标题： 大型-N 相互作用矩阵模型的变分主场 - 自由随机变量的试验 显示英文标题

标题： Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial

摘要： 如果控制其动力学的作用仅约束它们的特征值，即依赖于单个矩阵幂次的迹，则矩阵被视为表现得像自由非交换随机变量。作者结合最近发展的数学技术与标准变分原理，提出了一个用于矩阵模型的新变分方法。使用自由随机矩阵作为变分空间，找到了相互作用的大-N矩阵模型的近似变分解。考虑了几类具有不同相互作用类型的经典和量子力学矩阵模型，并将变分解与精确的蒙特卡罗和解析结果进行比较。在大多数情况下发现了显著的一致性。 显示英文摘要

摘要： Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed mathematical techniques in combination with a standard variational principle to formulate a new variational approach for matrix models. Approximate variational solutions of interacting large-N matrix models are found using the free random matrices as the variational space. Several classes of classical and quantum mechanical matrix models with different types of interactions are considered and the variational solutions compared with exact Monte Carlo and analytical results. Impressive agreement is found in a majority of cases.