Density of Avoided Crossings and Diabatic Representation
Electronic structure theory describes the properties of solids using Bloch states that correspond to highly symmetrical nuclear configurations. However, nuclear thermal motion destroys translation symmetry. Here, we describe two approaches relevant to the time evolution of electronic states in the p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/5/751 |
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| author | Anatoly E. Obzhirov Eric J. Heller |
| author_facet | Anatoly E. Obzhirov Eric J. Heller |
| author_sort | Anatoly E. Obzhirov |
| collection | DOAJ |
| description | Electronic structure theory describes the properties of solids using Bloch states that correspond to highly symmetrical nuclear configurations. However, nuclear thermal motion destroys translation symmetry. Here, we describe two approaches relevant to the time evolution of electronic states in the presence of thermal fluctuations. On the one hand, the direct solution of the time-dependent Schrodinger equation for a tight-binding model reveals the diabatic nature of time evolution. On the other hand, because of random nuclear configurations, the electronic Hamiltonian falls into the class of random matrices, which have universal features in their energy spectra. In the end, we discuss combining two approaches to obtain new insights into the influence of thermal fluctuations on electronic states. |
| first_indexed | 2024-03-11T03:45:52Z |
| format | Article |
| id | doaj.art-8af468f0b12443c4bd8f59913981af72 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T03:45:52Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-8af468f0b12443c4bd8f59913981af722023-11-18T01:15:52ZengMDPI AGEntropy1099-43002023-05-0125575110.3390/e25050751Density of Avoided Crossings and Diabatic RepresentationAnatoly E. Obzhirov0Eric J. Heller1Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, GermanyDepartment of Physics and Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USAElectronic structure theory describes the properties of solids using Bloch states that correspond to highly symmetrical nuclear configurations. However, nuclear thermal motion destroys translation symmetry. Here, we describe two approaches relevant to the time evolution of electronic states in the presence of thermal fluctuations. On the one hand, the direct solution of the time-dependent Schrodinger equation for a tight-binding model reveals the diabatic nature of time evolution. On the other hand, because of random nuclear configurations, the electronic Hamiltonian falls into the class of random matrices, which have universal features in their energy spectra. In the end, we discuss combining two approaches to obtain new insights into the influence of thermal fluctuations on electronic states.https://www.mdpi.com/1099-4300/25/5/751time evolution of quantum systemsstructure of eigenstates and energy spectrarandom matrix theorysemiclassical methods and resultsatomic, molecular and solid-state systems |
| spellingShingle | Anatoly E. Obzhirov Eric J. Heller Density of Avoided Crossings and Diabatic Representation Entropy time evolution of quantum systems structure of eigenstates and energy spectra random matrix theory semiclassical methods and results atomic, molecular and solid-state systems |
| title | Density of Avoided Crossings and Diabatic Representation |
| title_full | Density of Avoided Crossings and Diabatic Representation |
| title_fullStr | Density of Avoided Crossings and Diabatic Representation |
| title_full_unstemmed | Density of Avoided Crossings and Diabatic Representation |
| title_short | Density of Avoided Crossings and Diabatic Representation |
| title_sort | density of avoided crossings and diabatic representation |
| topic | time evolution of quantum systems structure of eigenstates and energy spectra random matrix theory semiclassical methods and results atomic, molecular and solid-state systems |
| url | https://www.mdpi.com/1099-4300/25/5/751 |
| work_keys_str_mv | AT anatolyeobzhirov densityofavoidedcrossingsanddiabaticrepresentation AT ericjheller densityofavoidedcrossingsanddiabaticrepresentation |