Cooperative Phenomena in Condensed Matter Systems

几个关于自旋玻璃问题的基本未解决的问题，如有序相的性质和可重入行为，将被研究。对这些问题的更快的模拟算法的研究将进行。神经网络的学习和计算行为将从统计力学的角度进行分析，并研究产生更好的网络的算法。为了理解最近发现的高温超导体的机制，将对超导的其他模型进行数值模拟。多重分形中的相关指数将用于测量表征此类系统的维度频谱，并将研究有关缩放维度中包含的信息量的问题。系统的统计性质涉及环形聚合物将分析使用新的和有效的算法为他们的产生。脉冲场电泳技术是一项在生物工程中具有重要意义的新技术。关于混沌在量子力学中的作用的基本问题，这些问题是由最近在强磁场中对氢原子进行的实验所激发的。硬球（如洛伦兹气体）的量子力学将在高维中进行研究，以探索吉布斯分布在封闭量子系统中的有效性，并提供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.