Diffusion: formalism and applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2014
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XV, 292 S. Ill., graph. Darst. |
| ISBN: | 9781439895573 |
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MARC
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| 020 | |a 9781439895573 |c hardback |9 978-1-4398-9557-3 | ||
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| 245 | 1 | 0 | |a Diffusion |b formalism and applications |c Sushanta Dattagupta |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2014 | |
| 300 | |a XV, 292 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| _version_ | 1804151860459732992 |
|---|---|
| adam_text | Physics
Within a unifying framework, Diffusion: Formalism and Applications
covers both classical and quantum domains, along with numerous
applications. The author explores the more than two centuries-old
history of diffusion, expertly weaving together a variety of topics from
physics, mathematics, chemistry, and biology.
The book examines the two distinct paradigms of diffusion—physical
and stochastic-introduced by Fourier and Laplace and later unified
by Einstein in his groundbreaking work on Brownian motion. The au¬
thor describes the role of diffusion in probability theory and stochas¬
tic calculus and discusses topics in materials science and metallurgy,
such as defect-diffusion, radiation damage, and spinodal decompo¬
sition. In addition, he addresses the impact of translational/rotational
diffusion on experimental data and covers reaction-diffusion equa¬
tions in biology. Focusing on diffusion in the quantum domain, the
book also investigates dissipative tunneling, Landau diamagnetism,
coherence-to-decoherence transition, quantum information pro¬
cesses, and electron localization.
Features
•
Offers a lucid account of the history of diffusion from the last
200
years
•
Familiarizes you with the necessary formalism and practical
applications
•
Covers stochastic processes, enabling you to acquire a solid
mathematical foundation
•
Describes interdisciplinary topics from many areas of science
and engineering, including nanoscience and quantum coherence
•
Links the theory of diffusion and spectroscopy
Contents
Preface
......................................................................................................................xi
Acknowledgments
..............................................................................................
x
About the Author
..................................................................................................
iXV
Section I Classical Diffusion
1
Introduction to Brownian Motion
...............................................................3
1.1
Introductory Remarks
..........................................................................3
1.2
Fourier Equation
...................................................................................3
1.3
Random Walk
........................................................................................5
1.4
Random Walk on a Lattice and Its Continuum Limit
.....................9
1.5
Einstein on Brownian Motion
...........................................................11
1.5.1
Dressed Viscosity
...................................................................11
1.5.2
Synergy of Thermodynamics and Kinetics
.......................12
1.5.3
Brownian Motion and Stochastic Diffusion
......................14
1.6
Concluding Remarks
..........................................................................16
Exercises
..........................................................................................................16
References
.......................................................................................................16
2
Markov Processes
.........................................................................................19
2.1
Genesis of Markov Concept
...............................................................19
2.2
Definition
..............................................................................................20
2.2.1
Joint and Conditional Probabilities
.....................................21
2.3
Stationary Markov Process
................................................................22
References
.......................................................................................................25
3
Gaussian Processes
......................................................................................27
3.1
Introduction
.........................................................................................27
3.1.1
Moments and
Cumulants
.....................................................29
3.1.2
Characteristic Function
.........................................................30
3.1.3
Cumulant
Generating Function
...........................................31
3.2
Gaussian Stochastic Processes
..........................................................32
3.2.1
Novikov Theorem
..................................................................33
3.2.2
Moment Theorem
..................................................................33
3.2.3
Characteristic Functional
......................................................34
3.3
Stationary Gauss-Markov Process
...................................................34
3.3.1
Doob s Theorem
.....................................................................35
Exercises
..........................................................................................................37
References
.......................................................................................................38
V
vi Cotitcnts
4
Langevin
Equations
.....................................................................................39
4.1
Introduction
.........................................................................................39
4.2
Free Particle in Momentum Space
....................................................40
4.3
Free Particle in Position Space
...........................................................47
4.3.1
High-Friction Brownian Regime
.........................................51
4.3.2
Summary of Results
..............................................................54
4.4
Harmonic Oscillator
...........................................................................55
4.5
Diffusive Cyclotron Motion
...............................................................57
Exercises
..........................................................................................................60
References
.......................................................................................................60
5
Fokker—
Planck Equation
.............................................................................61
5.1
Introduction
.........................................................................................61
5.2
FP Equation in Velocity
......................................................................62
5.3
FP Equation in Position: Stochastic Diffusion
................................63
5.4
FP Equation in Force Field: Kramers Equation
...............................64
5.5
FP Equation in Force Field in High-Friction Limit:
Smoluchowski Equation
