Diffusion Monte Carlo Simulations Research Articles

Ground-state properties of a quasi-one-dimensional electron gas within a dynamical self-consistent mean-field approximation

The ground-state properties of the quasi-one-dimensional electron gas are determined theoretically within the quantum/dynamical version of the self-consistent mean-field approximation of Singwi, Tosi, Land, and Sj\"olander (the so-called qSTLS approach). The transverse motion of electrons is assumed to be confined by a harmonic potential. The calculated static structure factor, pair-correlation function, and correlation energy are compared directly with the recent findings of lattice regularized diffusion Monte Carlo simulation study due to Casula et al. It has been found that the qSTLS results are overall in better agreement with the simulation data than the predictions based upon static mean-field theories. Results for the dynamic local-field correction, dynamic structure factor, and plasmon excitation energy are also reported. The qSTLS approach is found to yield an inadequate description of the dynamic properties; for instance, the dynamic structure factor was seen to become negative over a range of frequencies. Our theoretical predictions, seen in conjunction with similar studies on the three- and two-dimensional electron systems, lead us to conclude that the correlation effects are relatively more pronounced in one-dimensional electron gas.

Bose condensation of two-dimensional dipolar excitons: Simulation by the quantum Monte Carlo method

The Bose condensation of two-dimensional dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system.

Modeling diffusion on heterogeneous lattices: Simple cubic lattice

In our previous work, general analytical expressions for the chemical and jump diffusion coefficients have been derived in the case of strong inhomogeneity for lattices of different symmetries and dimensionalities. It has been shown that the character of the particle migration depends crucially on the relative jump frequencies of particles located in deep and shallow sites. If these frequencies differ insignificantly, particle diffusion proceeds by single uncorrelated jumps, while widely differing jump frequencies result in pairs of strongly correlated jumps. We have checked the expressions for the case of square inhomogeneous lattice using kinetic Monte Carlo simulations. Here, we present results of particle migration over three-dimensional inhomogeneous simple cubic lattice. The density dependences obtained by the analytical expressions for different temperatures and signs of the lateral pairwise interaction are compared with the results of the direct kinetic Monte Carlo simulations of the particle diffusion. Almost perfect agreement between the respective results has been found.

Improved quantum hard-sphere ground-state equations of state

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a "sphere-of-influence" picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Padé and other approximants, but whose ultimate density is irregular or random closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L -expansion data for two-component fermions.

Simulation of laser-induced nanopattern formation

Over the last decade it has been shown theoretically and experimentally that a near-resonant standing wave light field can be used during deposition to deflect collimated neutral atoms, thereby constraining them to form periodic structures. Another effect studied in recent experiments is that a laser interference pattern in contact with a substrate can also result in patterns mimicking the interference fringes. This patterning has tentatively been attributed to thermal gradients resulting from non-uniform heating induced by the interference patterns. We developed a model and a computer program to investigate the possibility of making these two laser effects interact constructively to refine the resolution. The simulations proceed in two stages: first, atom trajectories in a laser field are simulated using classical-mechanical equations of motion in an effective potential to obtain the deposition profile; then, the obtained profile is used as an input in a kinetic Monte Carlo (KMC) simulation of atom diffusion on a substrate with spatially varying temperature. Our results show substantial improvement in quality of the patterns compared to that achieved by using either effect alone. We examine many growth conditions in addition to the different laser parameter settings for optimal constructive interference of the two effects. The computer code used in the simulations is designed to run efficiently on both simple PC platforms and supercomputers; its design, data structures used and other features are described in detail.

Three-dimensional Monte Carlo simulations of intracellular diffusion and reaction of signaling proteins

We show that the Monte Carlo technique makes it possible to perform three-dimensional simulations of intracellular protein-mediated signal transduction with realistic ratio of the rates of protein diffusion and association with genes. Specifically, we illustrate that in the simplest case when the protein degradation and phosphorylation/dephosphorylation are negligible the distribution of the first passage time for this process is close to exponential provided that the number of target genes is between 1 and 100.

