Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] abto_v1_0.gz(98 Kbytes)|
|Manuscript Title: Programs for symmetry adaption coefficients for semisimple symmetry chains: the completely symmetric representations.|
|Authors: T. Nomura, M. Ramek, B. Gruber|
|Program title: LIE_S1,LIE_S2|
|Catalogue identifier: ABTO_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 61(1990)410|
|Programming language: Pascal.|
|Computer: VAX 11/750, VAX SERVER 3600, IBM 3090.|
|Operating system: VAX/VMS, CMS, COMPILER: PASCALVS.|
|RAM: 120K words|
|Word size: 8|
|Keywords: General purpose, Semisimple symmetry chains, Lie algebra embedding, Symmetrization, Quantum states.|
Nature of problem:
1. Calculation of orthonormal bases for the completely symmetric irreducible unitary representations [[N]] of the special unitary algebras (groups) SU(l+1), and of orthonormal bases for direct products of representations [[N1]] otimes [[N2]] otimes [[N3]]... of the algebras SU(l1+1) otimes SU(l2+1) otimes SU(l3+1)... . (N denotes the number of particles and [[N]] denotes the completely symmetric representations of the pair (SU(l+1), SN), SN being the symmetric group generated by N particles.)
2. Calculation of orthonormal bases of irreducible unitary representations of the Lie algebras L = SU(l'+1), SO(2l'), SO(2l'+1), Sp(2l'), l'<= l, and direct products of these algebras, considered as subalgebras of an algebra SU(l+1) or a direct product of SU(l+1)'s. That is, the bases for the irreducible unitary representations of the subalgebras L are obtained in terms of the bases of the completely symmetric representations [[N]] of an algebra SU(l+1) by following a symmetry chain of algebras SU(l+1) -> L (symmetrization of states according to a symmetry chain).
3. The matrix elements for the generators of the Lie algebras are obtained together with the symmetrized wavefunctions.
4. The special cases SU(l+1) otimes SU(l+1) -> SU(l+1), SU(l+1) otimes SU(l+1) otimes SU(l+1) -> SU(l+1), etc. for the decomposition of a direct product of representations [[N1]] otimes [[N2]], [[N1]] otimes [[N2]], otimes [[N3]], etc. into its irreducible constituents are included.
Starting from the state vector corresponding to the highest weight of an irreducible representation of SU(l+1), repeated application of shift operators generates all states within this irreducible representation. The initial states of all other irreducible representations of the given symmetry chain, which are contained in a representation [[N]] of SU(l+1), are automatically generated using a precomputed list of all dominant subalgebra weights.
None except machine dependent storage limitations.
To avoid rounding errors, only integer arithmetic is used throughout the the programs. Linear combination coefficients, and all quantities related with these, are treated in the explicit form +- square root (p/q), p and q being integers stored and manipulated in portions of a few digits in several variables; the programs are therefore not restricted to any machine dependent integer arithmetic limitations. Final output may be obtained by pipelining output files generated by the programs to TEX.
Calculations of the embedding SU(6) -> SU(3) required the following CPU- times on a VAXserver 3600:
representation []: 6 sec; representation []: 15 sec; representation []: 44 sec; representation []: 2 min 24 sec; representation []: 7 min 14 sec; representation []: 20 min 53 sec; representation []: 1 h 05 min 53 sec; representation []: 1 h 59 min 17 sec.
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