17,887 research outputs found
Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces
A simple and stable method for computing accurate expectation values of
observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC)
algorithms is presented. The basic idea consists in replacing the usual
``bare'' estimator associated with the observable by an improved or
``renormalized'' estimator. Using this estimator more accurate averages are
obtained: Not only the statistical fluctuations are reduced but also the
systematic error (bias) associated with the approximate VMC or (fixed-node) DMC
probability densities. It is shown that improved estimators obey a
Zero-Variance Zero-Bias (ZVZB) property similar to the usual Zero-Variance
Zero-Bias property of the energy with the local energy as improved estimator.
Using this property improved estimators can be optimized and the resulting
accuracy on expectation values may reach the remarkable accuracy obtained for
total energies. As an important example, we present the application of our
formalism to the computation of forces in molecular systems. Calculations of
the entire force curve of the H,LiH, and Li molecules are presented.
Spectroscopic constants (equilibrium distance) and (harmonic
frequency) are also computed. The equilibrium distances are obtained with a
relative error smaller than 1%, while the harmonic frequencies are computed
with an error of about 10%
Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density
We construct improved quantum Monte Carlo estimators for the spherically- and
system-averaged electron pair density (i.e. the probability density of finding
two electrons separated by a relative distance u), also known as the
spherically-averaged electron position intracule density I(u), using the
general zero-variance zero-bias principle for observables, introduced by
Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by
replacing the average of the local delta-function operator by the average of a
smooth non-local operator that has several orders of magnitude smaller
variance. These new estimators also reduce the systematic error (or bias) of
the intracule density due to the approximate trial wave function. Used in
combination with the optimization of an increasing number of parameters in
trial Jastrow-Slater wave functions, they allow one to obtain well converged
correlated intracule densities for atoms and molecules. These ideas can be
applied to calculating any pair-correlation function in classical or quantum
Monte Carlo calculations.Comment: 13 pages, 9 figures, published versio
Pressure-energy correlations and thermodynamic scaling in viscous Lennard-Jones liquids
We use molecular dynamics simulation results on viscous binary Lennard-Jones
mixtures to examine the correlation between the potential energy and the
virial. In accord with a recent proposal [U. R. Pedersen et. al. Phys. Rev.
Lett. 100, 015701 (2008)], the fluctuations in the two quantities are found to
be strongly correlated, exhibiting a proportionality constant, Gamma,
numerically equal to one-third the slope of an inverse power law approximation
to the intermolecular potential function. The correlation is stronger at higher
densities, where interatomic separations are in the range where the inverse
power law approximation is more accurate. These same liquids conform to
thermodynamic scaling of their dynamics, with the scaling exponent equal to
Gamma. Thus, the properties of strong correlation between energy and pressure
and thermodynamic scaling both reflect the ability of an inverse power law
representation of the potential to capture interesting features of the dynamics
of dense, highly viscous liquids.Comment: 5 pages, 4 figures; published version, one figure remove
Funding Universal Service Obligations with an Essential Facility: Charges vs. Taxes and Subsidies
This paper compares three schemes for funding Universal Service Obligations in network industries with an essential facility: an uplift to the network access charge, the establishment of a Universal Service (US) fund financed through a lump-sum tax and a US fund financed through a unit tax. The comparison is made under a duopoly structure with a potential entrant and an incumbent, which owns the essential facility and is responsible for universal service. The incumbent is also constrained to offer the same price on all markets. Using a social welfare criteria, we show that the US fund financed with a lump sum tax dominates the other two schemes, while the US fund with unit tax is equivalent to the access charge uplift.UNIVERSAL SERVICE OBLIGATIONS; ACCESS CHARGES; REGULATION
Failure of classical elasticity in auxetic foams
A recent derivation [P.H. Mott and C.M. Roland, Phys. Rev. B 80, 132104
(2009).] of the bounds on Poisson's ratio, v, for linearly elastic materials
showed that the conventional lower limit, -1, is wrong, and that v cannot be
less than 0.2 for classical elasticity to be valid. This is a significant
result, since it is precisely for materials having small values of v that
direct measurements are not feasible, so that v must be calculated from other
elastic constants. Herein we measure directly Poisson's ratio for four
materials, two for which the more restrictive bounds on v apply, and two having
values below this limit of 0.2. We find that while the measured v for the
former are equivalent to values calculated from the shear and tensile moduli,
for two auxetic materials (v < 0), the equations of classical elasticity give
inaccurate values of v. This is experimental corroboration that the correct
lower limit on Poisson's ratio is 0.2 in order for classical elasticity to
apply.Comment: 9 pages, 2 figure
Are polar liquids less simple?
