Cooperative Phenomena in Condensed Matter Systems

关于自旋玻璃问题的几个基本悬而未决的问题，如有序相的性质和重入行为，将被研究。将对这些问题进行更快的模拟算法的研究。将从统计力学的角度分析神经网络用于学习和计算的行为，并将研究产生更好网络的算法。将对不同的超导模型进行数值模拟，目的是了解最近发现的高温超导体的机制。多重分形学中的关联指数将被用来测量表征这种系统的维度的频谱，并将调查有关标度维度中包含的信息量的问题。我们将使用一种新的高效算法来分析涉及环聚合物的体系的统计特性。DNA分子动力学的研究将在脉冲场电泳法的背景下进行，这是一项在生物工程中具有重要意义的新技术。有关混沌在量子力学中的作用的基本问题，将被最近在强磁场中对氢原子的实验所激发。我们将高维研究坚硬球体的量子力学，如洛伦兹气体，以探索封闭量子系统中吉布斯分布的有效性，并提供一种涉及有限个自由度的能量耗散的替代模型。

Several basic unsolved questions concerning the spin glass problem, such as the nature of the ordered phase and reentrant behavior, will be investigated. Studies of faster simulation algorithms for these problems will be undertaken. The behavior of neural networks for learning and computation will be analyzed from a statistical mechanics perspective, and algorithms for producing better networks will be investigated. Numerical simulations of alternative models of superconductivity will be undertaken with the goal of understanding the mechanism responsible for the recently discovered high temperature superconductors. Correlation exponents in multifractals will be used to measure the spectrum of dimensions that characterize such systems, and questions concerning the amount of information contained in the scaling dimensions will be investigated. The statistical properties of systems involving ring polymers will be analyzed using a new and efficient algorithm for their generation. The dynamics of DNA molecules will be studied in the context of pulsed field electrophoresis, which is a new technique of great importance in bioengineering. Fundamental questions regarding the role of chaos in quantum mechanics that have been stimulated by recent experiments on hydrogen atoms in strong magnetic fields will be examined. The quantum mechanics of hard spheres, such as a Lorentz gas, will be studied in high dimension, to explore the validity of the Gibbs distribution in closed quantum systems, and to provide an alternative model of energy dissipation involving a finite number of degrees of freedom.