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Akiva Novoselsky - One of the best experts on this subject based on the ideXlab platform.
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Harmonic Oscillator SU3 States with Arbitrary Permutational Symmetry
Annals of Physics, 2002Co-Authors: Akiva Novoselsky, Jacob KatrielAbstract:Abstract Many-particle harmonic oscillator states that belong to a given SU3 irreducible representation and are at the same time characterized by a Yamanouchi symbol specifying their Permutational Symmetry, are constructed recursively, using the SU3 coefficients of fractional parentage. These coefficients are the eigenvectors of the two-cycle class operators of the symmetric group in the appropriate basis. In the recursion procedure only the matrix element of the transposition of the last two particles has to be calculated in each step. This matrix element is obtained by using the SU3 Racah coefficients. The significance of this procedure for nuclear physics as well as for quark calculations is briefly pointed out.
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hyperspherical wave functions with orthogonal and Permutational Symmetry
Physical Review A, 1998Co-Authors: N Barnea, Akiva NovoselskyAbstract:Hyperspherical harmonic basis functions, expressed in terms of the Jacobi coordinates and belonging to well-defined irreducible representations of the orthogonal and symmetric groups, were recently introduced. The usefulness of these basis functions is presented and the two-body matrix elements between these functions are evaluated, using the various hyperspherical coefficients of fractional parentage. The appropriate rotation, necessary for this evaluation, is achieved by using the rotational Symmetry of these functions. Therefore, the representation matrices of the orthogonal group are sufficient for the calculation of the two-body matrix elements. Thus, the Raynal-Revai and the $T$ coefficients are unnecessary. These results make this basis set suitable for few-body calculations in nuclear, atomic, and molecular physics, as well as for microscopic calculations of collective modes in nuclear physics.
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Symmetrized harmonic oscillatorSU _3 states for multi-cluster systems
Zeitschrift für Physik A Hadrons and Nuclei, 1994Co-Authors: Akiva Novoselsky, J. KatrielAbstract:An algorithm is presented for the construction of single- and multi-cluster harmonic oscillator wave functions that are coupled into well-defined irreducible representations of SU _3 as well as of the symmetric group S _ N . The single-cluster harmonic oscillator SU _3 wave functions are constructed recursively, using the SU _3 coefficients of fractional parentage. To construct multi-cluster wave functions with a well-defined Permutational Symmetry we diagonalize an appropriate set of single-cycle class operators of the symmetric group involving all the constituent particles. The formalism is applicable to the study of multi-cluster systems in nuclear physics where the wave functions are expressed in terms of harmonic oscillator SU _3 states
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Hyperspherical functions with arbitrary Permutational Symmetry.
Physical Review A, 1994Co-Authors: Akiva Novoselsky, Jacob KatrielAbstract:An algorithm is formulated for the construction of many-particle Permutational Symmetry adapted functions in hyperspherical coordinates. A recursive procedure is proposed, introducing hyperspherical coefficients of fractional parentage (hscfps). These coefficients are the eigenvectors of the transposition class sum of the symmetric group in an appropriate basis. Only the matrix element of the transposition of the last two particles has to be calculated in each step. This matrix element is obtained by using the hscfps calculated in the preceding step as well as the Raynal-Revai and the T coefficients. The results are applicable to the study of the atomic, molecular, and nuclear few-body problem.
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Construction of Permutational Symmetry Adapted Non-Spurious States for Multi-Cluster Systems
Clustering Phenomena in Atoms and Nuclei, 1992Co-Authors: Jacob Katriel, Akiva NovoselskyAbstract:An algorithm for the construction of multi-cluster non-spurious harmonic oscillator wavefunctions with arbitrary Permutational Symmetry is developed. Each cluster is presented in terms of harmonic oscillator wavefunctions, expressed in an appropriate set of Jacobi coordinates. The cluster wavefunctions are coupled into non-spurious multi-cluster states with an overall well-defined angular momentum and Permutational Symmetry. This is achieved by diag-onalizing an appropriate set of single-cycle class operators of the symmetric group involving all the constituent particles. The results are immediately applicable to the study of nuclear cluster models, nuclei as quark clusters, nuclear fusion, fission and multifragmentation, as well as in atomic and molecular physics.
Jacob Katriel - One of the best experts on this subject based on the ideXlab platform.
