论文标题
Q粒子及其渐近学的光谱作用
Spectral actions for q-particles and their asymptotics
论文作者
论文摘要
对于由平均粒子数量和由一般免费$ Q $ - 粒子制成的开放系统（包括Bose，Fermi和经典的粒子，分别为$ Q = \ pm 1 $和$ 0 $）的频谱动作，我们在自然临界值中计算了渐近扩展。我们将同时相关的情况相对于无质量和非相对论的大粒子，其中自然截止值为$ 1/β= k _ {\ rm b} t $和$ 1/\sqrtβ$。我们表明，与大规模的情况相比，无数情况的规律性较小。我们还详细介绍了相对论的大规模案例，而自然截止值再次为$ 1/β$。然后，我们考虑了连续体的通过，描述了热平衡中的无限扩展的开放系统，还通过讨论了类似玻璃的$ q $ - 零件，$ q \ in（0,1] $的凝结现象的出现。然后，我们将有限体积的情况（剥离光谱）与相应的无限量表进行比较（我们比较了有限体积的结果（vistrum）的结果（连续）。
For spectral actions consisting of the average number of particles and arising from open systems made of general free $q$-particles (including Bose, Fermi and classical ones corresponding to $q=\pm 1$ and $0$, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and non relativistic massive particles, where the natural cut-off is $1/β=k_{\rm B}T$ and $1/\sqrtβ$, respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also treat in some detail the relativistic massive case for which the natural cut-off is again $1/β$. We then consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium, by also discussing the appearance of condensation phenomena occurring for Bose-like $q$-particles, $q\in(0,1]$. We then compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).
