50,929 research outputs found
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
Flavour changing strong interaction effects on top quark physics at the LHC
We perform a model independent analysis of the flavour changing strong
interaction vertices relevant to the LHC. In particular, the contribution of
dimension six operators to single top production in various production
processes is discussed, together with possible hints for identifying signals
and setting bounds on physics beyond the standard model.Comment: Authors corrections (references added
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
Lorentz-violating nonminimal coupling contributions in mesonic hydrogen atoms and generation of photon higher-order derivative terms
We have studied the contributions of Lorentz-violating CPT-odd and CPT-even
nonminimal couplings to the energy spectrum of the mesonic hydrogen and the
higher-order radiative corrections to the effective action of the photon sector
of a Lorentz-violating version of the scalar electrodynamics. By considering
the complex scalar field describes charged mesons (pion or kaon), the
non-relativistic limit of the model allows to attain upper-bounds by analyzing
its contribution to the mesonic hydrogen energy. By using the experimental data
for the strong correction shift and the pure QED transitions , the best upper-bound for the CPT-odd coupling is
and for the CPT-even one is
. Besides, the CPT-odd radiative correction to the
photon action is a dimension-5 operator which looks like a higher-order
Carroll-Field-Jackiw term. The CPT-even radiative contribution to the photon
effective action is a dimension-6 operator which would be a higher-order
derivative version of the minimal CPT-even term of the standard model
extension
Gaussian quantum Monte Carlo methods for fermions
We introduce a new class of quantum Monte Carlo methods, based on a Gaussian
quantum operator representation of fermionic states. The methods enable
first-principles dynamical or equilibrium calculations in many-body Fermi
systems, and, combined with the existing Gaussian representation for bosons,
provide a unified method of simulating Bose-Fermi systems. As an application,
we calculate finite-temperature properties of the two dimensional Hubbard
model.Comment: 4 pages, 3 figures, Revised version has expanded discussion,
simplified mathematical presentation, and application to 2D Hubbard mode
Radial distribution function of penetrable sphere fluids to second order in density
The simplest bounded potential is that of penetrable spheres, which takes a
positive finite value if the two spheres are overlapped, being 0
otherwise. In this paper we derive the cavity function to second order in
density and the fourth virial coefficient as functions of (where is the Boltzmann constant and is the
temperature) for penetrable sphere fluids. The expressions are exact, except
for the function represented by an elementary diagram inside the core, which is
approximated by a polynomial form in excellent agreement with accurate results
obtained by Monte Carlo integration. Comparison with the hypernetted-chain
(HNC) and Percus-Yevick (PY) theories shows that the latter is better than the
former for only. However, even at zero temperature (hard sphere
limit), the PY solution is not accurate inside the overlapping region, where no
practical cancelation of the neglected diagrams takes place. The exact fourth
virial coefficient is positive for , reaches a minimum
negative value at , and then goes to zero from below as
for high temperatures. These features are captured qualitatively,
but not quantitatively, by the HNC and PY predictions. In addition, in both
theories the compressibility route is the best one for , while
the virial route is preferable if .Comment: 10 pages, 2 figures; v2: minor changes; to be published in PR
Strong flavour changing effective operator contributions to single top quark production
We study the effects of dimension six effective operators on the production
of single top quarks at the LHC. The operator set considered includes terms
with effective gluon interactions and four-fermion terms. Analytic expressions
for the several partonic cross sections of single top production will be
presented, as well as the results of their integration on the parton density
functions.Comment: 20 pages, 7 fig
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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