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Volumn 72, Issue 14, 2005, Pages

Integrable dynamics of coupled Fermi-Bose condensates

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EID: 29644434133     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.72.144524     Document Type: Article
Times cited : (66)

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    • The coordinate, x and the momentum, p of the oscillator are related to the fields b and b̄ as x=2bx=(b+b̄)/2 and p=2by=(b̄-b)/(2i). Then, we have the usual coordinate-momentum (canonical) brackets {x,p}=1, while the second term in the Hamiltonian 2 3 reads b̄b=p2/2+x2/2.
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    • Note that if the root E0 is real, it has to be degenerate, since according to Eq. 5 9 Q2n+2(u)≥0 for real u. In this case L2(E0)=0 implies Lz(E0)=L-(E0) and, since zeros of L-(u) are separation variables, one of them has to be frozen at E0.
    • Note that if the root E0 is real, it has to be degenerate, since according to Eq. 5 9 Q2n+2(u)≥0 for real u. In this case L2(E0)=0 implies Lz(E0)=L-(E0) and, since zeros of L-(u) are separation variables, one of them has to be frozen at E0.


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