A modified Cayley transform for SU(3) molecular dynamics simulations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910011292123136 |
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| author | Schäfers, Kevin Peardon, Michael Günther, Michael |
| author_facet | Schäfers, Kevin Peardon, Michael Günther, Michael |
| contents | We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group $\mathrm{SU}(3)$. The new mapping is used to construct splitting methods for separable Hamiltonian systems whose phase space is the cotangent bundle of $\mathrm{SU}(3)$ or, more general, $\mathrm{SU(3)}^N$, $N \in \mathbb{N}$. Special attention is given to the hybrid Monte Carlo algorithm for gauge field generation in lattice quantum chromodynamics. We show that the use of the modified Cayley transform instead of the matrix exponential neither affects the time-reversibility nor the volume-preservation of the splitting method. Furthermore, the advantages and disadvantages of the Cayley-based algorithms are discussed and illustrated in pure gauge field simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A modified Cayley transform for SU(3) molecular dynamics simulations Schäfers, Kevin Peardon, Michael Günther, Michael High Energy Physics - Lattice Numerical Analysis Mathematical Physics 81V05, 65P10, 65L05, 65L20, 37N20 We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group $\mathrm{SU}(3)$. The new mapping is used to construct splitting methods for separable Hamiltonian systems whose phase space is the cotangent bundle of $\mathrm{SU}(3)$ or, more general, $\mathrm{SU(3)}^N$, $N \in \mathbb{N}$. Special attention is given to the hybrid Monte Carlo algorithm for gauge field generation in lattice quantum chromodynamics. We show that the use of the modified Cayley transform instead of the matrix exponential neither affects the time-reversibility nor the volume-preservation of the splitting method. Furthermore, the advantages and disadvantages of the Cayley-based algorithms are discussed and illustrated in pure gauge field simulations. |
| title | A modified Cayley transform for SU(3) molecular dynamics simulations |
| topic | High Energy Physics - Lattice Numerical Analysis Mathematical Physics 81V05, 65P10, 65L05, 65L20, 37N20 |
| url | https://arxiv.org/abs/2406.11337 |