Title | Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions |

Publication Type | Journal Article |

Year of Publication | 2012 |

Authors | Correggi, M, Dell'Antonio, G, Finco, D, Michelangeli, A, Teta, A |

Journal | Rev. Math. Phys. 24 (2012), 1250017 |

Abstract | We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs. |

URL | http://hdl.handle.net/1963/6069 |

DOI | 10.1142/S0129055X12500171 |

## Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions

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