6,660 research outputs found
An efficient variational principle for the direct optimization of excited states
We present a variational function that targets excited states directly based
on their position in the energy spectrum, along with a Monte Carlo method for
its evaluation and minimization whose cost scales polynomially for a wide class
of approximate wave functions. Being compatible with both real and Fock space
and open and periodic boundary conditions, the method has the potential to
impact many areas of chemistry, physics, and materials science. Initial tests
on doubly excited states show that using this method, the Hilbert space Jastrow
antisymmetric geminal power ansatz can deliver order-of-magnitude improvements
in accuracy relative to equation of motion coupled cluster theory, while a very
modest real space multi-Slater Jastrow expansion can achieve accuracies within
0.1 eV of the best theoretical benchmarks for the carbon dimer.Comment: 6 pages, 4 figure
Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory
We present an approach to studying optical band gaps in real solids in which
quantum Monte Carlo methods allow for the application of a rigorous variational
principle to both ground and excited state wave functions. In tests that
include small, medium, and large band gap materials, optical gaps are predicted
with a mean-absolute-deviation of 3.5% against experiment, less than half the
equivalent errors for typical many-body perturbation theories. The approach is
designed to be insensitive to the choice of density functional, a property we
exploit in order to provide insight into how far different functionals are from
satisfying the assumptions of many body perturbation theory. We explore this
question most deeply in the challenging case of ZnO, where we show that
although many commonly used functionals have shortcomings, there does exist a
one particle basis in which perturbation theory's zeroth order picture is
sound. Insights of this nature should be useful in guiding the future
application and improvement of these widely used techniques.Comment: 8 pages, 5 figures, 2 table
Density Functional Extension to Excited-State Mean-Field Theory.
We investigate an extension of excited-state mean-field theory in which the energy expression is augmented with density functional components in an effort to include the effects of weak electron correlations. The approach remains variational and entirely time independent, allowing it to avoid some of the difficulties associated with linear response and the adiabatic approximation. In particular, all of the electrons' orbitals are relaxed state specifically, and there is no reliance on Kohn-Sham orbital energy differences, both of which are important features in the context of charge transfer. Preliminary testing shows clear advantages for single-component charge transfer states, but the method, at least in its current form, is less reliable for states in which multiple particle-hole transitions contribute significantly
A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo
We present a modification to variational Monte Carlo's linear method
optimization scheme that addresses a critical memory bottleneck while
maintaining compatibility with both the traditional ground state variational
principle and our recently-introduced variational principle for excited states.
For wave function ansatzes with tens of thousands of variables, our
modification reduces the required memory per parallel process from tens of
gigabytes to hundreds of megabytes, making the methodology a much better fit
for modern supercomputer architectures in which data communication and
per-process memory consumption are primary concerns. We verify the efficacy of
the new optimization scheme in small molecule tests involving both the Hilbert
space Jastrow antisymmetric geminal power ansatz and real space multi-Slater
Jastrow expansions. Satisfied with its performance, we have added the optimizer
to the QMCPACK software package, with which we demonstrate on a hydrogen ring a
prototype approach for making systematically convergent, non-perturbative
predictions of Mott-insulators' optical band gaps.Comment: 9 pages, 3 tables, 4 figure
Mixed-Criticality Scheduling with I/O
This paper addresses the problem of scheduling tasks with different
criticality levels in the presence of I/O requests. In mixed-criticality
scheduling, higher criticality tasks are given precedence over those of lower
criticality when it is impossible to guarantee the schedulability of all tasks.
While mixed-criticality scheduling has gained attention in recent years, most
approaches typically assume a periodic task model. This assumption does not
always hold in practice, especially for real-time and embedded systems that
perform I/O. For example, many tasks block on I/O requests until devices signal
their completion via interrupts; both the arrival of interrupts and the waking
of blocked tasks can be aperiodic. In our prior work, we developed a scheduling
technique in the Quest real-time operating system, which integrates the
time-budgeted management of I/O operations with Sporadic Server scheduling of
tasks. This paper extends our previous scheduling approach with support for
mixed-criticality tasks and I/O requests on the same processing core. Results
show the effective schedulability of different task sets in the presence of I/O
requests is superior in our approach compared to traditional methods that
manage I/O using techniques such as Sporadic Servers.Comment: Second version has replaced simulation experiments with real machine
experiments, third version fixed minor error in Equation 5 (missing a plus
sign
A new phase space method for recovering index of refraction from travel times
We develop a new phase space method for reconstructing the index of refraction of a medium from travel time measurements. The method is based on the so-called Stefanov–Uhlmann identity which links two Riemannian metrics with their travel time information. We design a numerical algorithm to solve the resulting inverse problem. The new algorithm is a hybrid approach that combines both Lagrangian and Eulerian formulations. In particular the Lagrangian formulation in phase space can take into account multiple arrival times naturally, while the Eulerian formulation for the index of refraction allows us to compute the solution in physical space. Numerical examples including isotropic metrics and the Marmousi synthetic model are shown to validate the new method
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