NDLI: A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity

Content Provider	Springer Nature Link
Author	Michelangeli, A. Dell’Antonio, G. Correggi, M. Finco, D. Teta, A.
Copyright Year	2015
Abstract	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 $^{∗}$ ≃ (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 ∈ (m $^{∗}$,m $^{∗∗}$), where m $^{∗∗}$ ≃ (8.62)$^{−1}$, there is a further family of self-adjoint and lower bounded Hamiltonians H $_{0,β }$, β ∈ 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.
Ending Page	36
Page Count	36
Starting Page	1
File Format	PDF
ISSN	13850172
e-ISSN	15729656
Journal	Mathematical Physics, Analysis and Geometry
Issue Number	1
Volume Number	18
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-12-29
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Zero-range interactions Operator methods in interpolation, moment and extension problems Forms (bilinear, sesquilinear, multilinear) Theoretical, Mathematical and Computational Physics Ter-Martirosyan-Skornyakov boundary conditions Unitary gases Atomic physics Geometry Selfadjoint operator theory in quantum theory, including spectral analysis Zero-energy resonances Analysis Quadratic forms and self-adjoint extension theory Group Theory and Generalizations Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematical Physics Geometry and Topology

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