Unitary Basis Transformations in Mixed Quantum-Classical Dynamics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914768323870720 |
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| author | Miyazaki, Ken Krotz, Alex Tempelaar, Roel |
| author_facet | Miyazaki, Ken Krotz, Alex Tempelaar, Roel |
| contents | A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations, and propose their integration into mixed quantum-classical dynamics, enabling this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta are combined into a set of complex-valued classical coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary Basis Transformations in Mixed Quantum-Classical Dynamics Miyazaki, Ken Krotz, Alex Tempelaar, Roel Quantum Physics Chemical Physics A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations, and propose their integration into mixed quantum-classical dynamics, enabling this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta are combined into a set of complex-valued classical coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets. |
| title | Unitary Basis Transformations in Mixed Quantum-Classical Dynamics |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2404.15614 |