Partial dynamical symmetries

A. Leviatan

doi:10.1016/j.ppnp.2010.08.001

Partial dynamical symmetries

A. Leviatan

Racah Institute of Physics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Review article › peer-review

Abstract

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.

Original language	English
Pages (from-to)	93-143
Number of pages	51
Journal	Progress in Particle and Nuclear Physics
Volume	66
Issue number	1
DOIs	https://doi.org/10.1016/j.ppnp.2010.08.001
State	Published - Jan 2011

Keywords

Algebraic models
Dynamical symmetry
Pairing and seniority
Partial symmetry
Quantum phase transitions
Regularity and chaos

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

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10.1016/j.ppnp.2010.08.001

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title = "Partial dynamical symmetries",

abstract = "This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.",

keywords = "Algebraic models, Dynamical symmetry, Pairing and seniority, Partial symmetry, Quantum phase transitions, Regularity and chaos",

author = "A. Leviatan",

note = "Funding Information: The author is pleased to acknowledge a fruitful collaboration with Y. Alhassid, J. Escher, J.E. Garc{\'i}a-Ramos, J.N. Ginocchio, I. Sinai, M. Mamistvalov, P. Van Isacker and N.D. Whelan. Valuable discussions with F. Iachello, D.J. Rowe and I. Talmi on fundamental aspects of partial symmetries, and with R.F. Casten and N. Pietralla on their empirical manifestations, are much appreciated. To them and to many other colleagues who have shown interest in this avenue of research, my warm thanks. This work was supported in part by the Israel Science Foundation and in part by the US–Israel Binational Science Foundation.",

year = "2011",

month = jan,

doi = "10.1016/j.ppnp.2010.08.001",

language = "الإنجليزيّة",

volume = "66",

pages = "93--143",

journal = "Progress in Particle and Nuclear Physics",

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N1 - Funding Information: The author is pleased to acknowledge a fruitful collaboration with Y. Alhassid, J. Escher, J.E. García-Ramos, J.N. Ginocchio, I. Sinai, M. Mamistvalov, P. Van Isacker and N.D. Whelan. Valuable discussions with F. Iachello, D.J. Rowe and I. Talmi on fundamental aspects of partial symmetries, and with R.F. Casten and N. Pietralla on their empirical manifestations, are much appreciated. To them and to many other colleagues who have shown interest in this avenue of research, my warm thanks. This work was supported in part by the Israel Science Foundation and in part by the US–Israel Binational Science Foundation.

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N2 - This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.

AB - This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.

KW - Algebraic models

KW - Dynamical symmetry

KW - Pairing and seniority

KW - Partial symmetry

KW - Quantum phase transitions

KW - Regularity and chaos

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DO - 10.1016/j.ppnp.2010.08.001

M3 - مقالة مرجعية

SN - 0146-6410

VL - 66

SP - 93

EP - 143

JO - Progress in Particle and Nuclear Physics

JF - Progress in Particle and Nuclear Physics

IS - 1

ER -

Partial dynamical symmetries

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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