Energetics and Structure of Small Para-Hydrogen Clusters

Quantum diffusion Monte Carlo simulations have been performed to systematically analyze the energetics and structure of (p-H2)N clusters with N=3–50 molecules, with the aim of finding signals of magic sizes and discerning the cluster structure. The analysis of the calculated chemical potential as a function of N provides a definitive confirmation of the magic size N=13. The calculations show that (p-H2)N clusters exhibit a clear geometrical order, which excludes considering them as liquid droplets.

Stereographic Projection Diffusion Monte Carlo (SPDMC) Algorithms for Molecular Condensed Matter

We develop and test three algorithms for diffusion Monte Carlo simulations in non-Euclidean manifolds. The methods are based on the construction of the "velocity" distribution by rejection techniques and are capable of functioning in a broad class of non-Euclidean spaces generated by holonomic constraints. The formulation of the propagator for non-Euclidean manifolds avoids the use of Lagrange multipliers; it is derived instead from the Feynman quantization in manifolds proposed by DeWitt. The manifolds are mapped onto Rd by using stereographic projection coordinates. Numerical tests are conducted for the particle in a ring of unit radius subjected to a sinusoidal potential, for the electron in the field of an infinitely massive proton, and for a water molecule modeled as an asymmetric top subjected to an external field.

Renormalized mean-field theory for a two-component Fermi gas withs-wave interactions

A method is introduced to renormalize the zero-range interaction for use in mean-field and many-body theory, starting from two-body calculations. The density-renormalized delta-function interaction is then applied using mean-field theory to a two-component fermion gas, and compared with diffusion Monte Carlo simulations and conventional mean-field calculations. In the unitarity limit, the equation of state exhibits the expected behavior $\mu\propto\rho^{2/3}$, with a parameter $\beta= -0.492$, which is consistent with recent experiments \cite{partridge2006pap, bourdel2004esb, kinast2005hcs, Stewart06}.

Computer-built polyethylene spherulites for mesoscopic Monte Carlo simulation of penetrant diffusion: Influence of crystal widening and thickening

An algorithm able to mimic crystal lengthening, branching, widening and thickening was developed in order to build spherulites similar to those observed in polyethylene. The ranges of volume crystallinity and crystal width-to-thickness ratio attainable were ≤40% and 8–35, respectively. An on-lattice Monte Carlo-based algorithm was used to generate penetrant trajectories in the built spherulites. Diffusivity was assessed from the mean-square displacement of the penetrant molecules, normalized with respect to the mean-square displacement of the penetrant molecules in a crystal-free system, and compared with the geometrical impedance factor calculated from the Fricke theory using morphological data samples in the simulated spherulites. The crystal blocking effect was greater in the tangential plane than along the spherulite radius. All data, except that for the highest crystallinity system (40%), conformed to a linear relationship between the geometrical impedance factor obtained from the diffusivity data and the geometrical impedance factor calculated from morphological data; the latter being calculated according to the Fricke model using averages based on the squares of the crystal width-to-thickness ratio data. This finding suggests that wide crystals had a more pronounced effect on the geometrical impedance factor than was indicated by their number fraction weight. The system with the highest volume crystallinity (40%) showed a markedly higher geometrical impedance factor than predicted by the Fricke theory using the two aforementioned modifications.

