(Infinite) boundary corrections for the LMBW-equations and the TZ-formula of surface tension in the presence of spontaneous symmetry breaking

Requardt, Manfred; Wagner, Heinz-Jürgen

doi:10.1016/0378-4371(88)90187-2

Cited by 10 publications

(5 citation statements)

References 27 publications

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“…We already emphasized in [11] the important point that the interchange of limits in the derivation of the LMBW equation may be a delicate matter, as the various limits might behave in a highly nonuniform way. Here we have seen that in the canonical ensemble such nonuniform behavior is even indispensable in order to have meaningful thermodynamic limit states!…”

Section: Conclusion 22 In Case Of An Ideal Hard Wall the Lmbw Equatimentioning

confidence: 99%

“…Concerning this particular important point, we had an interesting discussion with R. Lovett some time ago ( [14]; see also [15]). He told us that [15] was in part influenced by our earlier work in [11] (see in particular section 5.3 of [15] to get a feeling of the epistemological problems underlying the need to perform a thermodynamic limit).…”

Section: The First Lmbw Equation In the Canonical Ensemblementioning

confidence: 99%

“…In [11] we started from the so-called Kubo-Martin-Schwinger (KMS) property of equilibrium systems which holds in finite as well as in infinite systems. We showed that both the BBGKY hierarchy and the first LMBW hierarchy emerge rigorously as the two opposite ends of one and the same scaling procedure, as long as certain cluster properties are fulfilled.…”

Section: The First Lmbw Equation In the Canonical Ensemblementioning

confidence: 99%

“…As a particular result of [11] it turns out that for finite systems held together by an explicit containing potential of the sort described above, the first LMBW equation rigorously holds in the canonical ensemble case (provided the containing potential is correctly dealt with). That is, we have for the first member of the hierarchy:…”

Section: The First Lmbw Equation In the Canonical Ensemblementioning

confidence: 99%

“…In [11] we discussed in quite some detail what can happen if there exist longrange correlations in the system or in the interface between coexisting phases (as, for example, for vanishing gravitational field in the liquid-gas interface). We note that one cannot avoid these problems by making the calculations in finite systems and passing to the thermodynamic limit afterwards.…”

Section: Introductionmentioning

confidence: 99%

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Modifications of the Ornstein–Zernike relation and the LMBW equations in the canonical ensemble via Hilbert-space methods

Requardt

Wagner

2004

J. Phys.: Condens. Matter

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Application of the density functional formalism to the canonical ensemble is of practical interest in cases where there is a marked difference between, say, the canonical and the grand canonical ensemble (cavities or pores). An important role is played by the necessary modification of the famous Ornstein-Zernike relation between pair correlation and direct correlation function, as the former is no longer invertible in a strict sense in (finite) canonical ensembles. Here we approach the problem from a different direction which may complement the density functional approach. In particular, we develop rigorous canonical ensemble versions of the LMBW equations, relating density gradient and exterior potential in the presence of explicit (singular) containing potentials. This is accomplished with the help of integral operator and Hilbert space methods, yielding among other things representations of the direct correlation function on certain subspaces. The results are particularly noteworthy and transparent if the segregating potential is a linear (gravitational) one. In that case the modifications in the LMBW equations can be expressed as pure, seemingly non-local integrations over the container boundaries.

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Section: Conclusion 22 In Case Of An Ideal Hard Wall the Lmbw Equatimentioning

confidence: 99%