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 -
TY - JOUR
T1 - Statistics in space dimension two
JF - Lett. Math. Phys. 40 (1997), no. 3, 235-256
Y1 - 1997
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Alessandro Teta
AB - 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).
PB - SISSA Library
UR - http://hdl.handle.net/1963/130
U1 - 12
U2 - LISNU
U3 - Interdisciplinary Laboratory for Advanced Studies
ER -
TY - THES
T1 - Singular perturbation of the Laplacian and connections with models of random media
Y1 - 1989
A1 - Alessandro Teta
PB - SISSA
UR - http://hdl.handle.net/1963/6348
U1 - 6281
U2 - Mathematics
U4 - -1
ER -