Voce esta aqui[JOINT SWIECA - UNUSUAL DAY] Stability and Clustering for Lattice Many-Body Quantum Hamilto- nians with Multiparticle Potentials

[JOINT SWIECA - UNUSUAL DAY] Stability and Clustering for Lattice Many-Body Quantum Hamilto- nians with Multiparticle Potentials


By bertuzzo - Posted on 09 junho 2015

Palestrante: 
Prof. Michael O'Carrol (UFMG)
Data: 
Segunda-feira, 15 Junho, 2015 - 13:30

 

We analyze a quantum system of N identical spinless particles of mass m, in the lattice Zd, given by a Hamiltonian HN=TN+VN, with kinetic energy TN>0 and potential VN=VN;2+VN;3 composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials VN;2 and VN;3 on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the HN spectrum, s(HN) > - cN, for c >0 independent of N. For VN;3= 0, HN is unstable, and the system collapses. If VN;3 is different from 0, HN is stable and, for strong enough repulsion, we obtain s(HN) > - c' N, where  c' N is the energy of (N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [s(VN)/N] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value Ns of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers Nr and Ns – Nr, with Nr = 1;...; Ns -1. This is a joint work with Paulo da Veiga.