Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity
arXiv:2202.12765 · doi:10.1007/s11785-023-01358-4
Abstract
We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the standard approach, one obtains the Ter-Martirosyan Skornyakov Hamiltonian which is unbounded from below. In order to avoid such instability problem, we introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles, i.e., the impurity and a boson, when another boson approaches the common position of the first two particles. We show that the Hamiltonian defined with such regularized interaction is self-adjoint and bounded from below if the strength of the three-body force is sufficiently large. The method of the proof is based on a careful analysis of the corresponding quadratic form.
arXiv comment38 pages
References in corpus (12)
- Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions
- Multiparticle Schrodinger operators with point interactions in the plane
- A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
- Stability of a fermionic particle system with point interactions
- Self-adjoint extension schemes and modern applications to quantum Hamiltonians
- Models of zero-range interaction for the bosonic trimer at unitarity
- Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
- The three-body problem in dimension one: From short-range to contact interactions
- Stability of the 2+2 fermionic system with point interactions
- From Short-Range to Contact Interactions in the 1d Bose Gas
- From Short-Range to Contact Interactions in Two-dimensional Many-Body Quantum Systems
- Triviality of a model of particles with point interactions in the thermodynamic limit