衡的一般分布。 Pauli的排除原则分别为N2和N1的兴奋状态和地下种群数字N1 = 1-N2。利用爱因斯坦对普兰克的黑体辐射定律的速率方程方法，我们得出了玻色子的等效量子原理，n1 = 1+n2。在整合热平衡的微分方程或通过将其输入玻尔兹曼分布时，利用两种量子原理，作为边界条件，提供Fermi-Dirac或Bose-Einstein分布。费米子或骨值比N2/N1遵循Boltzmann分布。这些结果表明，费米 - 迪拉克（Fermi-Dirac）和玻色网（Bose-Einstein）分布是鲍尔兹曼（Boltzmann）分布的特殊情况，由保利的排除原理或玻色子的量子原理统治。大规范的合奏等于玻尔兹曼的分布。费米斯/玻色子的相关原理和抑制/增强因子证实了量子原理。玻色子的量子原理包括真空状态。因此，所有玻色子都应存在人口稠密的真空状态。真空状态无法检测到，因此它们是黑色状态。所有玻色子的真空状态都导致了暗能量，而只有玻色子真空状态有助于暗物质，这支持了这样一个事实，即暗能量超过了宇宙中暗物质的数量。
We obtain the conditions constituting a thermal equilibrium between two energy levels: (i) the total energy is equal in both levels; (ii) the temperature is equal for all particles. Exploiting these conditions, we derive a differential equation of thermal equilibrium that holds for all particles. Integration delivers the Boltzmann distribution, suggesting that it is the general distribution of thermal equilibrium. With excited-state and ground-state population numbers n2 and n1, respectively, Pauli's exclusion principle is formalized as n1=1-n2. Exploiting Einstein's rate-equation approach to Planck's law of blackbody radiation, we derive the equivalent quantum principle for bosons, n1=1+n2. Utilizing either quantum principle, as a boundary condition when integrating the differential equation of thermal equilibrium or by entering it into the Boltzmann distribution, delivers the Fermi-Dirac or Bose-Einstein distribution. The fermionic or bosonic ratios n2/n1 follow the Boltzmann distribution. These results suggest that the Fermi-Dirac and Bose-Einstein distributions are special cases of the Boltzmann distribution, ruled by Pauli's exclusion principle or the quantum principle for bosons. The grand canonical ensemble equals the Boltzmann distribution. The relating principle and the inhibition/enhancement factors for fermions/bosons confirm the quantum principles. The quantum principle for bosons comprises a vacuum state. Consequently, a populated vacuum state should exist for all bosons. Vacuum states are not detectable, therefore, they are dark states. The vacuum states of all bosons contribute to dark energy, while only the matter-boson vacuum states contribute to dark matter, supporting the fact that the amount of dark energy exceeds that of dark matter in the universe.
