Computational physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 2. ed., reprint. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 620 S. Ill., graph. Darst. |
| ISBN: | 9780521833462 9781107677135 |
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MARC
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| 100 | 1 | |a Thijssen, J. M. |d 1958- |e Verfasser |0 (DE-588)132806800 |4 aut | |
| 245 | 1 | 0 | |a Computational physics |c Jos Thijssen |
| 250 | |a 2. ed., reprint. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XV, 620 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Mathematik | |
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| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Condensed matter |x Mathematics | |
| 650 | 4 | |a Physics |x Data processing | |
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Record in the Search Index
| _version_ | 1804143762445697024 |
|---|---|
| adam_text | Contents
Preface
to the first edition P^ge
xi
Preface to the second edition
xiv
1
Introduction
1
1.1
Physics and computational physics
1
1.2
Classical mechanics and statistical mechanics
1
1.3
Stochastic simulations
4
1.4
Electrodynamics and hydrodynamics
5
1.5
Quantum mechanics
6
1.6
Relations between quantum mechanics and classical
statistical physics
7
1
.7
Quantum molecular dynamics
8
1.8
Quantum field theory
9
1.9
About this book
9
Exercises
11
References
13
2
Quantum scattering with a spherically symmetric
potential
14
2.1
Introduction
14
2.2
A program for calculating cross sections
18
2.3
Calculation of scattering cross sections
25
Exercises
27
References
28
3
The variational method for the
Schrödinger
equation
29
3.1
Variational calculus
29
3.2
Examples of variational calculations
32
33
Solution of the generalised eigenvalue problem
36
3.4
Perturbation theory and variational calculus
37
vi
Contents
Exercises
39
References
41
4
The Hartree-Fock method
43
4.1
Introduction
43
4.2
The Born-Oppenheimer approximation and the
independent-particle method
44
4.3
The helium atom
46
4.4
Many-electron systems and the Slater determinant.
52
4.5
Self-consistency and exchange: Hartree-Fock theory
54
4.6
Basis functions
60
4.7
The structure of a Hartree-Fock computer program
69
4.8
Integrals involving Gaussian functions
73
4.9
Applications and results
77
4.10
improving upon the
Hartree-
Fock approximation
78
Exercises
80
References
87
5
Density functional theory
89
5.1
Introduction
89
5.2
The local density approximation
95
5.3
Exchange and correlation: a closer look
97
5.4
Beyond DFT: one- and two-particle excitations
101
5.5
A density functional program for the helium atom
109
5.6
Applications and results
114
Exercises
116
References
119
6
Solving the
Schrö
dinger equation in periodic solids
122
6.1
Introduction: definitions
123
6.2
Band structures and Bloch s theorem
124
6.3
Approximations
126
6.4
Band structure methods and basis functions
133
6.5
Augmented plane wave methods
135
6.6
The linearised APW (LAPW) method
141
6.7
The pseudopotential method
144
6.8
Extracting information from band structures
160
6.9
Some additional remarks
162
6.10
Other band methods
163
Contents
vii
Exercises
163
References
167
7
Classical equilibrium
statistica]
mechanics
169
7.1
Basic
theory
169
7.2
Examples of statistical models; phase transitions
176
7.3
Phase transitions
184
7.4
Determination of averages
m
simulations
192
Exercises
194
References
195
8
Molecular dynamics simulations
197
8.1
Introduction
197
8.2
Molecular dynamics at constant energy
200
8.3
A molecular dynamics simulation program for argon
208
8.4
Integration methods: symplectic integrators
211
8.5
Molecular dynamics methods for different ensembles
223
8.6
Molecular systems
232
8.7
Long-range interactions
241
8.8
Langevin
dynamics simulation
247
8.9
Dynamical quantities: noneqmlibrmm molecular dynamics
251
Exercises
253
References
259
9
Quantum molecular dynamics
263
9.1
Introduction
263
9.2
The molecular dynamics method
266
9.3
An example: quantum molecular dynamics for the hydrogen
molecule
272
9.4
Orthonormalisation;
conjugate gradient and RM-DILS
techniques
278
9.5
Implementation of the Car-Parrinello technique for
pseudopotential DFT
289
Exercises
290
References
293
10
The Monte Carlo method
295
10.1
Introduction
295
10.2
Monte Carlo integration
296
10.3
Importance sampling through Markov chains
299
viu
Contents
10.4
Other ensembles
10.5
Estimation of free energy and chemical potential
316
10.6
Further applications and Monte Carlo methods
319
10.7
The
temperature
of a finite system
330
Exercises
334
References
335
11
Transfer matrix and diagonalisation of spin chains
338
11.1
Introduction
338
11.2
The one-dimensional Ising model and the
transfer matrix
339
11.3
Two-dimensional spin models
343
11.4
More complicated models
347
11.5
