Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: spin-independent interactions and spin-dependent external fields

Abstract

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 wavefunctions 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 non-interacting particles. The sum rules are applied to perturbative analysis of energy spectra.

arXiv commentThe title and notation of the universal factors are changed

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Cited by in corpus (6)

• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• Molecular spectra in collective Dicke states
• Entanglement production by statistical operators
• Long-lived states with well-defined spins in spin-$1/2$ homogeneous Bose gases
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: II. Spin-dependent two-body interactions