Mathematical
challenges of zero-range Physics 2014:

rigorous results and open problems.

Main references referred to in the talks

rigorous results and open problems.

Main references referred to in the talks

S. Albeverio

Some remarks on spectral properties of Schrödinger operators with (many) concentric δ-shells and related topics

- Albeverio, Kostenko, Malamud, Neidhard - 2012 ("Schrödinger operators with concentric δ-shells")

J. Behrndt

Spectral properties of Schrödinger operators with singular interactions on Lipschitz surfaces

- Behrnt, Langer, Lotoreichik - 2013 ("Schrödinger operators with δ- and δ'-potentials supported on hypersurface")
- Behrnt, Exner,
Lotoreichik - 2013 ("Schrödinger operators with δ- and
δ'-interactions on Lipschitz surfaces and chromatic numbers
of associated partitions")

C. Cacciapuoti

Effective dynamics for shrinking waveguides

- Cacciapuoti, Finco - 2010 ("Graph-like models for thin waveguides with Robin boundary conditions")
- Cacciapuoti,
Exner - 2007 ("Nontrivial edge coupling from a
Dirichlet network squeezing: the case of a bent waveguide")

R. Carlone

Spectral theory of Gesztesy-Šeba realisations of 1D Dirac operators with point interactions

- Carlone,
Malamud, Posilicano - 2013 ("On
the spectral theory of Gesztesy-Šeba realizations of 1-D
Dirac operators with point interactions on a discrete
set")

D. Finco

Two fermions and a test particle: a detailed analysis.

- Correggi,
Dell'Antonio,
Finco,
Michelangeli,
Teta
- 2012 ("Stability for a system of
N fermions plus a different particle with zero-range interactions") - Finco, Teta - 2012 ("Quadratic forms for the fermionic unitary gas model")
- Minlos - 2013
("On Pointlike Interaction
between Three Particles: Two Fermions and Another
Particle. II.")

- Minlos
- 2012 ("On Pointlike Interaction between Three
Particles: Two Fermions and Another Particle.")

R. Figari

Spin-dependent point interactions used in models of quantum environments

- Figari, Teta - 2014 ("Quantum dynamics of a particle in a tracking chamber")
- Cacciapuoti, Carlone, Figari - 2007 ("A solvable model of a tracking chamber")
- Cacciapuoti, Carlone, Figari - 2007 ("Spin-dependent point potentials in one and three dimensions")

A. K. Motovilov

Three body systems with delta interactions with internal degrees of freedom

- Makarov, Melezhik, Motovilov - 1995 ("Point interactions in the problem of three quantum particles with internal structure")
- Kuperin, Makarov, Merkur'ev, Motovilov, Pavlov - 1988 ("Quantum few-body problem with internal structure. II.")

D. Noja

Non-linear Schrödinger equation and point interactions: localised defects and concentrated nonlinearities.

- Noja - 2013 ("Nonlinear Schrödinger equation on graphs: recent results and open problems")
- Adami, Noja, Ortoleva - 2013 ("Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three")
- Adami,
Cacciapuoti,
Finco, Noja - 2012 ("On
the structure of critical energy levels for the cubic
focusing NLS on star graphs")

A. Posilicano

Non-linear maximal monotone extensions of symmetric operators

- Posilicano
- 2007 ("Self-adjoint extensions of restrictions")

F. Werner

Few-body and many-body physics with zero-range interactions: theory and experiments with ultra-cold atomic gases

- Werner et al. - 2013 ("Lifetime of the Bose gas with resonant interactions")
- Castin, Werner - 2012 ("Third virial coefficient of the unitary Bose gas")
- Werner et al. - 2012 ("Feynman diagrams versus Fermi-gas Feynman emulator")
- Castin,
Werner - 2012 ("The unitary gas and its symmetry
properties")

on the Efimov effect:

- Efimov - 1970 ("Energy levels arising from resonant two-body forces in a three-body system")
- Efimov - 1971 ("Weakly bound states of three resonantly-interacting particles")
- Efimov - 1973 ("Energy levels of three resonantly interacting particles")
- Efimov
- 1979 ("Low energy properties of three resonantly
interacting particles")

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