From Short-Range to Contact Interactions in the 1d Bose Gas

For a system of N bosons in one space dimension with two-body δ -interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schrödinger operators with rescaled two-body potentials, and we estimate t...

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Bibliographic Details
Published inMathematical physics, analysis, and geometry Vol. 23; no. 2
Main Authors Griesemer, Marcel, Hofacker, Michael, Linden, Ulrich
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2020
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Bosons
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quadratic forms
Theoretical
Gamma convergence
Bose gas
Contact interaction
Konno-Kuroda formula
Short-range interaction
Many-body quantum system
Schrodinger operator with singular interactions
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Summary:For a system of N bosons in one space dimension with two-body δ -interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schrödinger operators with rescaled two-body potentials, and we estimate the rate of this convergence.
ISSN:1385-0172
1572-9656
DOI:10.1007/s11040-020-09344-4