Exact diagonalisation of quantum chains
349
11.6
Quantum
renormalisation m
real space
355
11.7
The density matrix rcnormalisation group method
358
Exercises
365
References
370
12
Quantum Monte Carlo methods
372
12.1
Introduction
372
12.2
The vanational Monte Carlo method
373
12.3
Diffusion Monte Carlo
387
12.4
Path-integral Monte Carlo
398
12.5
Quantum Monte Carlo on a lattice
410
12.6
The Monte Carlo transfer matrix method
414
Exercises
417
References
421
13
The finite element method for partial differential equations
423
13.1
Introduction
423
13.2
The
Poisson
equation
424
13.3
Linear elasticity
429
13.4
Error estimators
434
13.5
Local refinement
436
13.6
Dynamical finite element method
439
13.7
Concurrent coupling of length scales:
FEM
and MD
440
Exercises
445
References
446
Contents
їх
14
The lattice Boltzmann method for fluid dynamics
448
14.1
Introduction
448
14.2
Derivation of the Navier-Stokes equations
449
14.3
The lattice Boltzmann model
455
14.4
Additional remarks
458
14.5
Derivation of the Navier-Stokes equation from the
lattice Boltzmann model
460
Exercises
463
References
464
15
Computational methods for lattice field theories
466
15.1
Introduction
466
15.2
Quantum field theory
467
15.3
Interacting fields and
renormalisation
473
15.4
Algorithms for lattice field theories
477
15.5
Reducing critical slowing down
491
15.6
Comparison of algorithms for scalar field theory
509
15.7
Gauge field theones
510
Exercises
532
References
536
16
High performance computing and parallelism
540
16.1
Introduction
540
16.2
Pipelining
541
16.3
Parallelism
545
16.4
Parallel algorithms for molecular dynamics
552
References
556
Appendix A Numerical methods
557
Al
About numerical methods
557
A2 Iterative procedures for special functions
558
A3
Finding the root of a function
559
A4
Finding the optimum of a function
560
A5 Discretisation
565
A6 Numerical quadratures
566
A7 Differential equations
568
A
8
Linear algebra problems
590
A9 The fast Fourier transform
598
Exercises
601
References
603
χ
Contents
Appendix
В
Random number generators
605
Bl Random numbers and pseudo-random numbers
605
B2 Random number generators and properties of pseudo-random
numbers
606
B3 Nonumform random number generators
609
Exercises
611
References
612
Index
613
This Second Edition has been fully updated. The wide range of topics covered in the
First Edition has been extended with new chapters on finite efement methods and
[attice
Boltzmann simulation. New sections have been added to the chapters on
density functional theory, quantum molecular dynamics, Monte Carlo simulation,
and diagonalisation of one-dimensional quantum systems.
The book covers many different areas of physics research and different
computational methodologies, with an emphasis on condensed matter physics
and physical chemistry. It includes computational methods such as Monte Carlo
and molecular dynamics, various electronic structure methodologies, methods
for solving partial differential equations and lattice gauge theory. Throughout the
book, the relations between the methods used in different fields of physics are
emphasised. Several new programs are described and these can be downloaded from
www.cambridge.org/9781107677135.
The book requires a background in elementary programming, numerical analysis
and field theory, as well as undergraduate knowledge on condensed matter theory
and statistical physics. It will be of interest to graduate students and researchers in
theoretical, computational and experimental physics.
Jos Thijssen is a lecturer at the Kavli Institute of Nanoscience at Delft University of
Technology.
|
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| discipline | Physik Informatik Mathematik |
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| id | DE-604.BV037181105 |
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| language | English |
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| spelling | Thijssen, J. M. 1958- Verfasser (DE-588)132806800 aut Computational physics Jos Thijssen 2. ed., reprint. Cambridge [u.a.] Cambridge Univ. Press 2010 XV, 620 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Datenverarbeitung Mathematik Mathematische Physik Mathematical physics Condensed matter Mathematics Physics Data processing Computerphysik (DE-588)4273564-6 gnd rswk-swf Computerphysik (DE-588)4273564-6 s DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021095715&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021095715&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| subject_GND | (DE-588)4273564-6 |
| title | Computational physics |
| title_auth | Computational physics |
| title_exact_search | Computational physics |
| title_full | Computational physics Jos Thijssen |
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