State correlation

The essential characteristic of the equilibrium correlations is that they originate in a system starting from non-correlated states. We recall also that the correct form of the equilibrium correlations can be obtained if one admits that for long times the velocity distribution function takes a Maxwellian form. 

Within our exploratory calculation we will use a simplified description of the contribution of correlated states, considering only the bound state with an effective shift, which reproduces the correlated density. This shift is taken as a quadratic function in the densities, where the linear term is calculated from perturbation theory and the quadratic term is fitted to reproduce the results for the composition as found by the full microscopic calculation including the contribution of scattering states. 

One of the most amazing phenomena in quantum many-particle systems is the formation of quantum condensates. Of particular interest are strongly coupled fermion systems where bound states arise. In the low-density limit, where even-number fermionic bound states can be considered as bosons, Bose-Einstein condensation is expected to occur at low temperatures. The solution of Eq. (6) with = 2/j, gives the onset of pairing, the solution of Eq. (7) with EinP = 4/i the onset of quartetting in (symmetric) nuclear matter. At present, condensates are investigated in systems where the cross-over from Bardeen-Cooper-Schrieffer (BCS) pairing to Bose-Einstein condensation (BEC) can be observed, see [11,12], In these papers, a two-particle state is treated in an uncorrelated medium. Some attempts have been made to include the interaction between correlated states, see [7,13]. 

Fannes, M., Nachtergaele, B., Werner, R.F. Finitely correlated states on quantum spin chains. Comm. Math. Phys. 1992, 144(3), 443. 

The import of diabatic electronic states for dynamical treatments of conical intersecting BO potential energy surfaces is well acknowledged. This intersection is characterized by the non-existence of symmetry element determining its location in nuclear space [25]. This problem is absent in the GED approach. Because the symmetries of the cis and trans conformer are irreducible to each other, a regularization method without a correct reaction coordinate does not make sense. The slope at the (conic) intersection is well defined in the GED scheme. Observe, however, that for closed shell structures, the direct coupling of both states is zero. A configuration interaction is necessary to obtain an appropriate description in other words, correlation states such as diradical ones and the full excited BB state in the AA local minimum cannot be left out the scheme. 

Fisk. Z. et al. Heavy-Electro 11 Metals New Highly Correlated States of Matter,"... 

Figure 2 Peierls distortion of ID atom chains. The diagram shows adjacent chains in the correlated state below 7jq (reproduced by permission from Phys. Rep., 1978,40,203)...

If the energy of the scattered positron is very similar to that of the ejected electron the two particles may emerge in almost the same direction and in a highly correlated state, which can be considered as a continuum... 

Figure 1 Representative valence bond diagrams for benzene, their bit representation using two bits per site, and the integer Ik that encodes these correlated states with six 7r-electrons. The Kekule diagrams 1 > and 2 > are covalent singlets, as is the Dewar diagram 3 >, with one electron at each site. Diagram 4 > is an ionic singlet, while 15 > is a covalent triplet.

The coefficients Ck are real and Skk1 =< k k > is the overlap of normalized VB diagrams with identical electron distributions rij. Normalization illustrates the general problem of finding matrix elements between correlated states. We express an operator in second-quantized notation and consider exact eigenstates i> > and x > that may be in the same or different symmetry subspaces. The matrix elements Akk of A are obtained as shown in (11) to give... 

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