Coherent and incoherent SHG in fibrillar cellulose matrices

Second Harmonic Generation (SHG) microscopy probes the organization of tissue or material structure through morphological and polarization analyses. In terms of diagnostic or analytical potential, it is important to understand the coherent and incoherent aspects of the emission in highly scattering environments. It is also of fundamental importance whether the SHG polarization signatures are retained in such turbid media. We examine these issues for purified cellulose specimens, which, in analogy to structural proteins, comprise highly birefringent and chiral fibrillar structures. In these matrices we observe predominantly coherent forward directed emission as well as backwards contrast consisting of direct, coherent emission and an incoherent component arising from multiply scattered forward directed SHG. These processes display a pronounced depth dependence evidenced by changes in morphology as well in the measured forward-backwards ratio (F/B). Specifically, from regions near the surface the backwards channel displays small fibrils not present in the forward emission. In addition, at depths beyond one mean free path, the fibril morphologies become highly similar, suggesting the observed backwards contrast is also comprised of a component that arises from multiple scattering of the initially forward directed wave. The depth dependence of the forward to backward ratio is consistent with Monte Carlo simulations of photon diffusion based on the measured scattering coefficient mus of 75 cm-1 and anisotropy factor, g=0.94 at the SHG wavelength. Consistent with the experimental observations, these simulations indicate that the backwards channel becomes increasingly incoherent with increasing depth into the specimen. We also demonstrate that the polarization dependence of the SHG can be measured through 500 microm of thickness. Similarly, the SHG signal anisotropy is largely preserved through this depth with only a slight depolarization being observed.

Determination of fluence rate and temperature distributions in the rat brain; implications for photodynamic therapy

Light and heat distributions are measured in a rat glioma model used in photodynamic therapy. A fiber delivering 632-nm light is fixed in the brain of anesthetized BDIX rats. Fluence rates are measured using calibrated isotropic probes that are positioned stereotactically. Mathematical models are then used to derive tissue optical properties, enabling calculation of fluence rate distributions for general tumor and light application geometries. The fluence rates in tumor-free brains agree well with the models based on diffusion theory and Monte Carlo simulation. In both cases, the best fit is found for absorption and reduced scattering coefficients of 0.57 and 28 cm(-1), respectively. In brains with implanted BT(4)C tumors, a discrepancy between diffusion and Monte Carlo-derived two-layer models is noted. Both models suggest that tumor tissue has higher absorption and less scattering than normal brain. Temperatures are measured by inserting thermocouples directly into tumor-free brains. A model based on diffusion theory and the bioheat equation is found to be in good agreement with the experimental data and predict a thermal penetration depth of 0.60 cm in normal rat brain. The predicted parameters can be used to estimate the fluences, fluence rates, and temperatures achieved during photodynamic therapy.

QUANTUM MONTE CARLO STUDY OF OVERPRESSURIZED LIQUID 4He AT ZERO TEMPERATURE

We present a diffusion Monte Carlo simulation of metastable superfluid 4 He at zero temperature and pressures beyond freezing (~ 25 bar) up to 275 bar. The equation of state of liquid 4 He is extended to the overpressurized regime, where the pressure dependence of the static structure factor and the condensate fraction is obtained. Along this large pressure range, excited-state energy corresponding to the roton has been determined using the release-node technique. Our results show that both the roton energies and the condensate fraction decrease with increasing pressure but do not become zero. We compare our calculations to recent experimental data in overpressurized regime.

Multi-scale modeling of hydrogen isotope transport in porous graphite

We describe a general multi-scale method to model hydrogen isotope transport, over length scales from angstroms to centimeters and time scales from picoseconds to several seconds, in a complex three-dimensional porous geometry using molecular dynamics, kinetic Monte Carlo and Monte Carlo diffusion simulations. we present comparisons with experimental results for hydrogen diffusion and hydrogen atom desorption from graphite. Finally, we demonstrate the flexibility of the computational tools used to tackle problems at different scales.

Transverse dielectric matrix and shear mode dispersion in strongly coupled electronic bilayer liquids

The authors develop a transverse dielectric matrix and from it they calculate the shear mode dispersion in strongly coupled charged-particle bilayer liquids in the T=0 quantum domain. The formulation is based on the classical quasilocalized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development parallels and complements the development of a similarly extended longitudinal dielectric matrix formalism reported in a recent companion work [K. I. Golden, H. Mahassen, G. J. Kalman, G. Senatore, and F. Rapisarda, Phys. Rev. E 71, 036401 (2005)]. Using pair correlation function data generated from diffusion Monte Carlo simulations, the authors calculate the dispersion of the in-phase and out-of-phase shear modes over a wide range of high-r(s) values and layer separations. Over the coupling range 10< or =r(s)< or =30 and for layer separations 0.2/sqrt[pi(n)]< or =d< or =0.5/sqrt[pi(n)] , the present study predicts the existence of a robust out-of-phase gapped shear mode dispersion in the domain of the q,omega -plane above the left boundary of the RPA single-pair excitation region; under these conditions, the out-of-phase collective excitation is entirely immune to Landau damping and can be safely considered to be mostly unaffected by diffusive-migrational damping.

