Progress in Computational Physics of Matter

The following sections are included:

• CONTENTS

• PREFACE

We have recently developed a new computational scheme that allows for the simulation of solid-solid phase transformations. In this paper we review the new method and discuss its application to the study of the silicon phase diagram under pressure.

We treat systems of strongly interacting Bosons and, in particular, condensed phases of ⁴He. We review the motivations, the computational problems for these Monte Carlo simulations and the main applications of the variational theory based on shadow wave function (wf). First we treat the bulk ground state in the liquid and in the solid phase. Then we consider the phonon-maxon-roton excitations in superfluid ⁴He treated by the shadow wf and the properties of this system at finite temperature on the basis of a shadow density matrix. Next we consider the extension of the shadow wf in terms of a local density formulation and review the treatment of the liquid-solid coexistence and interface. We present recent unpublished work extending the treatment of roton excitations by building in the wf a more accurate representation of backflow and a novel extension of the shadow wf in order to treat a self-bound state. This last wf is noticeable because it has no classical analogue and the first applications to the case of a free standing film and of small clusters of ⁴He are presented. Finally, the prospects for further applications of this powerful method for treating strongly interacting Bosons are discussed.

We treat systems of strongly interacting Fermions within the framework of shadow wave functions (SWFs.) We give several arguments that building antisymmetric SWFs is best done by antisymmetrizing the shadow degrees of freedom. Such an ansatz is likely to give an accurate description of both the solid and liquid phases of ³He and therefore of the liquid-solid interface as well. We review some of the results obtained using antisymmetric SWFs in which the particle degrees of freedom are the ones that are antisymmetrized. Finally, we introduce two algorithmic ideas that may serve to make calculations with the better SWFs more efficient. One is to limit the random walk of the particles to that domain in which the function used to antisymmetrize the shadows is positive. The other uses “antishadows”, additional shadow degrees of freedom that can be made antithetic to the existing shadows.

The article will review a series of topics which are relevant for the simulation of electronic devices. The main algorithms implemented in self–consistent particle–based simulation programs are listed and discussed. A novel multigrid procedure for the solution of the Poisson's equation is presented, and some performance tests are shown. The computational techniques employed to optimize the programs are discussed as well, with particular emphasis on the use of clustered workstations as parallel platforms.

A computationally efficient molecular dynamics approach based on the method of holonomic constraints is described with reference to the task of estimating the rate constants of rare events that occur by activated processes. The system is constrained at “bottleneck” regions on a general many-body reaction coordinate and molecular dynamics trajectories sample phase space according to a biased configurational distribution. Averages can be taken from such a new, Blue Moon, ensemble with suitable reweighting and correct momentum distribution sampling, to study rare events. Applications to a variety of classical and quantum activated processes in the condensed phase are discussed together with the implementation of a highly parallel algorithm based on message passing.

The ‘ab initio’, Local Density Approximation, KKR-CPA is an efficient computational method for the calculation of electronic properties of metallic solid solution. Interestingly, charge correlation effects may be included to some extent in the algorithm with no extra computational effort. This method allows the determination of basic physical quantities such as total energies, spectral quantities and Fermi surfaces. In this paper we review the general theoretical scheme and discuss on the parallel implementation of the corresponding algorithm. Moreover we report on applications of this method to the determination of equilibrium crystal structure and phase equilibria for several metallic systems. We also discuss the relevance of KKR-CPA in the context of the Fermi liquid theory for the study of Electronic Topological Transitions. The studied systems are Ag-Pd and Fe-Al, Fe-Al-Ti.

We present the Surface Linear Muffin-Tin Orbital (SLMTO) method, suitable for ab-initio investigation of the microscopic properties of surface and interface systems. The SLMTO method is an all-electron approach, with the exchange and correlation potential treated through the density functional theory in the local density approximation. The feasibility of an all-electron calculation to the complex systems relays on the atomic sphere approximation (ASA), consisting in describing the solids as a collection of slightly overlapping spheres, the potential being spherically symmetric inside each sphere. In the occurence of a solid-vacuum interface, the SLMTO-ASA describes the vacuum regions as a collection of ‘empty spheres’, each of them caracterized by fictitious atoms with Z=0. The presented SLMTO-ASA approach produces accurate energies and wave-functions for both core and valence states. We presents its application to the investigation of clean surfaces, interfaces and ultra-thin silicon-based confined systems (quantum wires). Finally we present the extension of the program for the computation of the optical matrix elements. Results for the optical properties of Si-based quantum wires are presented.