@article {2012,
title = {Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions},
journal = {Rev. Math. Phys. 24 (2012), 1250017},
number = {arXiv:1201.5740;},
year = {2012},
publisher = {World Scientific},
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.},
doi = {10.1142/S0129055X12500171},
url = {http://hdl.handle.net/1963/6069},
author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta}
}
@article {1997,
title = {Statistics in space dimension two},
journal = {Lett. Math. Phys. 40 (1997), no. 3, 235-256},
number = {SISSA;5/96/ILAS/FM},
year = {1997},
publisher = {SISSA Library},
abstract = {We construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect).},
doi = {10.1023/A:1007361832622},
url = {http://hdl.handle.net/1963/130},
author = {Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Alessandro Teta}
}
@mastersthesis {1989,
title = {Singular perturbation of the Laplacian and connections with models of random media},
year = {1989},
school = {SISSA},
url = {http://hdl.handle.net/1963/6348},
author = {Alessandro Teta}
}