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weights of spin and Permutational Symmetry adapted states for arbitrary elementary spins
2004Co-Authors: Jacob KatrielAbstract:The number of the states with a given total spin, corresponding to well-defined irreducible representations of the appropriate symmetric group, is determined for few-particle systems with arbitrary elementary spins. Some features of the general pattern are explored.
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Harmonic Oscillator SU3 States with Arbitrary Permutational Symmetry
Annals of Physics, 2002Co-Authors: Akiva Novoselsky, Jacob KatrielAbstract:Abstract Many-particle harmonic oscillator states that belong to a given SU3 irreducible representation and are at the same time characterized by a Yamanouchi symbol specifying their Permutational Symmetry, are constructed recursively, using the SU3 coefficients of fractional parentage. These coefficients are the eigenvectors of the two-cycle class operators of the symmetric group in the appropriate basis. In the recursion procedure only the matrix element of the transposition of the last two particles has to be calculated in each step. This matrix element is obtained by using the SU3 Racah coefficients. The significance of this procedure for nuclear physics as well as for quark calculations is briefly pointed out.
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Hyperspherical functions with arbitrary Permutational Symmetry.
Physical Review A, 1994Co-Authors: Akiva Novoselsky, Jacob KatrielAbstract:An algorithm is formulated for the construction of many-particle Permutational Symmetry adapted functions in hyperspherical coordinates. A recursive procedure is proposed, introducing hyperspherical coefficients of fractional parentage (hscfps). These coefficients are the eigenvectors of the transposition class sum of the symmetric group in an appropriate basis. Only the matrix element of the transposition of the last two particles has to be calculated in each step. This matrix element is obtained by using the hscfps calculated in the preceding step as well as the Raynal-Revai and the T coefficients. The results are applicable to the study of the atomic, molecular, and nuclear few-body problem.
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Construction of Permutational Symmetry Adapted Non-Spurious States for Multi-Cluster Systems
Clustering Phenomena in Atoms and Nuclei, 1992Co-Authors: Jacob Katriel, Akiva NovoselskyAbstract:An algorithm for the construction of multi-cluster non-spurious harmonic oscillator wavefunctions with arbitrary Permutational Symmetry is developed. Each cluster is presented in terms of harmonic oscillator wavefunctions, expressed in an appropriate set of Jacobi coordinates. The cluster wavefunctions are coupled into non-spurious multi-cluster states with an overall well-defined angular momentum and Permutational Symmetry. This is achieved by diag-onalizing an appropriate set of single-cycle class operators of the symmetric group involving all the constituent particles. The results are immediately applicable to the study of nuclear cluster models, nuclei as quark clusters, nuclear fusion, fission and multifragmentation, as well as in atomic and molecular physics.
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Construction of multi‐cluster states for nuclear cluster models
1991Co-Authors: Akiva Novoselsky, Jacob KatrielAbstract:We consider a system of identical particles distributed in several clusters, each one of which is characterized by a Yamanouchi symbol specifying its Permutational Symmetry. A procedure for coupling the various clusters into an overall well‐defined angular momentum and Permutational Symmetry is presented. The results are immediately applicable to the study of nuclear cluster models as well as to nuclei as quark clusters.
J. Ignacio Cirac - One of the best experts on this subject based on the ideXlab platform.
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Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information
Journal of High Energy Physics, 2019Co-Authors: Christoph Sünderhauf, Lorenzo Piroli, Norbert Schuch, J. Ignacio CiracAbstract:We consider the Brownian SYK model of N interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the Rényi-2 tripartite information of the unitary evolution operator, which were proposed as diagnostic tools for quantum chaos and scrambling, respectively. We show that their averaged dynamics can be studied as a quench problem at imaginary times in a model of N qudits, where the Hamiltonian displays site-Permutational Symmetry. By exploiting a description in terms of bosonic collective modes, we show that for the quantities of interest the dynamics takes place in a subspace of the effective Hilbert space whose dimension grows either linearly or quadratically with N , allowing us to perform numerically exact calculations up to N = 10^6. We analyze in detail the interesting features of the OTOCs, including their dependence on the chosen observables, and of the tripartite information. We observe explicitly the emergence of a scrambling time t ^ ∗ ∼ ln N controlling the onset of both chaotic and scrambling behavior, after which we characterize the exponential decay of the quantities of interest to the corresponding Haar scrambled values.
Vladimir G Tyuterev - One of the best experts on this subject based on the ideXlab platform.
