萨尔佩特方程与复杂的哈密尔顿式
Fernando Alonso-Marroquin1, Yaoyue Tang2, Fatemeh Gharari3
1King Fahd University of Petroleum and Minerals, CIPR, Dhahran, 31261, Kingdom of Saudi Arabia.
Physical review. E
|June 19, 2025
概括
这项研究引入了非自旋相对论量子粒子的新传播器,使波传播分析成为可能. 巴默传播器描述了相对论扩散,在考契和高斯过程之间插曲,以获得时间依赖的异常扩散.
科学领域:
- 量子力学就是量子力学.
- 相对论量子力学的量子力学.
- 随机过程是指随机的过程.
背景情况:
- 萨尔佩特哈密尔顿式描述了相对论量子粒子.
- 了解波的传播和扩散在量子力学中至关重要.
- 异常扩散在建模随机过程中提出了挑战.
研究的目的:
- 为了获得一个 (1+1) 维的Salpeter Hamiltonian的传播者的分析表达式.
- 描述非自旋相对论量子粒子的波传播.
- 为了制定和分析一个相对论的随机过程与时间依赖的异常扩散.
主要方法:
- 使用 Salpeter 汉密尔顿推广器的积分表示和分析解决方案.
- 在特殊函数方面导出格林函数.
- 在复杂平面中使用哈密尔顿式的分析延伸来制定Bäumer方程.
- 计算传播器,以便在考西和高斯扩散模式之间进行插值.
主要成果:
- 为传播器 (绿色函数) 导出了一个明确的表达式.
- 大质量和无质量粒子的波传播是通过将格林函数与初始波函数卷曲来确定的.
- 制订了Bäumer方程,描述了具有时间变化的异常扩散的相对论随机过程.
- 一个Bäumer传播器被分析计算,在Cauchy和高斯扩散之间进行插曲.
结论:
- 导出的绿色函数为分析量子粒子波传播提供了一个框架.
- 巴默传播器提供了一种新的方法来建模与时间依赖的异常扩散的相对论扩散.
- 这项工作建立了量子力学和随机过程与时间依赖的异常扩散之间的联系.
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