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The Thirty-First foreign Workshop on Condensed topic Theories (CMT31) held in Bangkok desirous about the numerous roles performed via ab initio thought, modeling, and high-performance computing in condensed subject and fabrics technological know-how, supplying a discussion board for the dialogue of modern advances and exploration of recent difficulties. Fifty-six invited papers have been offered, of which 38 look as chapters during this quantity. studies of contemporary effects generated full of life debate on two-dimensional electron platforms, the metal-insulator transition, dilute magnetic semiconductors, results of sickness, magnetoresistence phenomena, ferromagnetic stripes, quantum corridor structures, strongly correlated Fermi platforms, superconductivity, dilute fermionic and bosonic gases, nanostructured fabrics, plasma instabilities, quantum fluid combos, and helium in lowered geometries.
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Ri−1 ; t) are the time-dependent i-body densities. The one-body equation is simply the (complex) continuity equation ∇0 j(r0 , t) + δ ρ˙ 1 (r0 , t) = 0 , (11) where δρ1 (r0 , t) and j(r0 , t) are functionals of δu1 , δu2 and δu3 given by δρ1 (r0 ; t) ≡ ρ1 (r0 ) δu1 (r0 ; t) + + 1 2 d3 ρ1 g2 (r0 , r1 )δu2 (r0 , r1 ; t) d3 ρ1 d3 ρ2 g3 (r0 , r1 , r2 )δu3 (r0 , r1 , r2 ; t) (12) and j1 (r0 ; t) ≡ = ΨIN +1 ˆjI (r0 )δU ΨIN +1 ΨIN +1 | ΨIN +1 2mI i ρ1 (r0 ) ∇0 δu1 (r0 ; t) + + 1 2 d3 ρ1 g2 (r0 , r1 )∇0 δu2 (r0 , r1 ; t) d3 ρ1 d3 ρ2 g3 (r0 , r1 , r2 )∇0 δu3 (r0 , r1 , r2 ; t) .
8. K. E. K¨ urten and M. L. Ristig, Phys. Rev. B 37, 3359 (1988). 9. K. E. K¨ urten and M. L. Ristig, Phys. Rev. B 31, 1346 (1985). 10. K. A. Gernoth, M. L. Ristig and T. Lindenau, Int. J. Mod. Phys. 21, 257 (2007); in Condensed Matter Theories, Vol. 22, edited by H. Reinholz, G. R¨ opke and M. de Llano (World Scientific, Singapore, 2007), pp. 117–128. 11. K. A. Gernoth, Ann. Phys. ) 285, 61 (2000); Ann. Phys. ) 291, 202 (2001); Z. Kristallogr. 218, 651 (2003). 12. I. Silvera and V. Goldman, J.
Vˆnl , [H (19) For a theory to be gauge invariant, all operators in the Hamiltonian must transform appropriately. This can be accomplished by postulating that the projector functions transform as r − Ri P A,(i) m → r − Ri P A ,(i) m = e−i e χ(r) r − Ri P A,(i) m . (20) Then, the non-local potential operator (17) is a gauge invariant, and, hence, the non-local part of the potential transforms under gauge transformation like e e Vˆnl (r, r ) → Vˆnl (r, r ) = e−i χ(r) Vˆnl (r, r )ei χ(r) = e−i e (i) vnl (r − Ri , r − Ri )ei χ(r) i e χ(r) .