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Ito; calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

HF in clusters of molecular hydrogen: II. Quantum solvation by H2 isotopomers, cluster rigidity, and comparison with CO-doped parahydrogen clusters

We present a comprehensive theoretical study of the quantum solvation of the HF molecule by small clusters of the H2 isotopomers, p-H2, HD, and o-D2, with up to 13 hydrogen solvent molecules. This complements our earlier work on the HF-doped parahydrogen clusters [H. Jiang and Z. Bacic, J. Chem. Phys. 122, 244306 (2005)]. The ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. Detailed information is obtained regarding the size and isotopomer dependences of the energetics, vibrationally averaged structures, and their rigidity. The rigidity of these clusters is investigated further by analyzing the distributions of their principal moments of inertia from the diffusion Monte Carlo simulations. The clusters are found to be rather rigid, especially when compared with the pure parahydrogen clusters of the same size. Extensive comparison is made with the quantum Monte Carlo results for the CO-doped parahydrogen clusters and significant differences are observed in the size evolution of certain properties, notably the chemical potential.

Accessing the Dynamics of End-Grafted Flexible Polymer Chains by Atomic Force-Electrochemical Microscopy. Theoretical Modeling of the Approach Curves by the Elastic Bounded Diffusion Model and Monte Carlo Simulations. Evidence for Compression-Induced Lateral Chain Escape

The dynamics of a molecular layer of linear poly(ethylene glycol) (PEG) chains of molecular weight 3400, bearing at one end a ferrocene (Fc) label and thiol end-grafted at a low surface coverage onto a gold substrate, is probed using combined atomic force-electrochemical microscopy (AFM-SECM), at the scale of approximately 100 molecules. Force and current approach curves are simultaneously recorded as a force-sensing microelectrode (tip) is inserted within the approximately 10 nm thick, redox labeled, PEG chain layer. Whereas the force approach curve gives access to the structure of the compressed PEG layer, the tip-current, resulting from tip-to-substrate redox cycling of the Fc head of the chain, is controlled by chain dynamics. The elastic bounded diffusion model, which considers the motion of the Fc head as diffusion in a conformational field, complemented by Monte Carlo (MC) simulations, from which the chain conformation can be derived for any degree of confinement, allows the theoretical tip-current approach curve to be calculated. The experimental current approach curve can then be very satisfyingly reproduced by theory, down to a tip-substrate separation of approximately 2 nm, using only one adjustable parameter characterizing the chain dynamics: the effective diffusion coefficient of the chain head. At closer tip-substrate separations, an unpredicted peak is observed in the experimental current approach curve, which is shown to find its origin in a compression-induced escape of the chain from within the narrowing tip-substrate gap. MC simulations provide quantitative support for lateral chain elongation as the escape mechanism.

Restricted diffusion in a model acinar labyrinth by NMR: Theoretical and numerical results

A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.

Vacancy-Assisted Diffusion in Silicon: A Three-Temperature-Regime Model

In this Letter we report kinetic lattice Monte Carlo simulations of vacancy-assisted diffusion in silicon. We show that the observed temperature dependence for vacancy migration energy is explained by the existence of three diffusion regimes for divacancies. This characteristic has been rationalized with an analytical model. In the intermediate temperature regime the divacancy dissociation plays a key role and an effective migration energy E{v}{m} approximately 2 eV is predicted, computed from either full ab initio values or mixed with experimental ones. The exact position of this temperature regime strongly depends on vacancy concentration. Previous contradictory experimental results are revisited using this viewpoint.