計(jì)算物理學(xué)

內(nèi)容概要

　　This Second Edition has been fully updated. The wide range of
topics covered inthe First Edition has been extended with new
chapters on finite element methodsand lattice Boltzmann simulation.
New sections have been added to the chapters ondensity functional
theory, quantum molecular dynamics, Monte Carlo simulationand
diagonalisation of one-dimensional quantum systems.
　　The book covers many different areas of physics research and
different computa-tional methodologies, with an emphasis on
condensed matter physics and physicalchemistry. It includes
computational methods such as Monte Carlo and moleculardynamics,
various electronic structure methodologies, methods for solving
par-tial differential equations, and lattice gauge theory.
Throughout the book, therelations between the methods used in
different fields of physics are emphas-ised. Several new programs
are described and these can be downloaded
fromwww.cambridge.org/9780521833462
　　The book requires a background in elementary programming,
numerical analysisand field theory, as well as undergraduate
knowledge of condensed matter theoryand statistical physics. It
will be of interest to graduate students and researchers
intheoretical, computational and experimental physics.Jos THIJSSEN
is a lecturer at the Kavli Institute of Nanoscience at Delft
Universityof Technology.

作者簡介

作者：（荷蘭）蒂森（J.M.Thijssen）

書籍目錄

preface to the first edition
preface to the second edition
1 introduction
　1.1 physics and computational physics
　1.2 classical mechanics and statistical mechanics
　1.3 stochastic simulations
　1.4 electrodynamics and hydrodynamics
　1.5 quantum mechanics
　1.6 relations between quantum mechanics and classical statistical
physics
　1.7 quantum molecular dynamics
　1.8 quantum field theory
　1.9 about this book
　exercises
　references
2 quantum scattering with a spherically symmetric
　potential
　2.1 introduction
　2.2 a program for calculating cross sections
　2.3 calculation of scattering cross sections
　exercises
　references
3 the variational method for the schr'odinger equation
　3.1 variational calculus
　3.2 examples of variational calculations
　3.3 solution of the generalised eigenvalue problem
　3.4 perturbation theory and variational calculus
　exercises
　references
4 the hartree-fock method
　4.1 introduction
　4.2 the bom-oppenheimer approximation and the independent-particle
method
　4.3 the helium atom
　4.4 many-electron systems and the slater determinant
　4.5 self-consistency and exchange: hartree-fock theory
　4.6 basis functions
　4.7 the structure of a hartree-fock computer program
　4.8 integrals involving gaussian functions
　4.9 applications and results
　4.10 improving upon the hartree-fock approximation
　exercises
　references
5 density functional theory
　5.1 introduction
　5.2 the local density approximation
　5.3 exchange and correlation: a closer look
　5.4 beyond dft: one- and two-particle excitations
　5.5 a density functional program for the helium atom
　5.6 applications and results
　exercises
　references
6 solving the schriodinger equation in periodic solids
　6.1 introduction: definitions
　6.2 band structures and bloch's theorem
　6.3 approximations
　6.4 band structure methods and basis functions
　6.5 augmented plane wave'methods
　6.6 the linearised apw (lapw) method
　6.7 the pseudopotential method
　6.8 extracting information from band structures
　6.9 some additional remarks
　6.10 other band methods
　exercises
　references
7 classical equilibrium statistical mechanics
　7.1 basic theory
　7.2 examples of statistical models; phase transitions
　7.3 phase transitions
　7.4 determination of averages in simulations
　exercises
　references
8　Molecular dynamics simulations
　8.1 introduction
　8.2 molecular dynamics at constant energy
　8.3 a molecular dynamics simulation program for argon
　8.4 integration methods: symplectic integrators
　8.5 molecular dynamics methods for different ensembles
　8.6 molecular systems
　8.7 long-range interactions
　8.8 langevin dynamics simulation
　8.9 dynamical quantities: nonequilibrium molecular dynamics
　exercises
　references
9 quantum molecular dynamics
　9.1 introduction
　9.2 the molecular dynamics method
　9.3 an example: quantum molecular dynamics for the hydrogen
molecule
　9.4 orthonormalisation; conjugate gradient and rm-diis
techniques
　9.5 implementation of the car-parrinello technique for
pseudopotential dft
　exercises
　references
10 the monte carlo method
　10.1 introduction
　10.2 monte carlo integration
　10.3 importance sampling through markov chains
　10.4 other ensembles
　10.5 estimation of free energy and chemical potential
　10.6 further applications and monte carlo methods
　10.7 the temperature of a finite system
　exercises
　references
11 transfer matrix and diagonalisation of spin chains
　11.1 introduction
　11.2 the one-dimensional ising model and the transfer matrix
　11.3 two-dimensional spin models
　11.4 more complicated models
　11.5 'exact' diagonalisation of quantum chains
　11.6 quantum renormalisation in real space
　11.7 the density matrix renormalisation group method
　exercises
　references
12 quantum monte carlo methods
　12.1 introduction
　12.2 the variational monte carlo method
　12.3 diffusion monte carlo
　12.4 path-integral monte carlo
　12.5 quantum monte carlo on a lattice
　12.6 the monte carlo transfer matrix method
　exercises
　references
13 the finite element method for partial differential
equations
　13.1 introduction
　13.2 the poisson equation
　13.3 linear elasticity
　13.4 error estimators
　13.5 local refinement
　13.6 dynamical finite element method
　13.7 concurrent coupling of length scales: fem and md
　exercises
　references
14 the lattice boltzmann method for fluid dynamics
　14.1 introduction
　14.2 derivation of the navier-stokes equations
　14.3 the lattice boltzmann model
　14.4 additional remarks
　14.5 derivation of the navier-stokes equation from the
　lattice boltzmann model
　exercises
　references
15 computational methods for lattice field theories
　15.1 introduction
　15.2 quantum field theory
　15.3 interacting fields and renormalisation
　15.4 algorithms for lattice field theories
　15.5 reducing critical slowing down
　15.6 comparison of algorithms for scalar field theory
　15.7 gauge field theories
　exercises
　references
16 high performance computing and parallelism
　16.1 introduction
　16.2 pipelining
　16.3 parallelism
　16.4 parallel algorithms for molecular dynamics
　references
Appendix a numerical methods
　A1 about numerical methods
　A2 iterative procedures for special functions
　A3 finding the root of a function
　A4 finding the optimum of a function
　A5 discretisation
　A6 numerical quadratures
　A7 differential equations
　A8 linear algebra problems
　A9 the fast fourier transform
　exercises
　references
　appendix b random number generators
　B1 random numbers and pseudo-random numbers
　B2 random number generators and properties of pseudo-random
numbers
　B3 nonuniform random number generators
　exercises
　references
　index

章節(jié)摘錄

版權(quán)頁：插圖：Now we can define the problems in a more abstract way. It is convenient toconsider continuum problems. The candidate solutions （for example the possibleconformations） form a phase space, and the merit function has some complicatedshape on that space - it contains many valleys and mountains, which can be verysteep. The solution we seek corresponds to the lowest valley in the landscape. Notethat the landscape is high-dimensional. You may think, naively, that a standardnumerical minimum finder can solve this problem for you. However, this is notthe case as such an algorithm always needs a starting point, from which it findsthe nearest local minimum, which is not necessarily the best you can find in theconformation space. The set of points which would go to one particular local min-imum when fed into a steepest descent or other minimum-finder （see AppendixA4） is called the basin of attraction of that minimum. Once we are in the basinof attraction of the global minimum we can easily find this global minimum; theproblem is to find its basin of attraction.

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