Smash线代数上的随机游动与扩散
Random Walk and Diffusion on a Smash Line Algebra
摘要：
在Hopf代数的框架下，构造了一个由实线代数和任意线代数合并而成的空间上的随机游动和相应的扩散方程.从技术上讲，这种合并结构是一个smash代数，即一个由实数与任意线代数的辫子张量产生的代数。引入粉碎的动机是由于随机游动中必须有非交换增量。基于观测状态的基本Hopf结构所提供的对偶性，该结构被转换成两种对偶形式：一种使用密度概率函数确定的泛函，另一种使用相关的马尔可夫转移算子。随后的扩散方程具有三角矩阵实现。研究是通过在上述随机行走模型中引入Hamilton动力学，并通过构造一般纠缠密度函数问题的统计矩所服从的动力学方程来完成的。
英文摘要：
Working withing the framework of Hopf algebras, a random walk and the associated diffusion equation are constructed on a space that is algebraically described as the merging of the real line algebra with the anyonic line algebra. Technically this merged structure is a smash algebra, namely an algebra resulting by a braided tensoring of real with anyonic line algebras. The motivation of introducing the smashing results from the necessity of having non commuting increments in the random walk. Based on the observable-state duality provided by the underlying Hopf structure, the construction is cast into two dual forms: one using functionals determined by density probability functions and the other using the associated Markov transition operator. The ensuing diffusion equation is shown to possess triangular matrix realization. The study is completed by the incorporation of Hamiltonian dynamics in the above random walk model, and by the construction of the dynamical equation obeyed by statistical moments of the problem for generic entangled density functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
