6,025 research outputs found
Structure of hard-hypersphere fluids in odd dimensions
The structural properties of single component fluids of hard hyperspheres in
odd space dimensionalities are studied with an analytical approximation
method that generalizes the Rational Function Approximation earlier introduced
in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A
{\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial
distribution function to first order in density and extends it to finite
density by assuming a rational form for a function defined in Laplace space,
the coefficients being determined by simple physical requirements. Fourier
transform in terms of reverse Bessel polynomials constitute the mathematical
framework of this approximation, from which an analytical expression for the
static structure factor is obtained. In its most elementary form, the method
recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike
equation for hyperspheres at odd dimension. The present formalism allows one to
go beyond by yielding solutions with thermodynamic consistency between the
virial and compressibility routes to any desired equation of state. Excellent
agreement with available computer simulation data at and is
obtained. As a byproduct of this study, an exact and explicit polynomial
expression for the intersection volume of two identical hyperspheres in
arbitrary odd dimensions is given.Comment: 18 pages, 7 figures; v2: new references added plus minor changes; to
be published in PR
Long-Range Correlations in Self-Gravitating N-Body Systems
Observed self-gravitating systems reveal often fragmented non-equilibrium
structures that feature characteristic long-range correlations. However, models
accounting for non-linear structure growth are not always consistent with
observations and a better understanding of self-gravitating -body systems
appears necessary. Because unstable gravitating systems are sensitive to
non-gravitational perturbations we study the effect of different dissipative
factors as well as different small and large scale boundary conditions on
idealized -body systems. We find, in the interval of negative specific heat,
equilibrium properties differing from theoretical predictions made for
gravo-thermal systems, substantiating the importance of microscopic physics and
the lack of consistent theoretical tools to describe self-gravitating gas.
Also, in the interval of negative specific heat, yet outside of equilibrium,
unforced systems fragment and establish transient long-range correlations. The
strength of these correlations depends on the degree of granularity, suggesting
to make the resolution of mass and force coherent. Finally, persistent
correlations appear in model systems subject to an energy flow.Comment: 20 pages, 21 figures. Accepted for publication in A&
Equation of state for five-dimensional hyperspheres from the chemical-potential route
We use the Percus-Yevick approach in the chemical-potential route to evaluate
the equation of state of hard hyperspheres in five dimensions. The evaluation
requires the derivation of an analytical expression for the contact value of
the pair distribution function between particles of the bulk fluid and a solute
particle with arbitrary size. The equation of state is compared with those
obtained from the conventional virial and compressibility thermodynamic routes
and the associated virial coefficients are computed. The pressure calculated
from all routes is exact up to third density order, but it deviates with
respect to simulation data as density increases, the compressibility and the
chemical-potential routes exhibiting smaller deviations than the virial route.
Accurate linear interpolations between the compressibility route and either the
chemical-potential route or the virial one are constructed.Comment: 9 pages, 6 figures; v2: Change in one referenc
Geometrical effects on energy transfer in disordered open quantum systems
We explore various design principles for efficient excitation energy
transport in complex quantum systems. We investigate energy transfer efficiency
in randomly disordered geometries consisting of up to 20 chromophores to
explore spatial and spectral properties of small natural/artificial
Light-Harvesting Complexes (LHC). We find significant statistical correlations
among highly efficient random structures with respect to ground state
properties, excitonic energy gaps, multichromophoric spatial connectivity, and
path strengths. These correlations can even exist beyond the optimal regime of
environment-assisted quantum transport. For random configurations embedded in
spatial dimensions of 30 A and 50 A, we observe that the transport efficiency
saturates to its maximum value if the systems contain 7 and 14 chromophores
respectively. Remarkably, these optimum values coincide with the number of
chlorophylls in (Fenna-Matthews-Olson) FMO protein complex and LHC II monomers,
respectively, suggesting a potential natural optimization with respect to
chromophoric density.Comment: 11 pages, 10 figures. Expanded from the former appendix to
arXiv:1104.481
Energy non-equipartition in multicomponent granular mixtures
We study non-equipartition of energy in granular fluids composed by an
arbitrarily large number of components. We focus on a simple mean field model,
based upon a Maxwell collision operator kernel, and predict the temperature
ratios for the species. Moreover, we perform Direct Monte Carlo simulations in
order to verify the predictions.Comment: submitted to PR
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