메뉴 건너뛰기




Volumn 123, Issue 3-4, 2009, Pages 237-247

Combinatorics of angular momentum recoupling theory: Spin networks, their asymptotics and applications

Author keywords

[No Author keywords available]

Indexed keywords


EID: 67449127102     PISSN: 1432881X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00214-009-0519-y     Document Type: Article
Times cited : (31)

References (74)
  • 4
    • 34547237400 scopus 로고    scopus 로고
    • The discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors
    • 104 (9 pages)
    • Anderson RW, Aquilanti V (2006) The discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors. J Chem Phys 124:214,104 (9 pages)
    • (2006) J Chem Phys , vol.124 , pp. 214
    • Anderson, R.W.1    Aquilanti, V.2
  • 5
    • 55349115713 scopus 로고    scopus 로고
    • Exact computation and large angular momentum asymptotics of 3nj symbols: Semiclassical disentangling of spin networks
    • RW Anderson V Aquilanti C daSilva Ferreira 2008 Exact computation and large angular momentum asymptotics of 3nj symbols: semiclassical disentangling of spin networks J Chem Phys 129 161,101 161,105
    • (2008) J Chem Phys , vol.129 , pp. 161
    • Anderson, R.W.1    Aquilanti, V.2    Dasilva Ferreira, C.3
  • 6
    • 0031561416 scopus 로고    scopus 로고
    • Molecular beam scattering of nitrogen molecules in supersonic seeded beams: A probe of rotational alignment
    • V Aquilanti D Ascenzi D Cappelletti R Fedeli F Pirani 1997 Molecular beam scattering of nitrogen molecules in supersonic seeded beams: a probe of rotational alignment J Phys Chem A 101 7648 7656 (Pubitemid 127627808)
    • (1997) Journal of Physical Chemistry A , vol.101 , Issue.41 , pp. 7648-7656
    • Aquilanti, V.1    Ascenzi, D.2    Cappelletti, D.3    Fedeli, R.4    Pirani, F.5
  • 7
    • 58149460407 scopus 로고    scopus 로고
    • Quantum and semiclassical spin networks: From atomic and molecular physics to quantum computing and gravity
    • V Aquilanti ACP Bitencourt C daSilva Ferreira A Marzuoli M Ragni 2008 Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity Phys Scr 78 058 103
    • (2008) Phys Scr , vol.78 , pp. 058-103
    • Aquilanti, V.1    Bitencourt, A.C.P.2    Dasilva Ferreira, C.3    Marzuoli, A.4    Ragni, M.5
  • 8
    • 0037175366 scopus 로고    scopus 로고
    • Sturmian approach to one-electron many-center systems: Integrals and iteration schemes
    • V Aquilanti A Caligiana 2002 Sturmian approach to one-electron many-center systems: integrals and iteration schemes Chem Phys Lett 366 157 164
    • (2002) Chem Phys Lett , vol.366 , pp. 157-164
    • Aquilanti, V.1    Caligiana, A.2
  • 9
    • 0037443634 scopus 로고    scopus 로고
    • Hydrogenic elliptic orbitals, coulomb sturmian sets. Recoupling coefficients among alternative bases
    • V Aquilanti A Caligiana S Cavalli 2003 Hydrogenic elliptic orbitals, coulomb sturmian sets. Recoupling coefficients among alternative bases Int J Quant Chem 92 99 117
    • (2003) Int J Quant Chem , vol.92 , pp. 99-117
    • Aquilanti, V.1    Caligiana, A.2    Cavalli, S.3
  • 10
    • 0037443809 scopus 로고    scopus 로고
    • Hydrogenic orbitals in momentum space and hyperspherical harmonics. Elliptic sturmian basis sets
    • V Aquilanti A Caligiana S Cavalli C Coletti 2003 Hydrogenic orbitals in momentum space and hyperspherical harmonics. Elliptic sturmian basis sets Int J Quant Chem 92 212 228
    • (2003) Int J Quant Chem , vol.92 , pp. 212-228
    • Aquilanti, V.1    Caligiana, A.2    Cavalli, S.3    Coletti, C.4
  • 11
    • 0034397899 scopus 로고    scopus 로고
    • Harmonic analysis and discrete polynomials. from semiclassical angular momentum theory to the hyperquantization algorithm
