TY - JOUR T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions JF - Rev. Math. Phys. 24 (2012), 1250017 Y1 - 2012 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - 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. PB - World Scientific UR - http://hdl.handle.net/1963/6069 U1 - 5955 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER -