%0 Journal Article
%J Rev. Math. Phys. 24 (2012), 1250017
%D 2012
%T Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions
%A Michele Correggi
%A Gianfausto Dell'Antonio
%A Domenico Finco
%A Alessandro Michelangeli
%A Alessandro Teta
%X 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.
%B Rev. Math. Phys. 24 (2012), 1250017
%I World Scientific
%G en
%U http://hdl.handle.net/1963/6069
%1 5955
%2 Mathematics
%3 Mathematical Physics
%4 -1
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T07:19:59Z\\nNo. of bitstreams: 1\\n1201.5740v1.pdf: 303047 bytes, checksum: eb2df0afd547514c235422e82f494584 (MD5)
%R 10.1142/S0129055X12500171
%0 Journal Article
%J Lett. Math. Phys. 40 (1997), no. 3, 235-256
%D 1997
%T Statistics in space dimension two
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%X 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).
%B Lett. Math. Phys. 40 (1997), no. 3, 235-256
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/130
%1 12
%2 LISNU
%3 Interdisciplinary Laboratory for Advanced Studies
%$ Made available in DSpace on 2004-09-01T12:22:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996
%R 10.1023/A:1007361832622
%0 Thesis
%D 1989
%T Singular perturbation of the Laplacian and connections with models of random media
%A Alessandro Teta
%I SISSA
%G en
%U http://hdl.handle.net/1963/6348
%1 6281
%2 Mathematics
%4 -1
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-12-20T10:24:13Z\\nNo. of bitstreams: 1\\nPhD_Teta_Alessandro.pdf: 7132993 bytes, checksum: 95123d37874902a4392f102bb70cd46f (MD5)