Classical and quantum dissipative systems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
2005
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 334 S. graph. Darst. |
| ISBN: | 1860945252 1860945309 |
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MARC
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| 245 | 1 | 0 | |a Classical and quantum dissipative systems |c Mohsen Razavy |
| 264 | 1 | |a London |b Imperial College Press |c 2005 | |
| 300 | |a XV, 334 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Dissipation d'énergie | |
| 650 | 7 | |a Mecânica quântica |2 larpcal | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Energy dissipation | |
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Quantum theory | |
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Record in the Search Index
| _version_ | 1804135426707947520 |
|---|---|
| adam_text | Contents
Dedication
v
Preface
vii
1
Introduction
1
2
Phenomenological
Equations of Motion for
Dissipative Systems
5
2.1
Frictional Forces Linear Velocity
.................. 5
2.2
Raleigh s Oscillator
.......................... 8
2.3
One-Dimensional Motion and Bopp
Transformation
............................ 8
2.4
The Classical Theory of Line Width
................ 11
2.5
Frictional Forces Quadratic in Velocity
............... 12
2.6
Non-Newtonian and Nonlocal Dissipative
Forces
................................. 13
3
Lagrangian Formulations
15
3.1
Rayleigh and Lur e Dissipative Functions
............. 15
3.2
Inverse Problem of Analytical Dynamics
.............. 20
3.3
Some Examples of the Lagrangians for
Dissipative Systems
......................... 24
ix
x
Classical and Quantum Dissipative Systems
3.4
Non-Uniqueness of the Lagrangian
................. 27
3.5
Acceptable Lagrangians for Dissipative
Systems
................................ 30
4
Hamiltonian Formulation
33
4.1
Inverse Problem for the Hamiltonian
................ 33
4.2
Hamiltonians for Simple Dissipative Systems
........... 36
4.3
Ostrogradsky s Method
....................... 39
4.4
Complex or Leaky Spring Constant
................. 42
4.5
Dekker s Complex Coordinate Formulation
............ 42
4.6
Hamiltonian Formulation of the Motion
of a Particle with Variable Mass
.................. 44
4.7
Variable Mass Oscillator
....................... 45
4.8
Bateman s Damped-Amplified Harmonic
Oscillators
............................... 47
4.9
Dissipative Forces Quadratic in Velocity
.............. 48
4.10
Resistive Forces Proportional to Arbitrary
Powers of Velocity
.......................... 48
4.11
Universal Lagrangian and Hamiltonian
............... 49
4.12
Hamiltonian Formulation in Phase Space of
N-Dimensions .... 52
4.13
Symmetric Phase Space Formulation of
the Damped Harmonic Oscillator
.................. 55
4.14
Dynamical Systems Expressible as Linear Difference Equations
. 57
5
Hamilton-Jacobi Formulation
63
5.1
The Hamilton-Jacobi Equation for
Linear Damping
........................... 64
Contents xi
5.2
Classical Action for an Oscillator with
Leaky Spring Constant
........................ 66
5.3
More About the Hamilton-Jacobi
Equation for the Damped Motion
.................. 67
6
Motion of a Charged Particle in an External
Electromagnetic Field in the Presence of Damping
71
7
Noether and Non-Noether Symmetries and Conservation Laws
77
7.1
Non-Noether Symmetries and Conserved
Quantities
............................... 84
7.2
Noether s Theorem for a Scalar Field
................ 86
8
Dissipative Forces Derived from Many-Body Problems
91
8.1
The
Schrödinger
Chain
........................ 91
8.2
A Particle Coupled to a Chain
................... 93
8.3
Dynamics of a Non-Uniform Chain
................. 94
8.4
Mechanical System Coupled to a Heat Bath
............ 98
8.5
Euclidean Lagrangian
........................ 104
9
A Particle Coupled to a Field
107
9.1
Harmonically Bound Radiating Electron
..............107
9.2
An Oscillator Coupled to a String of Finite Length
........109
9.3
An Oscillator Coupled to an Infinite String
............112
10
