On the virtual level of two-body interactions and applications to three-body systems in higher dimensions

作者: Simon Barth , Andreas Bitter

DOI: 10.1063/1.5120366

关键词:

摘要: We consider a system of three particles in dimension 4 and higher interacting via short-range potentials, where the two-body Hamiltonians have virtual level at bottom essential spectrum. In dimensions 2 (in case fermions) 3 corresponding three-body Hamiltonian admits an infinite number bound states, which is known as Efimov effect. this work we prove that not dimensions. investigate how symmetries influence effect finiteness discrete spectrum Hamiltonian.

参考文章(27)
V.N. Efimov, WEAKLY BOUND STATES OF THREE RESONANTLY INTERACTING PARTICLES. Yadern. Fiz. 12: 1080-91(Nov 1970).. ,(1970)
Dmitry K. Gridnev, Proof of the Super Efimov Effect arXiv: Mathematical Physics. ,(2014) , 10.1088/1751-8113/47/50/505204
Arne Jensen, Tosio Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions Duke Mathematical Journal. ,vol. 46, pp. 583- 611 ,(1979) , 10.1215/S0012-7094-79-04631-3
Hideo Tamura, The Efimov effect of three-body Schrödinger operators Journal of Functional Analysis. ,vol. 95, pp. 433- 459 ,(1991) , 10.1016/0022-1236(91)90038-7
D R Jafaev, ON THE POINT SPECTRUM IN THE QUANTUM-MECHANICAL MANY-BODY PROBLEM Mathematics of The Ussr-izvestiya. ,vol. 10, pp. 861- 896 ,(1976) , 10.1070/IM1976V010N04ABEH001819
Yusuke Nishida, Sergej Moroz, Dam Thanh Son, Super Efimov effect of resonantly interacting fermions in two dimensions. Physical Review Letters. ,vol. 110, pp. 235301- ,(2013) , 10.1103/PHYSREVLETT.110.235301
S. A. Vugal'ter, G. M. Zhislin, On the discrete spectrum of the energy operator of one- and two-dimensional quantum three-particle systems Theoretical and Mathematical Physics. ,vol. 55, pp. 493- 502 ,(1983) , 10.1007/BF01015810
A. V. Sobolev, The Efimov effect. Discrete spectrum asymptotics Communications in Mathematical Physics. ,vol. 156, pp. 101- 126 ,(1993) , 10.1007/BF02096734
Viakalathur Shankar Sunder, Paul Richard Halmos, Bounded integral operators on L²spaces ,(1978)