Integral Monte Carlo Method Research Articles

Optimization design of the large area Dynode-MCP-PMT

The optimization work of a newly proposed 20-in. photomultiplier tube based on dynode and microchannel plates (Dynode-MCP-PMT) are conducted in this paper. Three-dimensional models are developed in CST STUDIO SUITE to systematically investigate the effects of the size and bias voltage of the two focusing electrodes, dynode and the glass envelop handle based on the Finite Integral Technique and Monte Carlo method. Results predict that the collection efficiency and the transit time spread of the optimized design are substantially improved which are 100% and 3.7 ns.

A four-channel ICCD framing camera with nanosecond temporal resolution and high spatial resolution

In this paper, a high spatial resolution, high gating speed framing camera capable of four separate two-dimensional images is designed and tested. A mirror-based image splitter has been designed and developed to provide a separate image for each arm with equal path length and equal intensity splitting while having a spectral flat response. Fast gating of a single frame is accomplished by using a proximity-focused microchannle-plate image-intensifier (MCPII) gated by a MOSFET-based pulse module with adjustable gate width from 3 ns to D.C. operation. Multiple frames are obtained by using multiple gated tubes with time intervals between consecutive frames can be adjusted flexibly. Its spatial resolution reaches 36.5 lp/mm with each frame having a 4.6-ns gate width. Furthermore, a three-dimensional MCPII model is developed to investigate the transit time and spatial resolution of the proximity-focused MCPII based on the Finite Integral Technique (FIT) and Monte Carlo method (M–C method).

Quantum-Mechanical Model of Neural Network Elements

A model of a neural-network-like quantum-mechanical system is considered. The role of neurons is played by quantum-mechanical particles which evolve under the action of an external double-well potential. An instanton is used as a spike. Neurons are connected by the interaction potential $${{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})$$ . The connection is directional owing to asymmetry of the interaction potential. Therefore, the complete Hamiltonian of the system is $$\hat {H} = \sum\nolimits_i \left( {\frac{1}{2}\hat {p}_{i}^{2} + {{V}_{0}}({{{\hat {q}}}_{i}})} \right) + \sum\nolimits_{i > j} \,{{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})$$ . The system is investigated by the path integral Monte Carlo (PIMC) method. It is shown that with a certain choice of parameters in this system it is possible to transfer activity in long chains of neurons.

Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials

We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz–Petrich–Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.

Improved Approach to Multiregion Supercritical Transient Analysis Based on the Integral Kinetic Model and Monte Carlo Method

An approach to multiregion supercritical transient analysis based on the integral kinetic model (IKM) and Monte Carlo method is further developed with new features. The IKM describes the region-dependent fission rate during the transient in a system of arbitrary geometry using a secondary fission probability density function, which takes the explicit neutron transport time between successive fissions across the regions into account. The new features of the improved approach include treatment of the multiregion transient using repeated multidimensional linear interpolation between pre-obtained kinetic functions (i.e., secondary probability density function), a new method for calculating the kinetic functions using the continuous-energy Monte Carlo code MVP2.0, and utilization of kinetic functions directly in the IKM without the fitting function that introduces a fitting error. The improved approach is verified by applying it to the supercritical transient in simple Godiva systems of different region combinations without feedback. In addition, we attempt to validate the improved approach by applying it to the supercritical transient in a simplified Godiva system with thermal expansion feedback and compare the obtained and experimental results. The verification results indicate the improved approach works well with different combinations of regions while the validation results show promising agreement with the experimental results. This study is part of an ongoing research activity on the development of Multi-region Integral Kinetic (MIK) code for general space- and time-dependent kinetic analyses.

Relativistic path integral Monte Carlo: Relativistic oscillator problem

Relativistic generalization of path integral Monte Carlo (PIMC) method has been proposed. The problem of relativistic oscillator has been studied in the framework of this approach. Ultra-relativistic and nonrelativistic limits have been discussed. We show that PIMC method can be effectively used for investigation of relativistic systems.

TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION

The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

WORM ALGORITHM PATH INTEGRAL MONTE CARLO APPLIED TO THE 3He–4He II SANDWICH SYSTEM

We present a numerical investigation of the thermal and structural properties of the 3 He –4 He sandwich system adsorbed on a graphite substrate using the worm algorithm path integral Monte Carlo (WAPIMC) method [M. Boninsegni, N. Prokof'ev and B. Svistunov, Phys. Rev. E74, 036701 (2006)]. For this purpose, we have modified a previously written WAPIMC code originally adapted for 4 He on graphite, by including the second 3 He -component. To describe the fermions, a temperature-dependent statistical potential has been used. This has proven very effective. The WAPIMC calculations have been conducted in the millikelvin temperature regime. However, because of the heavy computations involved, only 30, 40 and 50 mK have been considered for the time being. The pair correlations, Matsubara Green's function, structure factor, and density profiles have been explored at these temperatures.

