A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929350498058240 |
|---|---|
| author | Cheng, Xiangsong He, Xin Liu, Jian |
| author_facet | Cheng, Xiangsong He, Xin Liu, Jian |
| contents | Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys. 2016, 145, 204105; 2019, 151, 024105 and J. Phys. Chem. Lett. 2021, 12, 2496-2501, non-covariant phase space functions, time-dependent weight functions, and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system. The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation. The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite. We also prove that the triangle window function approach, albeit proposed as a heuristic empirical model in J. Chem. Phys. 2016, 145, 144108, is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions Cheng, Xiangsong He, Xin Liu, Jian Quantum Physics Statistical Mechanics Mathematical Physics Chemical Physics Computational Physics Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys. 2016, 145, 204105; 2019, 151, 024105 and J. Phys. Chem. Lett. 2021, 12, 2496-2501, non-covariant phase space functions, time-dependent weight functions, and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system. The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation. The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite. We also prove that the triangle window function approach, albeit proposed as a heuristic empirical model in J. Chem. Phys. 2016, 145, 144108, is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system. |
| title | A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2404.04868 |