Stability of $n$-particle pseudorelativistic systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 528-537
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For a system $Z_n$ of $n$ identical pseudorelativistic particles, we show
that under some restrictions on the pair interaction potentials, there is
an infinite sequence of numbers $n_s$, $s=1,2,\dots$, such that the system $Z_n$
is stable for $n=n_s$, and the inequality $\sup_sn_{s+1}n_s^{-1}+\infty$
holds. Furthermore, we show that if the system $Z_n$ is stable, then
the discrete spectrum of the energy operator for the relative motion of
the system $Z_n$ is nonempty for some values of the total momentum of
the particles in the system. The stability of $n$-particle systems was previously
studied only for nonrelativistic particles.
Keywords:
pseudorelativistic operator, many-particle system, stability, discrete spectrum.
@article{TMF_2007_152_3_a9,
author = {G. M. Zhislin},
title = {Stability of $n$-particle pseudorelativistic systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {528--537},
publisher = {mathdoc},
volume = {152},
number = {3},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a9/}
}
G. M. Zhislin. Stability of $n$-particle pseudorelativistic systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 528-537. http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a9/