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lifetimes and wave functions of ozone metastable vibrational states near the dissociation limit in a full Symmetry approach
Physical Review A, 2016Co-Authors: David Lapierre, Alexander Alijah, Roman V Kochanov, Viatcheslav Kokoouline, Vladimir G TyuterevAbstract:Energies and lifetimes (widths) of vibrational states above the lowest dissociation limit of $^{16}\mathrm{O}_{3}$ were determined using a previously developed efficient approach, which combines hyperspherical coordinates and a complex absorbing potential. The calculations are based on a recently computed potential energy surface of ozone determined with a spectroscopic accuracy [Tyuterev et al., J. Chem. Phys. 139, 134307 (2013)]. The effect of Permutational Symmetry on rovibrational dynamics and the density of resonance states in ${\mathrm{O}}_{3}$ is discussed in detail. Correspondence between quantum numbers appropriate for short- and long-range parts of wave functions of the rovibrational continuum is established. It is shown, by Symmetry arguments, that the allowed purely vibrational ($J=0$) levels of $^{16}\mathrm{O}_{3}$ and $^{18}\mathrm{O}_{3}$, both made of bosons with zero nuclear spin, cannot dissociate on the ground-state potential energy surface. Energies and wave functions of bound states of the ozone isotopologue $^{16}\mathrm{O}_{3}$ with rotational angular momentum $J=0$ and 1 up to the dissociation threshold were also computed. For bound levels, good agreement with experimental energies is found: The rms deviation between observed and calculated vibrational energies is 1 ${\mathrm{cm}}^{\ensuremath{-}1}$. Rotational constants were determined and used for a simple identification of vibrational modes of calculated levels.
Santopinto Elena - One of the best experts on this subject based on the ideXlab platform.
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Tetraquark spectroscopy
'American Physical Society (APS)', 2007Co-Authors: Santopinto Elena, Galata` GiuseppeAbstract:A complete classification of $qq \bar q \bar q$ tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The Permutational Symmetry properties of both the spin-flavour and orbital parts of the $qq$ and $\bar{q}\bar{q}$ subsystems are discussed. This complete classification is general and model independent and it is useful both for model builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a definite dynamical model. An evaluation of the tetraquark spectrum is obtained from the Iachello mass formula for normal mesons, here generalized to tetraquark systems. This mass formula is a generalization of the Gell-Mann Okubo mass formula, whose coefficients have been upgraded by a study of the latest PDG data. The ground state tetraquark nonet is identified with $f_{0}(600),\kappa(800), f_{0}(980), a_{0}(980)$. The mass splittings predicted by the Iachello mass formula are in agreement with the KLOE, Fermilab E791 and BES experimental data.Comment: Accepted for pubblication in Phys.Rev. C, 29 pages, 3 figures, Diquark-antidiquark limit added, references added, figures change
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Tetraquark states and spectrum
'World Scientific Pub Co Pte Lt', 2006Co-Authors: Santopinto Elena, Galatà GiuseppeAbstract:A general classification of tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The Permutational Symmetry properties of both the spin-flavour and orbital parts of the quark-quark and antiquark-antiquark subsystems are discussed in short. This classification is model indipendent and useful both for model-builders and experimentalists. An evaluation of the tetraquark spectrum is obtained from a generalization of a Iachello mass formula, originally developed for the $q\bar q$ mesons. The ground state tetraquark nonet is identified with $f_{0}(600)$, $\kappa(800)$, $f_{0}(980)$, $a_{0}(980)$.Comment: Invited talk at XI Conference on Problems in Theoretical Nuclear Physics (Cortona 2006), Cortona, Italy, 11-14 Oct, 200
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Spectroscopy of tetraquark mesons
2006Co-Authors: Santopinto Elena, Galatà GiuseppeAbstract:A classification of tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The Permutational Symmetry properties of both the spin-flavour and orbital parts of the quark-quark and antiquark-antiquark subsystems are briefly discussed. This classification is useful both for model-builders and experimentalists. An evaluation of the tetraquark spectrum is obtained from a Iachello mass formula for tetraquark systems. The ground state tetraquark nonet is identified with $f_{0}(600)$, $\kappa(800)$, $f_{0}(980)$, $a_{0}(980)$. The mass splittings predicted by this mass formula are in agreement with the KLOE, Fermilab E791 and BES experimental data.Comment: Invited talk at 26th International Colloquia in Group Theoretical Methods in Physics (XXVI ICGTMP), New York City, USA, 26-30 Jun, 200