599 research outputs found
Introduction to the Diffusion Monte Carlo Method
A self-contained and tutorial presentation of the diffusion Monte Carlo
method for determining the ground state energy and wave function of quantum
systems is provided. First, the theoretical basis of the method is derived and
then a numerical algorithm is formulated. The algorithm is applied to determine
the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen
atom, and the electronic ground state of the H2+ ion and of the H2 molecule. A
computer program on which the sample calculations are based is available upon
request.Comment: RevTeX 3.0, 14 pages, 8 EPS figures (included
Boundary Integral Method for Stationary States of Two-Dimensional Quantum Systems
The boundary integral method for calculating the stationary states of a
quantum particle in nano-devices and quantum billiards is presented in detail
at an elementary level. According to the method, wave functions inside the
domain of the device or billiard are expressed in terms of line integrals of
the wave function and its normal derivative along the domain's boundary; the
respective energy eigenvalues are obtained as the roots of Fredholm
determinants. Numerical implementations of the method are described and applied
to determine the energy level statistics of billiards with circular and stadium
shapes and demonstrate the quantum mechanical characteristics of chaotic
motion. The treatment of other examples as well as the advantages and
limitations of the boundary integral method are discussed.Comment: RevTeX3.0, 24 pages, 9 EPS figures (included); To be published in
Int. J. of Mod. Phys.
Quasicontinuum representations of atomic-scale mechanics: From proteins to dislocations
Computation is one of the centerpieces of both the physical and biological sciences. A key thrust in computational science is the explicit mechanistic simulation of the spatiotemporal evolution of materials ranging from macromolecules to intermetallic alloys. However, our ability to simulate such systems is in the end always limited in both the spatial extent of the systems that are considered, as well as the duration of the time that can be simulated. As a result, a variety of efforts have been put forth that aim to finesse these challenges in both space and time through new techniques in which constraint is exploited to reduce the overall computational burden. The aim of this review is to describe in general terms some of the key ideas that have been set forth in both the materials and biological setting and to speculate on future developments along these lines. We begin by developing general ideas on the exploitation of constraint as a systematic tool for degree of freedom thinning. These ideas are then applied to case studies ranging from the plastic deformation of solids to the interactions of proteins and DNA
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