616,019 research outputs found
Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum.
We develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons
Monte Carlo techniques for real-time quantum dynamics
The stochastic-gauge representation is a method of mapping the equation of
motion for the quantum mechanical density operator onto a set of equivalent
stochastic differential equations. One of the stochastic variables is termed
the "weight", and its magnitude is related to the importance of the stochastic
trajectory. We investigate the use of Monte Carlo algorithms to improve the
sampling of the weighted trajectories and thus reduce sampling error in a
simulation of quantum dynamics. The method can be applied to calculations in
real time, as well as imaginary time for which Monte Carlo algorithms are
more-commonly used. The method is applicable when the weight is guaranteed to
be real, and we demonstrate how to ensure this is the case. Examples are given
for the anharmonic oscillator, where large improvements over stochastic
sampling are observed.Comment: 28 pages, submitted to J. Comp. Phy
Lattice simulations of real-time quantum fields
We investigate lattice simulations of scalar and nonabelian gauge fields in
Minkowski space-time. For SU(2) gauge-theory expectation values of link
variables in 3+1 dimensions are constructed by a stochastic process in an
additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and
the use of a tilted real-time contour leads to converging results in general.
All fixed point solutions are shown to fulfil the infinite hierarchy of
Dyson-Schwinger identities, however, they are not unique without further
constraints. For the nonabelian gauge theory the thermal equilibrium fixed
point is only approached at intermediate Langevin-times. It becomes more stable
if the complex time path is deformed towards Euclidean space-time. We analyze
this behavior further using the real-time evolution of a quantum anharmonic
oscillator, which is alternatively solved by diagonalizing its Hamiltonian.
Without further optimization stochastic quantization can give accurate
descriptions if the real-time extend of the lattice is small on the scale of
the inverse temperature.Comment: 36 pages, 15 figures, Late
Embedded Network Test-Bed for Validating Real-Time Control Algorithms to Ensure Optimal Time Domain Performance
The paper presents a Stateflow based network test-bed to validate real-time
optimal control algorithms. Genetic Algorithm (GA) based time domain
performance index minimization is attempted for tuning of PI controller to
handle a balanced lag and delay type First Order Plus Time Delay (FOPTD)
process over network. The tuning performance is validated on a real-time
communication network with artificially simulated stochastic delay, packet loss
and out-of order packets characterizing the network.Comment: 6 pages, 12 figure
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