Damped Motion of the Central Particle
117
10.1
Diagonalization of the Hamiltonian
.................117
xii
Classical and Quantum Dissipative Systems
11
Classical Microscopic Models of Dissipation and Minimal
Coupling Rule
125
12
Quantization of Dissipative Systems
129
12.1
Early Attempts to Quantize the Damped Oscillator
.......129
12.2
Yang-Feldman Method of Quantization
..............136
12.3
Heisenberg s Equations of Motion
for Dekker s Formulation
......................138
12.4
Quantization of the Bateman Hamiltonian
............139
12.5
Fermi s Nonlinear Equation for Quantized Radiation Reaction
. 142
12.6
Attempts to Quantize Systems with a
Dissipative Force Quadratic in Velocity
..............145
12.7
Solution of the Wave Equation for
Linear and Newtonian Damping Forces
..............147
12.8
The Classical Limit of the
Schrödinger
Equation with Velocity-Dependent Forces
.............150
12.9
Quadratic Damping as an Externally
Applied Force
............................151
12.10
Motion in a Viscous Field of Force
Proportional to an Arbitrary Power of
Velocity
...............................153
12.11
The Classical Limit and the Van Vleck Determinant
.......154
13
Quantization of Explicitly Time-Dependent Hamiltonian
157
13.1
Wave Equation for the Kanai-Caldirola
Hamiltonian
.............................157
13.2
Coherent States of a Damped Oscillator
.............164
13.3
Squeezed State of a Damped Harmonic
Oscillator
...............................167
Contents xiii
13.4
Quantization of a System with Variable Mass
..........169
13.5
The
Schrödinger-Langevin
Equation for
Linear Damping
...........................172
13.6
An Extension of the Madelung
Formulation
.............................175
13.7
Quantization of a Modified Hamilton-
Jacobi Equation for Damped Systems
...............180
13.8
Exactly Solvable Cases of the
Schrödinger
-Langevin
Equation
.........................184
13.9
Harmonically Bound Radiating Electron
and the
Schrödinger-Langevin
Equation
..............187
13.10
Other Phenomenological Nonlinear
Potentials for Dissipative Systems
.................189
13.11
Scattering in the Presence of Factional Forces
..........192
13.12
Application of the Noether Theorem:
Linear and Nonlinear Wave Equations for Dissipative Systems
. 193
13.13
Wave Equation for Impulsive Forces
Acting at Certain Intervals
.....................196
13.14
Classical Limit for the Time-Dependent Problems
........197
14
Density Matrix and the Wigner Distribution Function
201
14.1
Classical Distribution Function for
Nonconservative
Motions
......................201
14.2
The Density Matrix
.........................205
14.3
Phase Space Quantization of Dekker s
Hamiltonian
.............................207
14.4
Density Operator and the Fokker-Planck
Equation
...............................209
14.5
The Density Matrix Formulation of a
Solvable Model
...........................213
xiv
Classical and Quantum Dissipative Systems
14.6
Wigner Distribution Function for the
Damped Oscillator
..........................216
14.7
Density Operator for a Particle Coupled to a Heat Bath
.....219
15
Path Integral Formulation of a Damped
Harmonic Oscillator
223
15.1
Propagator for the Damped Harmonic
Oscillator
...............................224
15.2
Path Integral Quantization of a Harmonic
Oscillator with Complex Spring
Constant
...............................230
15.3
Modified Classical Action and the
Propagator for the Damped Harmonic
Oscillator
...............................233
15.4
Path Integral Formulation of a System
Coupled to a Heat Bath
.......................235
16
Quantization of the Motion of an Infinite Chain
239
16.1
Quantum Mechanics of a Uniform Chain
..............239
16.2
Ground State of the Central Particle
................242
16.3
Wave Equation for a Non-Uniform Chain
.............244
16.4
Connection with Other Phenomenological Frictional Forces
. . . 246
16.5
Fokker-Planck Equation for the
Probability Density
...........................247
17
The
Heisenberg
Equations of Motion for a Particle Coupled