    • V Aquilanti G Capecchi 2000 Harmonic analysis and discrete polynomials. from semiclassical angular momentum theory to the hyperquantization algorithm Theor Chem Accounts 104 183 188
    • (2000) Theor Chem Accounts , vol.104 , pp. 183-188
    • Aquilanti, V.1    Capecchi, G.2
  • 12
    • 0034665608 scopus 로고    scopus 로고
    • Representation of potential energy surfaces by discrete polynomials: Proton transfer in malonaldehyde
    • V Aquilanti G Capecchi S Cavalli C Adamo V Barone 2000 Representation of potential energy surfaces by discrete polynomials: proton transfer in malonaldehyde Phys Chem Chem Phys 2 4095 4103
    • (2000) Phys Chem Chem Phys , vol.2 , pp. 4095-4103
    • Aquilanti, V.1    Capecchi, G.2    Cavalli, S.3    Adamo, C.4    Barone, V.5
  • 14
    • 36749106488 scopus 로고
    • Decoupling approximations in the quantum mechanical treatment of p-state atom collisions
    • V Aquilanti P Casavecchia A Laganà G Grossi 1980 Decoupling approximations in the quantum mechanical treatment of p-state atom collisions J Chem Phys 73 1173 1180
    • (1980) J Chem Phys , vol.73 , pp. 1173-1180
    • Aquilanti, V.1    Casavecchia, P.2    Laganà, A.3    Grossi, G.4
  • 15
    • 0030685863 scopus 로고    scopus 로고
    • The d-dimensional hydrogen atom: Hyperspherical harmonics as momentum space orbitals and alternative Sturmian basis sets
    • PII S0301010496003102
    • V Aquilanti S Cavalli C Coletti 1997 The d-dimensional hydrogen atom: hyperspherical harmonics as momentum space orbitals and alternative sturmian basis sets Chem Phys 214 1 13 (Pubitemid 127346249)
    • (1997) Chemical Physics , vol.214 , Issue.1 , pp. 1-13
    • Aquilanti, V.1    Cavalli, S.2    Coletti, C.3
  • 16
    • 11744336041 scopus 로고    scopus 로고
    • Hyperspherical symmetry of hydrogenic orbitals and recoupling coefficients among alternative bases
    • V Aquilanti S Cavalli C Coletti 1998 Hyperspherical symmetry of hydrogenic orbitals and recoupling coefficients among alternative bases Phys Rev Lett 80 3209 3212 (Pubitemid 128621762)
    • (1998) Physical Review Letters , vol.80 , Issue.15 , pp. 3209-3212
    • Aquilanti, V.1    Cavalli, S.2    Coletti, C.3
  • 17
    • 0001421952 scopus 로고    scopus 로고
    • Angular and hyperangular momentum recoupling, harmonic superposition and Racah polynomials: A recursive algorithm
    • DOI 10.1016/S0009-2614(01)00756-4, PII S0009261401007564
    • V Aquilanti S Cavalli C Coletti 2001 Angular and hyperangular momentum recoupling, harmonic superposition and racah polynomials. a recursive algorithm Chem Phys Lett 344 587 600 (Pubitemid 33628403)
    • (2001) Chemical Physics Letters , vol.344 , Issue.5-6 , pp. 587-600
    • Aquilanti, V.1    Cavalli, S.2    Coletti, C.3
  • 18
    • 0035215376 scopus 로고    scopus 로고
    • Hyperspherical harmonics as Sturmian orbitals in momentum space: A systematic approach to the few-body Coulomb problem
    • DOI 10.1080/01442350110075926
    • V Aquilanti S Cavalli C Coletti D Di Domenico G Grossi 2001 Hyperspherical harmonics as sturmian orbitals in momentum space: a systematic approach to the few-body coulomb problem Int Rev Phys Chem 20 673 709 (Pubitemid 33134710)
    • (2001) International Reviews in Physical Chemistry , vol.20 , Issue.4 , pp. 673-709
    • Aquilanti, V.1    Cavalli, S.2    Coletti, C.3    Domenico, D.D.4    Grossi, G.5
  • 19
    • 0002566284 scopus 로고    scopus 로고
    • Hyperangular momentum: Applications to atomic and molecular science
    • Tsipis CA, Popov VS, Herschbach DR, Avery JS (eds) Kluwer, Dordrecht
    • Aquilanti V, Cavalli S, Coletti C, De Fazio D, Grossi G (1996) Hyperangular momentum: Applications to atomic and molecular science. In: Tsipis CA, Popov VS, Herschbach DR, Avery JS (eds) New Methods in Quantum Theory. Kluwer, Dordrecht pp 233-250
