2022/07/01 by Daniele Ferretti, Ferretti, Daniele, Alessandro Teta +1 · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum chaos and dynamical systems #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2207.00313
We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In order to avoid the well known instability phenomenon, we consider the so-called Minlos-Faddeev regularization of such Hamiltonian, heuristically corresponding to the introduction of a three-body repulsion. We review the main concerning results recently obtained. In particular, starting from a suitable quadratic form Q, the self-adjoint and bounded from below Hamiltonian \mathcal H can be constructed provided that the strength γ of the three-body force is larger than a threshold parameter γc. Moreover, we give an alternative and much simpler proof of the above result whenever γ> γ'c, with γ'c strictly larger than γc. Finally, we show that the threshold value γc is optimal, in the sense that the quadratic form Q is unbounded from below if γ<γc.