to a Heat Bath
249
17.1 Heisenberg
Equations for a Damped
Harmonic Oscillator
.........................249
17.2
Density Matrix for the Motion of a
Particle Coupled to a Field
.....................260
Contents xv
17.3
Equations
of Motion for the Central
Particle
................................ 263
17.4
Wave Equation for the Motion of the
Central Particle
............................ 264
17.5
Motion of the Center-of-Mass in Viscous Medium
......... 269
17.6
Invariance
Under Galilean Transformation
............. 272
17.7
Velocity Coupling and Coordinate Coupling
............ 273
17.8
Equation of Motion for a Harmonically
Bound Radiating Electron
...................... 274
18
Quantum Mechanical Models of Dissipative Systems
279
18.1
Forced Vibration with Damping
................... 279
18.2
The Wigner-
Weisskopf
Model
.................... 282
18.3
Quantum Theory of Line Width
.................. 286
18.4
The Optical Potential
........................ 291
18.5
Gisin s Nonlinear Wave Equation
.................. 295
18.6
Nonlinear Generalization of the Wave
Equation
............................... 298
18.7
Dissipation Arising from the Motion of the Boundaries
...... 301
18.8
Decaying States in a Many-Boson System
............. 308
19
More on the Concept of Optical Potential
315
19.1
The Classical Analogue of the Nonlocal Interaction
........ 315
19.2
Minimal and/or Maximal Coupling
................. 319
19.3
Damped Harmonic Oscillator and Optical Potential
........ 323
19.4
Quantum Mechanical Analogue of the
Raleigh Oscillator
........................... 326
Index
331
|
| adam_txt |
Contents
Dedication
v
Preface
vii
1
Introduction
1
2
Phenomenological
Equations of Motion for
Dissipative Systems
5
2.1
Frictional Forces Linear Velocity
. 5
2.2
Raleigh's Oscillator
. 8
2.3
One-Dimensional Motion and Bopp
Transformation
. 8
2.4
The Classical Theory of Line Width
. 11
2.5
Frictional Forces Quadratic in Velocity
. 12
2.6
Non-Newtonian and Nonlocal Dissipative
Forces
. 13
3
Lagrangian Formulations
15
3.1
Rayleigh and Lur'e Dissipative Functions
. 15
3.2
Inverse Problem of Analytical Dynamics
. 20
3.3
Some Examples of the Lagrangians for
Dissipative Systems
. 24
ix
x
Classical and Quantum Dissipative Systems
3.4
Non-Uniqueness of the Lagrangian
. 27
3.5
Acceptable Lagrangians for Dissipative
Systems
. 30
4
Hamiltonian Formulation
33
4.1
Inverse Problem for the Hamiltonian
. 33
4.2
Hamiltonians for Simple Dissipative Systems
. 36
4.3
Ostrogradsky's Method
. 39
4.4
Complex or Leaky Spring Constant
. 42
4.5
Dekker's Complex Coordinate Formulation
. 42
4.6
Hamiltonian Formulation of the Motion
of a Particle with Variable Mass
. 44
4.7
Variable Mass Oscillator
. 45
4.8
Bateman's Damped-Amplified Harmonic
Oscillators
. 47
4.9
Dissipative Forces Quadratic in Velocity
. 48
4.10
Resistive Forces Proportional to Arbitrary
Powers of Velocity
. 48
4.11
Universal Lagrangian and Hamiltonian
. 49
4.12
Hamiltonian Formulation in Phase Space of
N-Dimensions . 52
4.13
Symmetric Phase Space Formulation of
the Damped Harmonic Oscillator
. 55
4.14
Dynamical Systems Expressible as Linear Difference Equations
. 57
5
Hamilton-Jacobi Formulation
63
5.1
The Hamilton-Jacobi Equation for
Linear Damping
. 64
Contents xi
5.2
Classical Action for an Oscillator with
Leaky Spring Constant
. 66
5.3
More About the Hamilton-Jacobi
Equation for the Damped Motion
. 67
6
Motion of a Charged Particle in an External
Electromagnetic Field in the Presence of Damping
71
7
Noether and Non-Noether Symmetries and Conservation Laws
77
7.1
Non-Noether Symmetries and Conserved
Quantities
. 84
7.2
Noether's Theorem for a Scalar Field
. 86
8
Dissipative Forces Derived from Many-Body Problems
91
8.1
The
Schrödinger
Chain
. 91
8.2
A Particle Coupled to a Chain
. 93
8.3
Dynamics of a Non-Uniform Chain
. 94
8.4
Mechanical System Coupled to a Heat Bath
. 98
8.5
Euclidean Lagrangian
. 104
9
A Particle Coupled to a Field
107
9.1
Harmonically Bound Radiating Electron
.107
9.2
An Oscillator Coupled to a String of Finite Length
.109
9.3