QUANTUM DOT GEOMETRY AS A DESIGNING TOOL FOR DOT-IN-A-WELL STRUCTURES

In this paper, we report results of our investigation on the effect of quantum dot (QD) geometry on desirable properties of a dot-in-a-well (DWELL) structure. Our simulation results reveal that QD geometry plays a key role in tuning the electronic properties of DWELL structure and can be employed as a designing tool. The structure under investigation consists of an InAs QD confined in an InGaAs well of size ~12.3 nm which in turn is sandwiched in a GaAs bulk. Using the path integral Monte Carlo (PIMC) method, we calculate the electronic properties of DWELL structure for QDs of spherical, ellipsoidal, and conical shapes. We demonstrate the dependence of the electron energy on QD geometry. We show that although the stronger confinement within the conical quantum dot (CQD) forces its maximum capacity (N max ) to be smaller than those of the spherical quantum dot (SQD) and ellipsoidal quantum dot (EQD), the overall maximum capacity of a DWELL with conical dot (CDWELL) is larger than those of the DWELLs with spherical and ellipsoidal dots (SDWELL and EDWELL). Moreover, we show that the electron distribution within the structure is a strong function of the QD geometry inside the well.

Path integral Monte Carlo study of CO2 solvation in He4 clusters

We present a finite temperature quantum mechanical study of the dynamical and structural properties of small (4)He(N)-CO(2) clusters (N< or =17) using a path integral Monte Carlo (PIMC) method. The simulations were based on a He-CO(2) interaction potential with explicit dependence on the asymmetric stretch of the CO(2) molecule obtained at the CCSD(T) level. The shift of the CO(2) antisymmetric stretching (nu(3)) band origin and effective rotational constant were calculated as a function of the cluster size. In excellent agreement with experimental observations, the CO(2) vibrational band origin shifts and rotational constant show a turnaround near N=5, corresponding to a donut structure with the He atoms in equatorial positions of the linear dopant molecule.

Path Integral Hybrid Monte Carlo Study on Structure of Small Helium-4 Clusters Doped with a Linear Molecule

Microscopic structure of small helium-4 clusters doped with a carbonyl sulfide molecule, OCS(4He)N, at 0.37 K is studied by the path integral hybrid Monte Carlo method; the size of the cluster N ranges from N=2 to N=5. In all the cases examined in the present study, the helium atoms are localized around the carbon atom of the OCS molecule, forming a doughnut-type structure around the molecular axis. Bosonic exchange among the helium atoms is found to be promoted in the doughnut region, showing an anisotropic “superfluid” response of the clusters.

The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory.

Path integral hybrid Monte Carlo calculation of the bosonic oscillators

In this paper, various correlation functions for a bosonic many-body system have been calculated using the path integral hybrid Monte Carlo method proposed by the authors [Chem. Phys. Lett. 308, 115 (1999)]. A system consisting of 32 independent particles in a harmonic well was chosen as a model problem. Calculations were carried out at two temperatures for the Boltzmann and Bose statistics. The large amplitude of the bosonic pair-correlation function around origin was found in comparison with the boltzmannoniac counterpart. This behavior can be interpreted by effective “attractive interaction” between particles arising from the Bose statistics.

Temperature Effects on the Absorption Spectra of Li in Solid H2 Under High Pressure: A Path Integral Monte Carlo Study

The temperature dependence (5–45 K) of the absorption spectra of a Li atom doped in solid hydrogen at P=1.2 GPa is investigated using the path integral Monte Carlo (PIMC) method with a constant pressure ensemble. Higher temperature in our research range does not cause rearrangement of the trapping site structures. The significantly broadening and spreading of the three component absorptions with increasing temperature are observed. For the trapping site structures belonging to lower symmetry point groups, the singlet to doublet splitting decreases as temperature gets larger. An insight on the temperature-induced behaviors of the Li absorption spectrum in the doped system has been made by using the simulated results.

Routing problems revisited: path integral formalism and Monte Carlo methods

Routing problems revisited: path integral formalism and Monte Carlo methods