Application of hard sphere perturbation theory to a high‐temperature binary mixture

1989 ◽  
Vol 90 (12) ◽  
pp. 7395-7402 ◽  
Author(s):  
D. Saumon ◽  
G. Chabrier ◽  
J. J. Weis
Keyword(s):  
Perturbation Theory ◽  
High Temperature ◽  
Binary Mixture ◽  
Hard Sphere

scholarly journals Effective high-temperature estimates for intermittent maps

2017 ◽  
Vol 39 (8) ◽  
pp. 2159-2175
Author(s):  
BENOÎT R. KLOECKNER
Keyword(s):  
Perturbation Theory ◽  
High Temperature ◽  
Limit Theorem ◽  
Spectral Gap ◽  
Lipschitz Constant ◽  
Transfer Operator ◽  
Linear Operators ◽  
Suitable Assumption ◽  
Unimodal Map ◽  
Definition Of

Using quantitative perturbation theory for linear operators, we prove a spectral gap for transfer operators of various families of intermittent maps with almost constant potentials (‘high-temperature’ regime). Hölder and bounded $p$-variation potentials are treated, in each case under a suitable assumption on the map, but the method should apply more generally. It is notably proved that for any Pommeau–Manneville map, any potential with Lipschitz constant less than 0.0014 has a transfer operator acting on $\operatorname{Lip}([0,1])$ with a spectral gap; and that for any two-to-one unimodal map, any potential with total variation less than 0.0069 has a transfer operator acting on $\operatorname{BV}([0,1])$ with a spectral gap. We also prove under quite general hypotheses that the classical definition of spectral gap coincides with the formally stronger one used in Giulietti et al [The calculus of thermodynamical formalism. J. Eur. Math. Soc., to appear. Preprint, 2015, arXiv:1508.01297], allowing all results there to be applied under the high-temperature bounds proved here: analyticity of pressure and equilibrium states, central limit theorem, etc.

scholarly journals Entropy-driven formation of a superlattice in a hard-sphere binary mixture

Nature ◽  
1993 ◽  
Vol 365 (6441) ◽  
pp. 35-37 ◽  
Author(s):  
M. D. Eldridge ◽  
P. A. Madden ◽  
D. Frenkel
Keyword(s):  
Binary Mixture ◽  
Hard Sphere

Phase behavior of binary hard-sphere mixtures from perturbation theory

1999 ◽  
Vol 60 (3) ◽  
pp. 3158-3164 ◽  
Author(s):  
E. Velasco ◽  
G. Navascués ◽  
L. Mederos
Keyword(s):  
Perturbation Theory ◽  
Phase Behavior ◽  
Hard Sphere
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