On spectral equations for an evolution operator of a $q$-oscillator lattice
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918266095534080 |
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| author | Sergeev, Sergey |
| author_facet | Sergeev, Sergey |
| contents | We propose a set of algebraic equations describing eigenvalues and eigenstates of a relativistic evolution operator for a two-dimensional $q$-oscillator Kagomé lattice. Evolution operator is constructed with the help of $q$-oscillator solution of the Tetrahedron Equation. We focus on the unitary regime of the evolution operator, so our results are related to 3d integrable systems of the quantum mechanics. Our conjecture is based on a two-dimensional lattice version of the coordinate Bethe-Ansatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On spectral equations for an evolution operator of a $q$-oscillator lattice Sergeev, Sergey Mathematical Physics 81R12 81R50 We propose a set of algebraic equations describing eigenvalues and eigenstates of a relativistic evolution operator for a two-dimensional $q$-oscillator Kagomé lattice. Evolution operator is constructed with the help of $q$-oscillator solution of the Tetrahedron Equation. We focus on the unitary regime of the evolution operator, so our results are related to 3d integrable systems of the quantum mechanics. Our conjecture is based on a two-dimensional lattice version of the coordinate Bethe-Ansatz. |
| title | On spectral equations for an evolution operator of a $q$-oscillator lattice |
| topic | Mathematical Physics 81R12 81R50 |
| url | https://arxiv.org/abs/2512.24043 |