Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of $J^P=0^+$ ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of $J^P=0^+$ ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.

arXiv:nucl-th/0004032Revista Mexicana de FísicaApr 12, 20002 citations

The many-particle shell model

CO-PUBLISHED WITH IMPERIAL COLLEGE PRESS eBooksSep 1, 20040 citations

Geometry of random interactions

P. Chau Huu-Tai, Alejandro Frank, N. A. Smirnova +1 more

It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a $j=\frac{7}{2}$ shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. The extensions to more general situations are discussed.It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a $j=\frac{7}{2}$ shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. The extensions to more general situations are discussed.

arXiv:nucl-th/0301061Physical Review CDec 23, 200226 citations

Shell model Monte Carlo methods

S. E. Koonin, David J. Dean, Karlheinz Langanke

Physics ReportsJan 1, 1997458 citations

Geometry of random interactions

P. Chau Huu-Tai

It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a j = 72 shell. In both examples the probability for a specific state to become the ground state is shown to be related to a geometric property of a (hyper)polyhedron which is interaction‐independent and is determined solely by particle number, shell size and symmetry character of the state. Extensions of these ideas to more general situations are discussed.It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a j = 72 shell. In both examples the probability for a specific state to become the ground state is shown to be related to a geometric property of a (hyper)polyhedron which is interaction‐independent and is determined solely by particle number, shell size and symmetry character of the state. Extensions of these ideas to more general situations are discussed.

AIP conference proceedingsJan 1, 20020 citations

Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of

J^P=0^+

ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.

j=\frac{7}{2}

shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. The extensions to more general situations are discussed.