A quantization of interacting particle systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913279119458304 |
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| author | Akahori, Jirô Konno, Norio Okamoto, Rikuki Sato, Iwao |
| author_facet | Akahori, Jirô Konno, Norio Okamoto, Rikuki Sato, Iwao |
| contents | Interacting particle systems studied in this paper are probabilistic cellular automata with nearest-neighbor interaction including the Domany-Kinzel model. A special case of the Domany-Kinzel model is directed percolation. We regard the interacting particle system as a Markov chain on a graph. Then we present a new quantization of the interacting particle system. After that, we introduce a zeta function of the quantized model and give its determinant expression. Moreover, we calculate the absolute zeta function of the quantized model for the Domany-Kinzel model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A quantization of interacting particle systems Akahori, Jirô Konno, Norio Okamoto, Rikuki Sato, Iwao Quantum Physics Mathematical Physics Number Theory Probability Interacting particle systems studied in this paper are probabilistic cellular automata with nearest-neighbor interaction including the Domany-Kinzel model. A special case of the Domany-Kinzel model is directed percolation. We regard the interacting particle system as a Markov chain on a graph. Then we present a new quantization of the interacting particle system. After that, we introduce a zeta function of the quantized model and give its determinant expression. Moreover, we calculate the absolute zeta function of the quantized model for the Domany-Kinzel model. |
| title | A quantization of interacting particle systems |
| topic | Quantum Physics Mathematical Physics Number Theory Probability |
| url | https://arxiv.org/abs/2402.00280 |