Coherent States of Graphene Layer with and without a PT-symmetric Chemical Potential
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929558490447872 |
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| author | Bagarello, Fabio Gargano, Francesco Saluto, Lidia |
| author_facet | Bagarello, Fabio Gargano, Francesco Saluto, Lidia |
| contents | In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a $\mathcal{P}\mathcal{T}$-symmetric chemical potential $V$. In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for $V=0$ and for $V\neq0$. We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken $\mathcal{P}\mathcal{T}$-symmetry is discussed, in connection with the strength of $V$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coherent States of Graphene Layer with and without a PT-symmetric Chemical Potential Bagarello, Fabio Gargano, Francesco Saluto, Lidia Mathematical Physics In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a $\mathcal{P}\mathcal{T}$-symmetric chemical potential $V$. In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for $V=0$ and for $V\neq0$. We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken $\mathcal{P}\mathcal{T}$-symmetry is discussed, in connection with the strength of $V$. |
| title | Coherent States of Graphene Layer with and without a PT-symmetric Chemical Potential |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2410.19621 |