随机湍流中微扰重整化群存在阻碍的证据
Evidence for an Obstruction to Perturbative Renormalization Group in Stochastic Turbulence
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中文总结 AI 辅助
该研究通过五圈计算发现，随机湍流微扰重整化群在从ε=0外推到物理值ε=2时，不动点失去实数和红外稳定性，表明存在阻碍而非可控外推。
中文摘要 AI 辅助
我们检验了随机湍流的微扰重整化群（RG）区域能否从小参数 $\varepsilon$ 延续到对应大尺度强迫的物理值 $\varepsilon_{\mathrm{phys}}=2$。利用大 $d$ 极限下的简化，我们将修正指数 $\omega$ 计算到五圈阶，并发现一个暗示闭合解析形式的简单结构。该形式意味着在 $\varepsilon=0$ 附近稳定的不动点在到达 $\varepsilon_{\mathrm{phys}}=2$ 之前不再同时是实数和红外稳定的，这表明红外区域可能发生变化，而非受控的微扰 RG 外推。
英文摘要
We examine whether the perturbative renormalization group (RG) regime of stochastic turbulence can be continued from small $\varepsilon$ to the physical value $\varepsilon_{\mathrm{phys}}=2$, corresponding to large-scale forcing. Exploiting the simplifications of the large-$d$ limit, we calculate the correction exponent $ω$ to five-loop order and find a simple structure suggesting a closed analytic form. This form implies that the fixed point stable near $\varepsilon=0$ ceases to be simultaneously real and infrared stable before reaching $\varepsilon_{\mathrm{phys}}=2$, pointing to a possible change of infrared regime rather than a controlled perturbative RG extrapolation.
发表机构
- Saint Petersburg State University（圣彼得堡国立大学）
- Joint Institute for Nuclear Research（杜布纳联合核研究所）
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