    • (1996) New Methods in Quantum Theory , pp. 233-250
    • Aquilanti, V.1    Cavalli, S.2    Coletti, C.3    De Fazio, D.4    Grossi, G.5
  • 20
    • 0030587241 scopus 로고    scopus 로고
    • Alternative Sturmian bases and momentum space orbitals: An application to the hydrogen molecular ion
    • PII S0301010496001620
    • V Aquilanti S Cavalli C Coletti G Grossi 1996 Alternative sturmian bases and momentum space orbitals: an application to the hydrogen molecular ion Chem Phys 20 405 419 (Pubitemid 126316688)
    • (1996) Chemical Physics , vol.209 , Issue.2 SUPPL. 3 , pp. 405-419
    • Aquilanti, V.1    Cavalli, S.2    Coletti, C.3    Grossi, G.4
  • 21
    • 33751155408 scopus 로고
    • Angular and hyperangular momentum coupling coefficients as Hahn polynomials
    • V Aquilanti S Cavalli D De Fazio 1995 Angular and hyperangular momentum coupling coefficients as Hahn polynomials J Phys Chem 99 15,694 15,698
    • (1995) J Phys Chem , vol.99 , pp. 15
    • Aquilanti, V.1    Cavalli, S.2    De Fazio, D.3
  • 22
    • 0000492621 scopus 로고    scopus 로고
    • Hyperquantization algorithm. I. Theory for triatomic systems
    • DOI 10.1063/1.476979, PII S0021960698017346
    • V Aquilanti S Cavalli D De Fazio 1998 Hyperquantization algorithm: I. theory for triatomic systems J Chem Phys 109 3792 3804 (Pubitemid 128678586)
    • (1998) Journal of Chemical Physics , vol.109 , Issue.10 , pp. 3792-3804
    • Aquilanti, V.1    Cavalli, S.2    De Fazio, D.3
  • 26
    • 36549100638 scopus 로고
    • Hyperspherical coordinates for molecular dynamics by the method of trees and the mapping of potential energy surfaces for triatomic systems
    • V Aquilanti S Cavalli G Grossi 1986 Hyperspherical coordinates for molecular dynamics by the method of trees and the mapping of potential energy surfaces for triatomic systems J Chem Phys 86 1362 1375
    • (1986) J Chem Phys , vol.86 , pp. 1362-1375
    • Aquilanti, V.1    Cavalli, S.2    Grossi, G.3
  • 27
    • 0001130044 scopus 로고    scopus 로고
    • Hund's cases for rotating diatomic molecules and for atomic collisions: Angular momentum coupling schemes and orbital alignment
    • V Aquilanti S Cavalli G Grossi 1996 Hund's cases for rotating diatomic molecules and for atomic collisions: angular momentum coupling schemes and orbital alignment Z Phys D 36 215 219
    • (1996) Z Phys D , vol.36 , pp. 215-219
    • Aquilanti, V.1    Cavalli, S.2    Grossi, G.3
  • 28
    • 0034560256 scopus 로고    scopus 로고
    • Angular Momentum Coupling Schemes for Molecular Collisions: The Stereodirected Representation
    • V Aquilanti S Cavalli A Volpi 2000 Angular momentum coupling schemes for molecular collisions: the stereodirected representation Phys Essays 13 412 420 (Pubitemid 33273643)
    • (2000) Physics Essays , vol.13 , Issue.2-3 , pp. 412-420
    • Aquilanti, V.1    Cavalli, S.2    Volpi, A.3
  • 29
    • 0001027135 scopus 로고    scopus 로고
    • The A+BC reaction by the hyperquantization algorithm: the symmetric hyperspherical parametrization for J > 0
    • DOI 10.1016/S0065-3276(05)39007-1, PII S0065327605390071, New Perspectives in Quantum Systems in Chemistry and Physics, Part 1
    • V Aquilanti S Cavalli A Volpi D De Fazio 2001 The a+bc reaction by the hyperquantization algorithm: the symmetric hyperspherical parametrization for j > 0 Adv Quant Chem 39 103 121 (Pubitemid 33804514)
    • (2001) Advances in Quantum Chemistry , vol.39 , pp. 103-121
    • Aquilanti, V.1    Cavalli, S.2    De Fazio, D.3    Volpi, A.4
  • 30
    • 0002213385 scopus 로고    scopus 로고
    • 3nj-symbols and harmonic superposition coefficients: An icosahedral abacus
    • DOI 10.1016/S0009-2614(01)00757-6, PII S0009261401007576
    • V Aquilanti C Coletti 2001 3nj-symbols and harmonic superposition coefficients: an icosahedral abacus Chem Phys Lett 344 601 611 (Pubitemid 33628404)
