%0 Report
%D 2015
%T A class of Hamiltonians for a three-particle fermionic system at unitarity
%A Michele Correggi
%A Gianfausto Dell'Antonio
%A Domenico Finco
%A Alessandro Michelangeli
%A Alessandro Teta
%X We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34469
%1 34644
%2 Mathematics
%4 1
%$ Submitted by Alessandro Michelangeli (alemiche@sissa.it) on 2015-05-21T06:33:20Z
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%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 Annales Henri Poincare 11 (2010) 539-564
%D 2010
%T A time-dependent perturbative analysis for a quantum particle in a cloud chamber
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%X We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.
%B Annales Henri Poincare 11 (2010) 539-564
%I Springer
%G en_US
%U http://hdl.handle.net/1963/3969
%1 432
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-05T08:05:00Z\\nNo. of bitstreams: 1\\n0907.5503v1.pdf: 273181 bytes, checksum: 781ee2f8d4ce957ebbfbf866bcc40d2b (MD5)
%R 10.1007/s00023-010-0037-4
%0 Journal Article
%J Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137
%D 2004
%T Blow-up solutions for the SchrÃ¶dinger equation in dimension three with a concentrated nonlinearity
%A Riccardo Adami
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%X We present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions.
%B Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/2998
%1 1335
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:06:49Z\\nNo. of bitstreams: 1\\nadami.pdf: 209114 bytes, checksum: ea6a7059ff0728c6d55cdc3a16071631 (MD5)
%R 10.1016/j.anihpc.2003.01.002
%0 Journal Article
%J Annales Poincare Phys.Theor.69:413-424,1998
%D 1998
%T Diffusion of a particle in presence of N moving point sources
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%B Annales Poincare Phys.Theor.69:413-424,1998
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/134
%1 75
%2 LISNU
%3 Interdisciplinary Laboratory for Advanced Studies
%$ Made available in DSpace on 2004-09-01T12:22:22Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996
%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 Journal Article
%J Publ. Res. Inst. Math. Sci. 26 (1990), no. 5, 803--817
%D 1990
%T Quadratic forms for singular perturbations of the Laplacian
%A Alessandro Teta
%B Publ. Res. Inst. Math. Sci. 26 (1990), no. 5, 803--817
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/757
%1 3034
%2 Mathematics
%3 Mathematical Physics
%$ Made available in DSpace on 2004-09-01T12:37:11Z (GMT). No. of bitstreams: 1\\n165_88.pdf: 420094 bytes, checksum: 84ec202153b3f40e2584898048015e2a (MD5)\\n Previous issue date: 1988
%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)