.....................................................................66
5.6
FP Equation for Damped Harmonic Oscillator
..............................67
5.7
FP Equation for Cyclotron Motion
....................................................68
5.8
Diffusion across Barrier
.....................................................................69
Exercise
............................................................................................................73
References
.......................................................................................................73
6
Jump Diffusion
.............................................................................................75
6.1
Introduction
.........................................................................................75
6.2
Operator Notation
...............................................................................76
6.3
Two-State Jump and Telegraph Processes
.......................................79
6.4
Multi-State Jump Process
...................................................................81
6.5
Kubo-Anderson Process
....................................................................81
6.6
Interpolation Model
............................................................................83
6.7
Kangaroo Process
................................................................................84
Exercises
..........................................................................................................88
References
.......................................................................................................88
7
Random Walk and Anomalous Diffusion
..............................................89
7.1
Introduction to Continuous Time Random Walk (CTRW)
...........89
7.2
Non-Markovian Diffusion in CTRW Scheme
.................................92
7.2.1
Application to Interpolation Model
.....................................93
7. 2.2
Anomalous Diffusion
............................................................96
References
.......................................................................................................97
8
Spectroscopie
Structure Factor
...................................................................99
8.1
Introductory Remarks
........................................................................99
8.2.1
Weak Collision Model: Gaussian Process
........................100
Contents
8.2.1.1
Very Slow Collisions
............................................101
8.2.1.2
Very Fast Collisions
..............................................102
8.2.2
Strong Collision Model: Kubo-Anderson Process
..........102
8.2.2.1
No-Collision Term
................................................103
8.2.2.2
One-Collision Term
..............................................103
8.2.2.3
Two-Collision Term
..............................................104
8.2.2.4
Very Slow Collisions
............................................104
8.2.2.5
Very Fast Collisions
..............................................105
8.2.3
Boltzmann-Lorentz Model
.................................................106
8.2.3.1
No-Collision Term
................................................107
8.2.3.2
One-Collision Term
..............................................107
8.3
Cyclotron Motion in Weak Collision and Boltzmann-
Lorentz Models
..................................................................................109
8.3.1
Structure Factor in the Weak Collision Model
................109
8.3.2
Structure Factor in the Boltzmann-Lorentz Model
........
Ill
8.4
Neutron Scattering from a Damped Harmonic Oscillator
.........114
8.5
Restricted Diffusion over Discrete Sites
........................................115
8.5.1
Two-Site Case
........................................................................115
8.5.2
Cage Diffusion
......................................................................118
8.6
Unbounded Jump Diffusion in Empty Lattice
.............................121
8.6.1
Large Jumps in Random Directions
..................................123
8.6.2
Small Jumps in Random Directions
..................................123
8.7
Vacancy-Assisted Correlated Diffusion in Solids
........................124
8.7.1
Analytical Results in a Simple Cubic (SC) Case
..............130
Appendix
......................................................................................................135
References
.....................................................................................................139
Rotational Diffusion of Molecules
.........................................................141
9.1
Introduction
.......................................................................................141
9.2
Extended Diffusion Models
.............................................................144
9.3
M
Diffusion Model
...........................................................................146
9.3.1
No-Collision Term
...............................................................147
9.3.2
One-Collision Term
.............................................................148
9.4
J
Diffusion Model
..............................................................................149
9.4.1
No-Collision Term
...............................................................150
9.4.2
One-Collision Term
.............................................................150
9.5
Interpolation Model
..........................................................................151
9.5.1
No-Collision Term
...............................................................151
9.5.2
One-Collision Term
.............................................................151
9.5.3
Two-Collision Term
.............................................................152
9.6
Applications to Infrared and Raman
Rotational Spectroscopy
..............................................................155
References
.....................................................................................................159
viii Contents
10 Order Parameter Diffusion.......................................................................161
10.1 Cahn-Hilliard
Equation
..................................................................161
10.2 Pattern Formation.............................................................................165
10.3 Jump Diffusion in Ising Model: Relation
with
CH
Equation
.....168
10.4
Reaction-Diffusion Models and
Spatio
temporal Patterns
..........173
References
.....................................................................................................180
11
Diffusion of Rapidly Driven Systems
....................................................181
11.1
Introduction
.......................................................................................181
11.2
Langevin
Equation in Over-Damped Case
...................................184
11.2.1
Dynamical Symmetry Breaking
........................................185
11.2.2
Decay of Metastable State
...................................................186
11.3
Langevin
Equation for Arbitrary Damping
..................................187
11.4
Effective Diffusion in Periodic Potential
.......................................190
References
.....................................................................................................192
