发表机构
Institute for Theoretical Physics, Heidelberg University; Institute for Theoretical Physics, University of Tübingen; Department of Physics, University of Konstanz; Institute of Physics, Johannes Gutenberg University Mainz（海德堡大学理论物理研究所; 蒂宾根大学理论物理研究所; 康斯坦茨大学物理系; 美因茨约翰内斯·古腾堡大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过大N次领头阶展开，计算无质量标量场远离平衡态的普适标度指数，发现相对论与非相对论理论属于不同普适类，为线性色散系统的新应用奠定基础。
AI 中文摘要
我们计算了远离平衡态的无质量标量场论的普适标度指数和标度函数。利用大$N$展开到次领头阶，我们研究了与能量或有效粒子数向低频$\omega$和动量$\bar p$输运相关的非微扰红外行为。对于无质量色散关系$\omega = \bar{p}$，我们确定了分布函数的标度形式，其普适幂律尾部$f_S(\bar p) \sim 1/\bar{p}^\kappa$在$d=3$维空间中分别满足a)$\kappa = d+1$和b)$\kappa = d$。我们的结果表明，在这种情况下，相对论性和非相对论性理论不属于同一普适类，这为高能物理和具有线性色散的（量子）多体物理中的远离平衡态现象开辟了新的应用。
英文摘要
We compute universal scaling exponents and scaling functions for massless scalar field theories far from equilibrium. Using a large-$N$ expansion to next-to-leading order, we investigate the nonperturbative infrared behaviour associated with the transport of a) energy or b) effective particle number towards low frequencies $ω$ and momenta $\bar p$. For massless dispersion $ω= \bar{p}$, we determine the scaling form of the distribution function whose universal power-law tail $f_S(\bar p) \sim 1/\bar{p}^κ$ is found to be a) $κ= d+1$ and b) $κ= d$ in $d=3$ spatial dimensions. Our results establish that relativistic and nonrelativistic theories do not belong to the same universality class in this case, which opens up new applications to far-from-equilibrium phenomena in high-energy and (quantum) many-body physics with linear dispersions.
Comments22 pages, 5 figures
