标题： 安德森在随机度量中的局域化：对宇宙学的应用 显示英文标题

标题： Anderson's localization in a random metric: applications to cosmology

摘要： 被认为是随机度量中标量传播波场的李雅普诺夫指数$% \gamma $的方程。 在频率的一阶近似下，该方程被显式求解。 局域化长度$L_{c}$（Re($\gamma $) 的倒数）作为度量波动距离$\Delta R$（无序的函数）和波的频率$\omega $的函数获得。 具体来说，低频比高频传播得更远，即$L_{c}\omega ^{2}=C^{te}$。 直接应用宇宙学量，如背景微波辐射（$\lambda \sim 1/2\times 10^{-3}$[m]）和宇宙长度（“局域化长度”$L_{c}\sim 1.6\times 10^{25}$[m]），可以计算度规涨落距离为$\Delta R\sim 10^{-35}$[m]，这个数值在普朗克长度的数量级上。 显示英文摘要

摘要： It is considered an equation for the Lyapunov exponent $% \gamma $ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of Re($\gamma $)) is obtained as function of the metric-fluctuation-distance $\Delta R$ (function of disorder) and the frequency $\omega $ of the wave. Explicitly, low-frequencies propagate longer than high, that is $L_{c}\omega ^{2}=C^{te}$. Direct applications with cosmological quantities like background radiation microwave ($\lambda \sim 1/2\times 10^{-3}$ [m]) and the Universe-length (`localization length' $L_{c}\sim 1.6\times 10^{25}$ [m]) permits to evaluate the metric-fluctuations-distance as $\Delta R\sim 10^{-35}$ [m], a number at order of the Planck's length.