树张量网络状态方法用于解决运动的等级方程
1Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany.
The Journal of chemical physics
|June 1, 2023
概括
分层运动方程 (HEOM) 方法是一种量子动力学方法,使用树张量网络状态 (TTNS) 进行增强. 这种HEOM+TTNS方法加速了计算,同时保持了开放量子系统的准确性.
科学领域:
- 量子力学就是量子力学.
- 计算物理学的计算物理.
- 开放的量子系统是开放的.
背景情况:
- 层次运动方程 (HEOM) 是模拟开放量子系统的数值精确方法.
- HEOM依赖于浴室相关函数的指数式扩展,将环境映射成有效的浴室模式.
- 这允许在有限的温度下进行高效的计算,通过将系统转换为与非赫米特超级哈密尔顿式的施罗丁格式方程.
研究的目的:
- 使用树张量网络状态 (TTNS) 探索HEOM扩展波函数的表示.
- 开发和应用基于HEOM+TTNS方法的时间依赖变量原理的时间传播算法.
- 与传统的HEOM相比,评估拟议方法的计算效率和准确性.
主要方法:
- 在HEOM框架内,分别表示扩展波函数和超哈密尔顿函数作为树张量网络状态 (TTNS) 和运算符.
- 实现一个时间传播算法,利用时间依赖的变量原理.
- 使用自旋玻色子模型与缓慢放松的浴进行基准计算.
主要成果:
- 采用HEOM+TTNS方法的结果与传统的HEOM方法一致.
- 拟议的方法显著加速了开放量子系统动态的计算.
- 使用TTNS的模拟表明,与一维矩阵产品状态分解方案相比,速度提升了四倍.
结论:
- 树张量网络状态的集成为运动方法的等级方程提供了一个计算效率高,准确的替代方案.
- HEOM+TTNS方法为推进复杂开放量子系统的模拟提供了一个有希望的方向.
- 这项工作突出了张量子网络方法在加速量子力学计算中的潜力.
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