    • (2001) Chemical Physics Letters , vol.344 , Issue.5-6 , pp. 601-611
    • Aquilanti, V.1    Coletti, C.2
  • 31
    • 36749110696 scopus 로고
    • Angular momentum coupling schemes in the quantum mechanical treatment of p-state atom collisions
    • V Aquilanti G Grossi 1980 Angular momentum coupling schemes in the quantum mechanical treatment of p-state atom collisions J Chem Phys 73 1165 1172
    • (1980) J Chem Phys , vol.73 , pp. 1165-1172
    • Aquilanti, V.1    Grossi, G.2
  • 32
    • 51249183786 scopus 로고
    • Approximate selection rules for intramultiplet and depolarization cross sections in atomic collisions
    • V Aquilanti G Grossi A Laganà 1981 Approximate selection rules for intramultiplet and depolarization cross sections in atomic collisions Nuovo Cimento B 63 7 14
    • (1981) Nuovo Cimento B , vol.63 , pp. 7-14
    • Aquilanti, V.1    Grossi, G.2    Laganà, A.3
  • 34
    • 1842581280 scopus 로고    scopus 로고
    • Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets
    • V Aquilanti S Tonzani 2004 Three-body problem in quantum mechanics: hyperspherical elliptic coordinates and harmonic basis sets J Chem Phys 120 9 4066 4073
    • (2004) J Chem Phys , vol.120 , Issue.9 , pp. 4066-4073
    • Aquilanti, V.1    Tonzani, S.2
  • 35
    • 0001066491 scopus 로고
    • A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols
    • R Askey J Wilson 1979 A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols SIAM J Math Anal 10 1008
    • (1979) SIAM J Math Anal , vol.10 , pp. 1008
    • Askey, R.1    Wilson, J.2
  • 40
    • 0035911070 scopus 로고    scopus 로고
    • Hierarchies of invariant spin models
    • DOI 10.1016/S0550-3213(00)00729-X, PII S055032130000729X
    • G Carbone M Carfora A Marzuoli 2001 Hierarchies of invariant spin models Nucl Phys B 595 654 688 (Pubitemid 33376513)
    • (2001) Nuclear Physics B , vol.595 , Issue.3 , pp. 654-688
    • Carbone, G.1    Carfora, M.2    Marzuoli, A.3
  • 46
    • 33751537680 scopus 로고    scopus 로고
    • Quantum knitting
    • DOI 10.1134/S1054660X06110120
    • S Garnerone A Marzuoli M Rasetti 2006 Quantum knitting Laser Phys 11 1582 1594 (Pubitemid 44837932)
    • (2006) Laser Physics , vol.16 , Issue.11 , pp. 1582-1594
    • Garnerone, S.1    Marzuoli, A.2    Rasetti, M.3
  • 49
    • 0035530272 scopus 로고    scopus 로고
    • Diagram projection rules for recoupling diagrams in the Racah-Wigner category
    • WP Joyce 2001 Diagram projection rules for recoupling diagrams in the Racah-Wigner category J Math Phys 42 1346 1363
    • (2001) J Math Phys , vol.42 , pp. 1346-1363
    • Joyce, W.P.1
  • 50
    • 65449134702 scopus 로고    scopus 로고
    • Braiding and entanglement in spin networks: A combinatorial description of topological phases
    • arXiv:0806.3883
    • Kàdàr Z, Marzuoli A, Rasetti M (2008) Braiding and entanglement in spin networks: a combinatorial description of topological phases. Int J Quantum Inf (in press). arXiv:0806.3883
    • (2008) Int J Quantum Inf (In Press)
    • Kàdàr, Z.1
  • 52
    • 7044272740 scopus 로고    scopus 로고
    • Electronic interaction anisotropy between atoms in arbitrary angular momentum states
    • RV Krems GC Groenenboom A Dalgarno 2004 Electronic interaction anisotropy between atoms in arbitrary angular momentum states J Phys Chem A 108 8941 8948
    • (2004) J Phys Chem A , vol.108 , pp. 8941-8948
    • Krems, R.V.1    Groenenboom, G.C.2    Dalgarno, A.3
  • 53
    • 67449156473 scopus 로고    scopus 로고
    • Marzuoli A, Rasetti M (in preparation)
    • Marzuoli A, Rasetti M (in preparation)
  • 54
    • 0037203282 scopus 로고    scopus 로고
    • Spin network quantum simulator
    • A Marzuoli M Rasetti 2002 Spin network quantum simulator Phys Lett A 306 79 87
