Local and global properties of mixtures in one-dimensional systems. II. Exact results for the Kirkwood–Buff integrals

2009 ◽  
Vol 131 (16) ◽  
pp. 164512 ◽  
Author(s):  
Arieh Ben-Naim ◽  
Andrés Santos
Keyword(s):  
Exact Results ◽  
One Dimensional ◽  
Global Properties

Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology

1980 ◽  
Vol 22 (2) ◽  
pp. 477-496 ◽  
Author(s):  
J. F. Currie ◽  
J. A. Krumhansl ◽  
A. R. Bishop ◽  
S. E. Trullinger
Keyword(s):  
Solitary Wave ◽  
Statistical Mechanics ◽  
Scalar Fields ◽  
Ideal Gas ◽  
Exact Results ◽  
One Dimensional

scholarly journals Density-density correlations in a Luttinger liquid: Lattice approximation in the Calogero-Sutherland model

1999 ◽  
Vol 77 (5) ◽  
pp. 327-341 ◽  
Author(s):  
D Sen ◽  
R K Bhaduri
Keyword(s):  
Luttinger Liquid ◽  
Exact Results ◽  
Dimensional Model ◽  
Lattice Method ◽  
One Dimensional ◽  
Density Correlation ◽  
Time Correlations ◽  
Sutherland Model ◽  
Lattice Approximation ◽  
Density Correlations

For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice were used by Krivnov and Ovchinnikov to compute the ground-state wave function and the dynamical density-density correlations. We review this method, and apply it to the Calogero-Sutherland model, whose density-density correlation functions are exactly known for certain values of the coupling constant. We show numerically that the correlations obtained are quite accurate even if the coupling is not very large. Such comparisons have been made earlier by Forrester. The lattice method is considerably simpler than the ones used to derive the exact results, and yields expressions for the correlations- which are easily plotted. The equal-time correlations can be expanded in inverse powers of coupling; we show that the two leading order terms agree with the exact results which are known for integer values of the coupling. The strength-dependent power law fall-off is typical of a Luttinger liquid.In a general one-dimensional model where the two-body interaction decreases as a power of the relative distance, we argue, following Schulz, that at zero temperature the system behaves as a Luttinger liquid if the power exceeds 1, and as a Wigner crystal if it is less than 1.PACS Nos.: 63.20-e, 71.10Pm

Exact results for quantum chaotic systems and one-dimensional fermions from matrix models

1993 ◽  
Vol 409 (3) ◽  
pp. 487-508 ◽  
Author(s):  
B.D. Simons ◽  
P.A. Lee ◽  
B.L. Altshuler
Keyword(s):  
Matrix Models ◽  
Chaotic Systems ◽  
Exact Results ◽  
One Dimensional

scholarly journals Exact results for the one-dimensional self-organized critical forest-fire model

1993 ◽  
Vol 71 (23) ◽  
pp. 3739-3742 ◽  
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Forest Fire ◽  
Exact Results ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One
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