von Ferber C, Holovatch Y
School of Physics and Astronomy, Tel Aviv University, IL-69978 Tel Aviv, Israel.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jun;59(6):6914-23. doi: 10.1103/physreve.59.6914.
We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi(4)-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties that are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorption at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.
我们刻画了在吸收性星形聚合物附近布朗运动的多重分形行为。我们将该问题映射到一个(O(M))对称的(\phi(4))场论，该理论将布朗运动拉普拉斯场的高阶矩与相应的复合算符联系起来。这些算符的标度维数所得到的谱展示出了多重分形标度必然会出现的凸性性质，但在场论中对于场算符的幂次来说却是不寻常的。使用场论重整化群方法，我们得到了聚合物星核处吸收的多重分形谱作为一个渐近级数。我们使用重求和技术来评估这些级数。
