5,650 research outputs found
Comments on "State equation for the three-dimensional system of 'collapsing' hard spheres"
A recent paper [I. Klebanov et al. \emph{Mod. Phys. Lett. B} \textbf{22}
(2008) 3153; arXiv:0712.0433] claims that the exact solution of the
Percus-Yevick (PY) integral equation for a system of hard spheres plus a step
potential is obtained. The aim of this paper is to show that Klebanov et al.'s
result is incompatible with the PY equation since it violates two known cases:
the low-density limit and the hard-sphere limit.Comment: 4 pages; v2: title chang
On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids
The energy route to the equation of state of hard-sphere fluids is
ill-defined since the internal energy is just that of an ideal gas and thus it
is independent of density. It is shown that this ambiguity can be avoided by
considering a square-shoulder interaction and taking the limit of vanishing
shoulder width. The resulting hard-sphere equation of state coincides exactly
with the one obtained through the virial route. Therefore, the energy and
virial routes to the equation of state of hard-sphere fluids can be considered
as equivalent.Comment: 2 page
Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient
As is well known, approximate integral equations for liquids, such as the
hypernetted chain (HNC) and Percus--Yevick (PY) theories, are in general
thermodynamically inconsistent in the sense that the macroscopic properties
obtained from the spatial correlation functions depend on the route followed.
In particular, the values of the fourth virial coefficient predicted by
the HNC and PY approximations via the virial route differ from those obtained
via the compressibility route. Despite this, it is shown in this paper that the
value of obtained from the virial route in the HNC theory is exactly
three halves the value obtained from the compressibility route in the PY
theory, irrespective of the interaction potential (whether isotropic or not),
the number of components, and the dimensionality of the system. This simple
relationship is confirmed in one-component systems by analytical results for
the one-dimensional penetrable-square-well model and the three-dimensional
penetrable-sphere model, as well as by numerical results for the
one-dimensional Lennard--Jones model, the one-dimensional Gaussian core model,
and the three-dimensional square-well model.Comment: 8 pages; 4 figures; v2: slight change of title; proof extended to
multicomponent fluid
Are the energy and virial routes to thermodynamics equivalent for hard spheres?
The internal energy of hard spheres (HS) is the same as that of an ideal gas,
so that the energy route to thermodynamics becomes useless. This problem can be
avoided by taking an interaction potential that reduces to the HS one in
certain limits. In this paper the square-shoulder (SS) potential characterized
by a hard-core diameter , a soft-core diameter and a
shoulder height is considered. The SS potential becomes the HS one
if (i) , or (ii) , or (iii)
or (iv) and . The
energy-route equation of state for the HS fluid is obtained in terms of the
radial distribution function for the SS fluid by taking the limits (i) and
(ii). This equation of state is shown to exhibit, in general, an artificial
dependence on the diameter ratio . If furthermore the limit
is taken, the resulting equation of state for HS
coincides with that obtained through the virial route. The necessary and
sufficient condition to get thermodynamic consistency between both routes for
arbitrary is derived.Comment: 10 pages, 4 figures; v2: minor changes; to be published in the
special issue of Molecular Physics dedicated to the Seventh Liblice
Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic,
June 11-16, 2006
Full-vector analysis of a realistic photonic crystal fiber
We analyze the guiding problem in a realistic photonic crystal fiber using a
novel full-vector modal technique, a biorthogonal modal method based on the
nonselfadjoint character of the electromagnetic propagation in a fiber.
Dispersion curves of guided modes for different fiber structural parameters are
calculated along with the 2D transverse intensity distribution of the
fundamental mode. Our results match those achieved in recent experiments, where
the feasibility of this type of fiber was shown.Comment: 3 figures, submitted to Optics Letter
How `sticky' are short-range square-well fluids?
The aim of this work is to investigate to what extent the structural
properties of a short-range square-well (SW) fluid of range at a
given packing fraction and reduced temperature can be represented by those of a
sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective
stickiness parameter . Such an equivalence cannot hold for the radial
distribution function since this function has a delta singularity at contact in
the SHS case, while it has a jump discontinuity at in the SW case.
Therefore, the equivalence is explored with the cavity function .
Optimization of the agreement between y_{\sw} and y_{\shs} to first order
in density suggests the choice for . We have performed Monte Carlo (MC)
simulations of the SW fluid for , 1.02, and 1.01 at several
densities and temperatures such that , 0.2, and 0.5. The
resulting cavity functions have been compared with MC data of SHS fluids
obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)].
Although, at given values of and , some local discrepancies
between y_{\sw} and y_{\shs} exist (especially for ), the SW
data converge smoothly toward the SHS values as decreases. The
approximate mapping y_{\sw}\to y_{\shs} is exploited to estimate the internal
energy and structure factor of the SW fluid from those of the SHS fluid. Taking
for y_{\shs} the solution of the Percus--Yevick equation as well as the
rational-function approximation, the radial distribution function of the
SW fluid is theoretically estimated and a good agreement with our MC
simulations is found. Finally, a similar study is carried out for short-range
SW fluid mixtures.Comment: 14 pages, including 3 tables and 14 figures; v2: typo in Eq. (5.1)
corrected, Fig. 14 redone, to be published in JC
Large isotope effect on in cuprates despite of a small electron-phonon coupling
We calculate the isotope coefficients and for the
superconducting critical temperature and the pseudogap temperature
in a mean-field treatment of the t-J model including phonons. The
pseudogap phase is identified with the -charge-density wave (-CDW) phase
in this model. Using the small electron-phonon coupling constant obtained previously in LDA calculations in YBaCuO,
is negative but negligible small whereas increases
from about 0.03 at optimal doping to values around 1 at small dopings in
agreement with the general trend observed in many cuprates. Using a simple
phase fluctuation model where the -CDW has only short-range correlations it
is shown that the large increase of at low dopings is rather universal
and does not depend on the existence of sharp peaks in the density of states in
the pseudogap state or on specific values of the phonon cutoff. It rather is
caused by the large depletion of spectral weight at low frequencies by the
-CDW and thus should also occur in other realizations of the pseudogap.Comment: 8 pages, 5 figures, to be publ. in PR
Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-H\"uckel theory
The linearized Debye-H\"uckel theory for liquid state is shown to provide
thermodynamically consistent virial and energy routes for any potential and for
any dimensionality. The importance of this result for bounded potentials is
discussed.Comment: 4 pages, 1 figure; v2: minor change
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