Search results for "Path integral Monte Carlo"
showing 10 items of 14 documents
ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS
1992
In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator…
Quantum Effects and Phase Transitions in Adsorbed Molecular Layers
1998
Phase transitions in adsorbed (two dimensional) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo (PIMC), Gibbs ensemble Monte Carlo (GEMC) and finite size scaling techniques. Entropy driven phase transitions in systems with purely repulsive interactions are analyzed as well phase diagrams of fluids with internal quantum states. Adsorbed layers of H 2 molecules at a full monolayer coverage in the \(\sqrt 3 \times \sqrt 3 \) structure have a higher transition temperature to the disordered phase compared to the system with the heavier D 2 molecules, this effect is analyzed by PIMC. Linear N 2 molecules adsorbed on graphite show a transition…
Classical and Quantum Two-Dimensional Fluids in the Gibbs Ensemble
1994
We study the properties of model fluids in two spatial dimensions with Gibbs ensemble Monte Carlo (GEMC) techniques. In particular in the first part of the paper we study the entropy driven phase separation in case of a nonadditive symmetric hard disc fluid and locate by a combination of GEMC with finite size scaling techniques the critical line of nonadditivities as a function of the system density, which separates the mixing/demixing regions, we compare with a simple approximation. In the second part we successfully combine path integral Monte Carlo (PIMC) and GEMC techniques in order to locate the gas-liquid coexistence densities for a fluid with classical degrees of freedom and internal…
Path-integral Monte Carlo study of crystalline Lennard-Jones systems.
1995
The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate $^{40}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of $^{20}\mathrm{Ne}$ and $^{22}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo result…
Path integral Monte Carlo study of the internal quantum state dynamics of a generic model fluid
1996
We study the quantum dynamics of a generic model fluid with internal quantum states and classical translational degrees of freedom in two spatial dimensions. The path integral Monte Carlo data for the imaginary time correlation functions are presented and analyzed by the maximum entropy method. A comparison of the frequency distribution with those of a mean field approximation and virial expansion shows good agreement at high and low densities, respectively. \textcopyright{} 1996 The American Physical Society.
Path-Integral Monte Carlo Simulation for H2 and D2 Adsorbed on Graphite
1997
Molecular layers are very good realizations of two dimensional systems. Hydrogen molecules H 2,HD,D 2 adsorbed on graphite are excellent model systems for investigating the influence of substrate fields and of quantum effects on phase transitions. At a coverage of a complete commensurable layer in the √3 x √3 R30° structure experiments showed an anomalous effect, the system with the lighter H 2 molecules has a higher order-disorder transition temperature compared to the system with the heavier D 2 molecules. By a combination of path integral Monte Carlo and finite size scaling techniques we analyze this effect. In detail we study the order parameter and the cumulants and discuss the impact …
Quantum simulations in materials science: molecular monolayers and crystals
1999
Low temperature properties and anomalies in crystals and molecular monolayers are studied by path integral Monte Carlo (PIMC) simulations. For light particles (H 2 , D 2 ) adsorbed on graphite anomalies in the transition to the low temperature √3-phases have been observed in experiments and are analyzed by PIMC. The computed thermal expansion of various crystalline materials (Si, N 2 ) is in much better agreement with experiments compared to the results obtained with purely classical simulations.
Orthorhombic Phase of Crystalline Polyethylene: A Constant Pressure Path Integral Monte Carlo Study
1998
In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles. This work represents a quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918 (1997)). It is aimed both at exploring the applicability of the PIMC method on such polymer crystal systems, as well as on a detailed assessment of the importance of quantum effects on different quantities. We used the $NpT$ ensemble and simulated the system at zero pressure in the temperature range 25 - 300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size e…
Phase Transitions in Classical Fluids and Fluids with Internal Quantum States in Two Dimensions: Computer Simulations and Theory
1993
1)We investigate the properties of a model fluid whose molecules have classical degrees of freedom in two dimensions and two internal quantum states. The attractive interactions are “turned on” when the internal states are hybridized, corresponding to the molecules acquiring a “dipole” moment. The phase diagram of this system in the temperature- density plane is investigated by a combination of path integral Monte Carlo and block size analysis techniques. The results are compared with mean- field—theory predictions. 2) We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equi…
Rotational Motion of Linear Molecules in Three Dimensions. A Path-Integral Monte Carlo Approach
1994
Abstract A path-integral Monte Carlo (PIMC) simulation method for the rotational motion of linear molecules in three dimensions is presented. The technique is applied to an H2 impurity in a static crystal-field. The resulting orientational distributions from quantum and classical simulations are obtained and discussed. The algorithm suffers from the “sign problem” of quantum simulations. However, as can be seen by comparing the low temperature simulation result to the variational solution of the Schrodinger equation, the PIMC method captures the quantum fluctuations.