Strong correlation between equilibrium fluctuations of the potential energy,
U, and the virial, W, is a characteristic of a liquid that implies the presence
of certain dynamic properties, such as density scaling of the relaxation times
and isochronal superpositioning of the relaxation function. In this work we
employ molecular dynamics simulations (mds) on methanol and two variations,
lacking hydrogen bonds and a dipole moment, to assess the connection between
the correlation of U and W and these dynamic properties. We show, in accord
with prior results of others [T.S. Ingebrigtsen, T.B. Schroder, J.C. Dyre,
Phys. Rev. X 2, 011011 (2012).], that simple van der Waals liquids exhibit both
strong correlations and the expected dynamic behavior. However, for polar
liquids this correspondence breaks down - weaker correlation between U and W is
not associated with worse conformance to density scaling or isochronal
superpositioning. The reason for this is that strong correlation between U and
W only requires their proportionality, whereas the expected dynamic behavior
depends primarily on constancy of the proportionality constant for all state
points. For hydrogen-bonded liquids, neither strong correlation nor adherence
to the dynamic properties is observed; however, this nonconformance is not
directly related to the concentration of hydrogen bonds, but rather to the
greater deviation of the intermolecular potential from an inverse power law
(IPL). Only (hypothetical) liquids having interactions governed strictly by an
IPL are perfectly correlating and exhibit the consequent dynamic properties
over all thermodynamic conditions.Comment: 14 pages, 8 figure
Renormalization of the electron-phonon coupling in the one-band Hubbard model
We investigate the effect of electronic correlations on the coupling of
electrons to Holstein phonons in the one-band Hubbard model. We calculate the
static electron-phonon vertex within linear response of Kotliar-Ruckenstein
slave-bosons in the paramagnetic saddle-point approximation. Within this
approach the on-site Coulomb interaction U strongly suppresses the coupling to
Holstein phonons at low temperatures. Moreover the vertex function does not
show particularly strong forward scattering. Going to larger temperatures
kT\sim t we find that after an initial decrease with U, the electron-phonon
coupling starts to increase with U, confirming a recent result of Cerruti,
Cappelluti, and Pietronero. We show that this behavior is related to an unusual
reentrant behavior from a phase separated to a paramagnetic state upon
decreasing the temperature.Comment: 4 pages, 6 figure
Interference Phenomena in Medium Induced Radiation
We consider the interference pattern for the medium-induced gluon radiation
produced by a color singlet quark-antiquark antenna embedded in a QCD medium
with size and `jet quenching' parameter . Within the BDMPS-Z
regime, we demonstrate that, for a dipole opening angle , the interference between the
medium--induced gluon emissions by the quark and the antiquark is suppressed
with respect to the direct emissions. This is so since direct emissions are
delocalized throughout the medium and thus yield contributions proportional to
while interference occurs only between emissions at early times, when both
sources remain coherent. Thus, for \tqq \gg\theta_c, the medium-induced
radiation is the sum of the two spectra individually produced by the quark and
the antiquark, without coherence effects like angular ordering. For \tqq
\ll\theta_c, the medium--induced radiation vanishes.Comment: 4 pages, 2 figures; Proceedings of the "Quark Matter 2011" conferenc
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