    • (2002) Phys Lett A , vol.306 , pp. 79-87
    • Marzuoli, A.1    Rasetti, M.2
  • 55
    • 20944442561 scopus 로고    scopus 로고
    • Computing spin networks
    • DOI 10.1016/j.aop.2005.01.005, PII S0003491605000102
    • A Marzuoli M Rasetti 2005 Computing spin networks Ann Phys 318 345 407 (Pubitemid 40869740)
    • (2005) Annals of Physics , vol.318 , Issue.2 , pp. 345-407
    • Marzuoli, A.1    Rasetti, M.2
  • 56
    • 20944443799 scopus 로고    scopus 로고
    • Spin network setting of topological quantum computation
    • DOI 10.1142/S0219749905000499, PII S0219749905000499
    • A Marzuoli M Rasetti 2005 Spin network setting of topological quantum computation Int J Quant Inf 3 65 72 (Pubitemid 44103154)
    • (2005) International Journal of Quantum Information , vol.3 , Issue.1 , pp. 65-72
    • Marzuoli, A.1    Rasetti, M.2
  • 57
    • 34250208461 scopus 로고    scopus 로고
    • Coupling of quantum angular momenta: An insight into analogic/discrete and local/global models of computation
    • DOI 10.1007/s11047-006-9018-4, Natural Processes and Models of Computation
    • A Marzuoli M Rasetti 2007 Coupling of angular momenta: an insight into analogic/discrete and local/global models of computation Nat Computing 6 151 168 (Pubitemid 46895172)
    • (2007) Natural Computing , vol.6 , Issue.2 , pp. 151-168
    • Marzuoli, A.1    Rasetti, M.2
  • 61
    • 7444224205 scopus 로고    scopus 로고
    • Problems on invariants of knots and 3-manifolds, rims geometry and topology monographs. eprint math
    • T Ohtsuki 2002 Problems on invariants of knots and 3-manifolds, rims geometry and topology monographs. eprint math GT/0406190 4 377 572
    • (2002) GT/0406190 , vol.4 , pp. 377-572
    • Ohtsuki, T.1
  • 64
    • 51649208939 scopus 로고
    • General relativity without coordinates
    • T Regge 1961 General relativity without coordinates Nuovo Cimento 19 558 571
    • (1961) Nuovo Cimento , vol.19 , pp. 558-571
    • Regge, T.1
  • 65
    • 0034385504 scopus 로고    scopus 로고
    • Discrete structures in gravity
    • T Regge RM Williams 2008 Discrete structures in gravity J Math Phys 41 3964 3984
    • (2008) J Math Phys , vol.41 , pp. 3964-3984
    • Regge, T.1    Williams, R.M.2
  • 66
    • 1842855789 scopus 로고    scopus 로고
    • Cambridge University Press Cambridge
    • Rovelli C (2007) Quantum gravity. Cambridge University Press, Cambridge
    • (2007) Quantum Gravity
    • Rovelli, C.1
  • 67
    • 36749112519 scopus 로고
    • Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta
    • K Schulten RG Gordon 1975 Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta J Math Phys 16 1961 1970
    • (1975) J Math Phys , vol.16 , pp. 1961-1970
    • Schulten, K.1    Gordon, R.G.2
  • 68
    • 36749106106 scopus 로고
    • Semiclassical approximations to 3j and 6j-coefficients for quantum-mechanical coupling of angular momenta
    • K Schulten RG Gordon 1975 Semiclassical approximations to 3j and 6j-coefficients for quantum-mechanical coupling of angular momenta J Math Phys 16 1971 1988
    • (1975) J Math Phys , vol.16 , pp. 1971-1988
    • Schulten, K.1    Gordon, R.G.2
  • 69
    • 44049114062 scopus 로고
    • State sum invariants of 3-manifolds and quantum-6j symbols
    • V Turaev OY Viro 1992 State sum invariants of 3-manifolds and quantum-6j symbols Topology 31 865 902
    • (1992) Topology , vol.31 , pp. 865-902
    • Turaev, V.1    Viro, O.Y.2
  • 72
    • 0001751343 scopus 로고
    • Regge calculus: A bibliography and brief review
    • RM Williams 1992 Regge calculus: a bibliography and brief review Class Quantum Grav 9 1409 1422
    • (1992) Class Quantum Grav , vol.9 , pp. 1409-1422
    • Williams, R.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.