Section II Quantum Diffusion
12
Quantum
Langevin
Equations
................................................................195
12.1
Introduction
.......................................................................................195
12.2
Derivation of the Classical
Langevin
Equation
............................197
12.2.1
Ohmic Dissipation
...............................................................200
12.3
Quantum Generalization
.................................................................202
12.4
Free Particle
........................................................................................203
12.5
Diffusive Quantum Cyclotron Motion
..........................................204
12.6
Diffusive Landau Diamagnetism
...................................................208
References
.....................................................................................................213
13
Path Integral Treatment of Quantum Diffusion
..................................215
13.1
Introduction
.......................................................................................215
13.2
Basic Model
........................................................................................217
13.3
Ohmic Dissipation and Classical Limit
.........................................219
13.4
Master Equation in High-Temperature Limit
...............................221
13.5
Application to Dissipative Diamagnetism
....................................222
References
.....................................................................................................226
14
Quantum Continuous Time Random Walk Model
.............................227
14.1
Introduction
.......................................................................................227
14.2
Formulation
........................................................................................228
14.2.1
Zero-Collision Term
............................................................229
14.2.2
One-Collision Term
.............................................................229
14.2.3
Two-Collision Term
.............................................................230
Contents
їх
14.3 Applications.......................................................................................231
14.3.1 Quantum Harmonie
Oscillator
..........................................231
14.3.2 Spin Relaxation.....................................................................233
14.4
Finite Temperature Effects
...............................................................234
14.4.1 Relaxation
of the Harmonic Oscillator at Finite
Temperatures
........................................................................234
14.4.2
Phase Space Dynamics and Free Particle Limit
..............236
14.4.3
Spin Relaxation at Finite Temperatures: Bloch-
Redfield Equations
...............................................................236
References
.....................................................................................................237
15
Quantum Jump Models
.............................................................................239
15.1
Introduction
.......................................................................................239
15.1.1
Spin Lattice Relaxation in Solids
.......................................240
15.1.2
Quantum Tunneling in Symmetric Double Well
............240
15.1.3
Tunneling in Asymmetric Double Well
...........................241
15.1.4
Dephasing of Qubit
.............................................................241
15.2
Formalism
..........................................................................................242
15.2.1
Cumulant
Expansion
...........................................................242
15.2.2
Resolvent Expansion
...........................................................248
15.3
Polaronic Transformation
................................................................249
15.3.1
Asymmetric Spin Boson Model
.........................................251
15.4
Qubit
...................................................................................................255
15.5
Neutron Structure Factor for
H
Diffusion in Metals
...................259
15.6
Spin Relaxation of Muon Diffusion in Metals
..............................262
References
.....................................................................................................264
16
Quantum Diffusion: Decoherence and Localization
..........................265
16.1
Introductory Comments
..................................................................265
16.2
Landau to Bohr-van
Leeuwen
Transition of Diamagnetism
.....267
16.3
Harmonic Oscillator in Quantum Diffusive Regime
..................269
16.4
Decoherence in Spin Boson Model
.................................................271
16.5
Dissipationless Decoherence
...........................................................271
16.6
Retrieving Quantum Information Despite Decoherence
............275
16.7
Localization of Electronic States in Disordered Systems
............279
References
.....................................................................................................282
Index
........................ ................................................................................283
|
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| id | DE-604.BV041638962 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:01:32Z |
| institution | BVB |
| isbn | 9781439895573 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027079800 |
| oclc_num | 886688896 |
| open_access_boolean | |
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| owner_facet | DE-91G DE-BY-TUM DE-703 DE-M49 DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XV, 292 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Dattagupta, Sushanta 1947- Verfasser (DE-588)128838574 aut Diffusion formalism and applications Sushanta Dattagupta Boca Raton, Fla. [u.a.] CRC Press 2014 XV, 292 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Diffusion (DE-588)4012277-3 gnd rswk-swf Diffusion (DE-588)4012277-3 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027079800&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027079800&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Dattagupta, Sushanta 1947- Diffusion formalism and applications Diffusion (DE-588)4012277-3 gnd |
| subject_GND | (DE-588)4012277-3 |
| title | Diffusion formalism and applications |
| title_auth | Diffusion formalism and applications |
| title_exact_search | Diffusion formalism and applications |
| title_full | Diffusion formalism and applications Sushanta Dattagupta |
| title_fullStr | Diffusion formalism and applications Sushanta Dattagupta |
| title_full_unstemmed | Diffusion formalism and applications Sushanta Dattagupta |
| title_short | Diffusion |
| title_sort | diffusion formalism and applications |
| title_sub | formalism and applications |
| topic | Diffusion (DE-588)4012277-3 gnd |
| topic_facet | Diffusion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027079800&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027079800&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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