Numerical simulations show that the ground state spin of a finite many-body system with random but rotationally invariant interactions is predominantly zero. This means that it is not sufficient to explain the zero ground state spin of even-even nuclei only by pairing correlations. Simple explanations based on a statistical multiplicity, width of the level density, effective pairing, formation of condensates etc. do not work. We suggest statistical theory based on the effective mean field and geometric chaoticity of angular momentum coupling of individual particles. The results show a significant role of symmetry arguments in finite systems.Numerical simulations show that the ground state spin of a finite many-body system with random but rotationally invariant interactions is predominantly zero. This means that it is not sufficient to explain the zero ground state spin of even-even nuclei only by pairing correlations. Simple explanations based on a statistical multiplicity, width of the level density, effective pairing, formation of condensates etc. do not work. We suggest statistical theory based on the effective mean field and geometric chaoticity of angular momentum coupling of individual particles. The results show a significant role of symmetry arguments in finite systems.

International Journal of Modern Physics BJul 30, 20061 citation

Do we understand the role of incoherent interactions in many-body physics?

Vladimir Zelevinsky, Declan Mulhall, Alexander Volya

Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.

Physics of Atomic NucleiMar 1, 200112 citations

Effects of Random Interactions in a Finite Fermi System

Jennifer R. Glick, Vladimir Zelevinsky

Bulletin of the American Physical SocietyMar 30, 20130 citations

Spin I ground state probabilities of integrable systems under random interactions

Yi Lu, Y. M. Zhao, A. Arima

In this paper we revisit spin $I$ ground state probabilities (denoted by $P(I))$ of a few integrable systems under random interactions. We obtain explicit and simple formulas of $P(I)$ for $d$ -boson systems and fermions in a $j=5/2$ shell.In this paper we revisit spin $I$ ground state probabilities (denoted by $P(I))$ of a few integrable systems under random interactions. We obtain explicit and simple formulas of $P(I)$ for $d$-boson systems and fermions in a $j=5/2$ shell.

Physical Review CFeb 9, 20153 citations

In this paper we revisit spin

I

ground state probabilities (denoted by

P(I))

of a few integrable systems under random interactions. We obtain explicit and simple formulas of

P(I)

for

d

-boson systems and fermions in a

j=5/2

shell.