- #1
babylonia
- 11
- 0
Hi all,
I read on some paper that for a system of Fock state |...nk...>, and with the field operator expanded as
[tex]\Psi[/tex](r)=[tex]\sum[/tex]ak [tex]\phi[/tex]k(r), the second order density correlation function can be expressed as
G(2)=<[tex]\Psi[/tex]+(r)[tex]\Psi[/tex]+(r')[tex]\Psi[/tex](r')[tex]\Psi[/tex](r)>=<n(r)><n(r')>+|<[tex]\Psi[/tex](r)+[tex]\Psi[/tex](r')>|2-[tex]\sum[/tex][tex]^{N}_{k}[/tex] nk ( nk +1) |[tex]\phi[/tex]*(r)|2|[tex]\phi[/tex](r')|2.
I have no idea how the last term, ie. the term after the minus sign, come out? If I use the Wick's theorem for
<a+ka+laman>=<a+kam><a+lan>[tex]\delta[/tex]k,m[tex]\delta[/tex]l,n+<a+kan><a+lam>[tex]\delta[/tex]k,n[tex]\delta[/tex]l,m,
so why in the 2nd correlation there are additional terms after '-'?
This seems really strange, can anybody help me? Thank you.
I read on some paper that for a system of Fock state |...nk...>, and with the field operator expanded as
[tex]\Psi[/tex](r)=[tex]\sum[/tex]ak [tex]\phi[/tex]k(r), the second order density correlation function can be expressed as
G(2)=<[tex]\Psi[/tex]+(r)[tex]\Psi[/tex]+(r')[tex]\Psi[/tex](r')[tex]\Psi[/tex](r)>=<n(r)><n(r')>+|<[tex]\Psi[/tex](r)+[tex]\Psi[/tex](r')>|2-[tex]\sum[/tex][tex]^{N}_{k}[/tex] nk ( nk +1) |[tex]\phi[/tex]*(r)|2|[tex]\phi[/tex](r')|2.
I have no idea how the last term, ie. the term after the minus sign, come out? If I use the Wick's theorem for
<a+ka+laman>=<a+kam><a+lan>[tex]\delta[/tex]k,m[tex]\delta[/tex]l,n+<a+kan><a+lam>[tex]\delta[/tex]k,n[tex]\delta[/tex]l,m,
so why in the 2nd correlation there are additional terms after '-'?
This seems really strange, can anybody help me? Thank you.
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