TY - JOUR

T1 - Sum rules for spin- 1/2 quantum gases in states with well-defined spins

T2 - Spin-independent interactions and spin-dependent external fields

AU - Yurovsky, Vladimir A.

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/5/1

Y1 - 2015/5/1

N2 - Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin - the states built from spin and spatial wave functions belonging to multidimensional irreducible representations of the symmetric group, unless the total spin has the maximal allowed value. For spin-dependent one-body interactions with external fields and spin-independent two-body ones between the particles, the sum dependence on the many-body states is given by universal factors, which are independent of the interaction details and Hamiltonians of noninteracting particles. The sum rules are applied to perturbative analysis of energy spectra.

AB - Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin - the states built from spin and spatial wave functions belonging to multidimensional irreducible representations of the symmetric group, unless the total spin has the maximal allowed value. For spin-dependent one-body interactions with external fields and spin-independent two-body ones between the particles, the sum dependence on the many-body states is given by universal factors, which are independent of the interaction details and Hamiltonians of noninteracting particles. The sum rules are applied to perturbative analysis of energy spectra.

UR - http://www.scopus.com/inward/record.url?scp=84929339936&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.91.053601

DO - 10.1103/PhysRevA.91.053601

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AN - SCOPUS:84929339936

SN - 2469-9926

VL - 91

JO - Physical Review A

JF - Physical Review A

IS - 5

M1 - 053601

ER -