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Non-linear contact interactions: a partly variational approach

Speaker: 
Gianfausto Dell'Antonio
Institution: 
SISSA and Roma "La Sapienza"
Schedule: 
Thursday, June 1, 2023 - 14:00 to 15:30
Location: 
A-005
Abstract: 

We discuss, in the frame of self-adjoint operators in Quantum Mechanics, contact interactions, i.e. interactions supported by a point. On three dimensions we shall consider two, three and four particles "contact" interactions (point interactions).

The corresponding hamiltonians are self-adjoint operators; they are limits, in the strong resolvent sense, of hamiltonians with potentials of decreasing support. The sequence has no limit in the sense of quadratic forms. 

Within this framework we discuss e.g. the Efimov effect in low nuclear Physics, Bose-Einstein condensation and Bogolybov theory, and the energy spectrum of conduction electrons in a crystal (the Fermi sea). Our approach is partly variational.

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