Efimov Effect for a Three-Particle System with Two Identical Fermions

被引:10
作者
Basti, Giulia [1 ]
Teta, Alessandro [1 ]
机构
[1] Sapienza Univ Roma, Dipartimento Matemat G Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy
来源
ANNALES HENRI POINCARE | 2017年 / 18卷 / 12期
关键词
3-BODY SCHRODINGER-OPERATORS; BOUND-STATES; PARTICLES; ASYMPTOTICS; NUMBER;
D O I
10.1007/s00023-017-0608-8
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider a three-particle quantum system in dimension three composed of two identical fermions of mass one and a different particle of mass m. The particles interact via two-body short range potentials. We assume that the Hamiltonians of all the two-particle subsystems do not have bound states with negative energy and, moreover, that the Hamiltonians of the two subsystems made of a fermion and the different particle have a zero-energy resonance. Under these conditions and for , we give a rigorous proof of the occurrence of the Efimov effect, i.e., the existence of infinitely many negative eigenvalues for the three-particle Hamiltonian H. More precisely, we prove that for the number of negative eigenvalues of H is finite and for the number N(z) of negative eigenvalues of H below has the asymptotic behavior for . Moreover, we give an upper and a lower bound for the positive constant .
引用
收藏
页码:3975 / 4003
页数:29
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