Search results for "Method"
showing 10 items of 13253 documents
Monte Carlo simulation approach for a quantitative characterization of the band edge in InGaN quantum wells
2005
Monte Carlo simulation approach based on exciton hopping through randomly distributed localized states is proposed for quantitative characterization of the band edge of InxGa1–xN/GaN multiple quantum wells with different indium content (x ≈ 0.22–0.27). The band edge dynamics is investigated in the 10–300 K range by analyzing the measured S- and W-shaped temperature behavior of the photoluminescence peak position and linewidth, respectively. The simulation of the W-shaped temperature dependence using double-scaled potential profile model enabled us to estimate the scale of the potential fluctuations due to variation of indium content inside and among In-rich regions formed in InGaN alloy. In…
Monte Carlo Simulations of Alloy Phase Transformations
1994
The use of Monte Carlo simulation methods for study of order-disorder phase transitions in lattice models of alloys is reviewed, with an emphasis on interfacial phenomena and the kinetics of ordering and/or phase separation. Topics discussed include the attempt to predict the phase diagram of Fe-Al alloys from recent measurements of effective interaction parameters, competition between magnetic and crystallographic ordering in such alloys, and the structure of their antiphase domain boundaries. Both an interfacial roughening transition of this domain wall and interfacial enrichment phenomena are predicted. Then simulations of alloy-vacuum surfaces are discussed, and it is shown that both ca…
Exact and Variational Treatment of Ferroelectric Thin Films with Different Materials of Electrodes
2005
We trace the influence of metallic electrodes on the properties of thin ferroelectric films. This has been done in the framework of the phenomenological Landau theory. We present both exact analytical solution of the problem in terms of Weierstrass elliptic functions and the variational solution. We calculate polarization, dielectric susceptibility, pyroelectric coefficient and depolarization field. We have shown that the ferroelectric phase of the film can be destroyed by the choice of material of electrodes with screening length exceeding some critical value. This demonstrates that we can control the physical properties of thin ferroelectric films by the proper choice of the electrode mat…
Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey
2019
This paper provides an overview of numerical methods in order to solve fuzzy equations (FEs). It focuses on different numerical methodologies to solve FEs, dual fuzzy equations (DFEs), fuzzy differential equations (FDEs) and partial fuzzy differential equations (PFDEs). The solutions which are produced by these equations are taken to be the controllers. This paper also analyzes the existence of the roots of FEs and some important implementation problems. Finally, several examples are reviewed with different methods.
Quasi-continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature
2013
We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard mo…
Hartree-Fock-Bogoliubov theory of polarized Fermi systems
2008
Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory or Hartree-Fock-Bogoliubov (HFB) theory. We discuss the method based on introducing two chemical potentials for different superfluid components, whereby one may change the particle-number parity of the underlying quasiparticle vacuum. Formally, this method is a variant of non-collective cranking, and the procedure is equivalent to the so-called blocking. We present and exemplify relations between the two-chemical-potential method and the cranking approxi…
Néel Transition of Lattice Fermions in a Harmonic Trap: A Real-Space Dynamic Mean-Field Study
2010
We study the magnetic ordering transition for a system of harmonically trapped ultracold fermions with repulsive interactions in a cubic optical lattice, within a real-space extension of dynamical mean-field theory. Using a quantum Monte Carlo impurity solver, we establish that antiferromagnetic correlations are signaled, at strong coupling, by an enhanced double occupancy. This signature is directly accessible experimentally and should be observable well above the critical temperature for long-range order. Dimensional aspects appear less relevant than naively expected.
Mott transitions in ternary flavor mixtures of ultracold fermions on optical lattices
2009
Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal, repulsive on-site interactions U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a ``semi-compressible'' state observed for large U near half filling.
Orbital-selective Mott transitions in two-band Hubbard models
2006
The anisotropic two-orbital Hubbard model is investigated at low temperatures using high-precision quantum Monte Carlo (QMC) simulations within dynamical mean-field theory (DMFT). We demonstrate that two distinct orbital-selective Mott transitions (OSMTs) occur for a bandwidth ratio of 2 even without spin-flip contributions to the Hund exchange, and we quantify numerical errors in earlier QMC data which had obscured the second transition. The limit of small inter-orbital coupling is introduced via a new generalized Hamiltonian and studied using QMC and Potthoff's self-energy functional method, yielding insight into the nature of the OSMTs and the non-Fermi-liquid OSM phase and opening the p…
Efficiency of quantum Monte Carlo impurity solvers for dynamical mean-field theory
2007
Since the inception of the dynamical mean-field theory, numerous numerical studies have relied on the Hirsch-Fye quantum Monte Carlo (HF-QMC) method for solving the associated impurity problem. Recently developed continuous-time algorithms (CT-QMC) avoid the Trotter discretization error and allow for faster configuration updates, which makes them candidates for replacing HF-QMC. We demonstrate, however, that a state-of-the-art implementation of HF-QMC (with extrapolation of discretization delta_tau -> 0) is competitive with CT-QMC. A quantitative analysis of Trotter errors in HF-QMC estimates and of appropriate delta_tau values is included.