تقرير
A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
| العنوان: | A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity |
|---|---|
| المؤلفون: | Correggi, M., Dell'Antonio, G., Finco, D., Michelangeli, A., Teta, A. |
| المصدر: | Math. Phys. Anal. Geom. 18 (2015), 1-36 |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Quantum Gases |
| الوصف: | We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $ m $, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $ m $ larger than a critical value $ m^* \simeq (13.607)^{-1} $ a self-adjoint and lower bounded Hamiltonian $ H_0 $ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $ m \in( m^*,m^{**}) $, where $ m^{**} \simeq (8.62)^{-1} $, there is a further family of self-adjoint and lower bounded Hamiltonians $ H_{0,\beta} $, $ \beta \in \mathbb{R} $, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide. Comment: 30 pages; pdfLaTeX. Some comments and remarks added |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s11040-015-9195-4 |
| URL الوصول: | http://arxiv.org/abs/1505.04132 |
| رقم الأكسشن: | edsarx.1505.04132 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s11040-015-9195-4 |
|---|