Abstract
Quantum systems composed of N distinct particles in mathbb {R}^2 with two-body contact interactions of TMS type are shown to arise as limits—in the norm resolvent sense—of Schrödinger operators with suitably rescaled pair potentials.
Highlights
Many-particle quantum systems with short-range interactions are often described by simplified models with zero-range interactions
In the present paper we fully justify this idealization for 2d many-particle systems with two-body forces
We prove norm resolvent convergence for suitably rescaled Schrodinger operators towards TMS Hamiltonians [6]
Summary
Many-particle quantum systems with short-range interactions are often described by simplified models with zero-range (contact) interactions. TMS Hamiltonians like H in Theorem 1.1 have been described as resolvent limits of N -body Hamiltonians, where the regularized two-body contact interaction is an integral operator, rather than a potential, and the regularization is achieved by an ultraviolet cutoff [6,7,9] or a reversed heat flow [8]. In these cases the convergence is easier to establish than in the case studied here.
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