製造企業勤務R&D．数理物理(対称性，可解系，可積分系，変数分離可能系，SUSY QM)と物性理論(トポロジカル物性，超伝導，不純物)が趣味です．子育てをしています．アイコンはChatGPT作．
- Tweets172K
- Following9.5K
- Followers8.9K
- Likes665K
![We study a one-dimensional single-excitation model of a scalar photon field coupled to a continuum of two-level atoms with quadratic density. The resulting matrix Hamiltonian has an unbounded spatially varying coupling and is not semibounded. We prove that it is essentially self-adjoint and determine its spectrum explicitly. The continuous spectrum is the half-line (-∞,Ω], where Ω is the atomic resonance frequency, while the spectrum above Ω consists of a strictly increasing sequence of simple eigenvalues. These eigenvalues are characterized by the interlaced zeros of the Airy function and its derivative and satisfy ω_n = (3πg n/4)¹/2 + fracΩ4 + O(n^-1/2). The analysis is based on a nonlinear spectral reduction that yields a confining massless relativistic oscillator above Ω and an inverted oscillator below Ω.](https://pbs.twimg.com/media/HUoHPgmW4AAnkyh.png?name=orig)
ALT We study a one-dimensional single-excitation model of a scalar photon field coupled to a continuum of two-level atoms with quadratic density. The resulting matrix Hamiltonian has an unbounded spatially varying coupling and is not semibounded. We prove that it is essentially self-adjoint and determine its spectrum explicitly. The continuous spectrum is the half-line (-∞,Ω], where Ω is the atomic resonance frequency, while the spectrum above Ω consists of a strictly increasing sequence of simple eigenvalues. These eigenvalues are characterized by the interlaced zeros of the Airy function and its derivative and satisfy ω_n = (3πg n/4)¹/2 + fracΩ4 + O(n^-1/2). The analysis is based on a nonlinear spectral reduction that yields a confining massless relativistic oscillator above Ω and an inverted oscillator below Ω.