An Oscillator Coupled to an Infinite String
.112
10
Damped Motion of the Central Particle
117
10.1
Diagonalization of the Hamiltonian
.117
xii
Classical and Quantum Dissipative Systems
11
Classical Microscopic Models of Dissipation and Minimal
Coupling Rule
125
12
Quantization of Dissipative Systems
129
12.1
Early Attempts to Quantize the Damped Oscillator
.129
12.2
Yang-Feldman Method of Quantization
.136
12.3
Heisenberg's Equations of Motion
for Dekker's Formulation
.138
12.4
Quantization of the Bateman Hamiltonian
.139
12.5
Fermi's Nonlinear Equation for Quantized Radiation Reaction
. 142
12.6
Attempts to Quantize Systems with a
Dissipative Force Quadratic in Velocity
.145
12.7
Solution of the Wave Equation for
Linear and Newtonian Damping Forces
.147
12.8
The Classical Limit of the
Schrödinger
Equation with Velocity-Dependent Forces
.150
12.9
Quadratic Damping as an Externally
Applied Force
.151
12.10
Motion in a Viscous Field of Force
Proportional to an Arbitrary Power of
Velocity
.153
12.11
The Classical Limit and the Van Vleck Determinant
.154
13
Quantization of Explicitly Time-Dependent Hamiltonian
157
13.1
Wave Equation for the Kanai-Caldirola
Hamiltonian
.157
13.2
Coherent States of a Damped Oscillator
.164
13.3
Squeezed State of a Damped Harmonic
Oscillator
.167
Contents xiii
13.4
Quantization of a System with Variable Mass
.169
13.5
The
Schrödinger-Langevin
Equation for
Linear Damping
.172
13.6
An Extension of the Madelung
Formulation
.175
13.7
Quantization of a Modified Hamilton-
Jacobi Equation for Damped Systems
.180
13.8
Exactly Solvable Cases of the
Schrödinger
-Langevin
Equation
.184
13.9
Harmonically Bound Radiating Electron
and the
Schrödinger-Langevin
Equation
.187
13.10
Other Phenomenological Nonlinear
Potentials for Dissipative Systems
.189
13.11
Scattering in the Presence of Factional Forces
.192
13.12
Application of the Noether Theorem:
Linear and Nonlinear Wave Equations for Dissipative Systems
. 193
13.13
Wave Equation for Impulsive Forces
Acting at Certain Intervals
.196
13.14
Classical Limit for the Time-Dependent Problems
.197
14
Density Matrix and the Wigner Distribution Function
201
14.1
Classical Distribution Function for
Nonconservative
Motions
.201
14.2
The Density Matrix
.205
14.3
Phase Space Quantization of Dekker's
Hamiltonian
.207
14.4
Density Operator and the Fokker-Planck
Equation
.209
14.5
The Density Matrix Formulation of a
Solvable Model
.213
xiv
Classical and Quantum Dissipative Systems
14.6
Wigner Distribution Function for the
Damped Oscillator
.216
14.7
Density Operator for a Particle Coupled to a Heat Bath
.219
15
Path Integral Formulation of a Damped
Harmonic Oscillator
223
15.1
Propagator for the Damped Harmonic
Oscillator
.224
15.2
Path Integral Quantization of a Harmonic
Oscillator with Complex Spring
Constant
.230
15.3
Modified Classical Action and the
Propagator for the Damped Harmonic
Oscillator
.233
15.4
Path Integral Formulation of a System
Coupled to a Heat Bath
.235
16
Quantization of the Motion of an Infinite Chain
239
16.1
Quantum Mechanics of a Uniform Chain
.239
16.2
Ground State of the Central Particle
.242
16.3
Wave Equation for a Non-Uniform Chain
.244
16.4
Connection with Other Phenomenological Frictional Forces
. . . 246
16.5
Fokker-Planck Equation for the
Probability Density
.247
17
The
Heisenberg
Equations of Motion for a Particle Coupled
to a Heat Bath
249
17.1 Heisenberg
Equations for a Damped
Harmonic Oscillator
.249
17.2
Density Matrix for the Motion of a
Particle Coupled to a Field
.260
Contents xv
17.3
Equations
of Motion for the Central
Particle
. 263
17.4
Wave Equation for the Motion of the
Central Particle
. 264
17.5
Motion of the Center-of-Mass in Viscous Medium
. 269
17.6
Invariance
Under Galilean Transformation
. 272
17.7
Velocity Coupling and Coordinate Coupling
. 273
17.8
Equation of Motion for a Harmonically
Bound Radiating Electron
. 274
18
Quantum Mechanical Models of Dissipative Systems
279
18.1
Forced Vibration with Damping
. 279
18.2
The Wigner-
Weisskopf
Model
. 282
18.3
Quantum Theory of Line Width
. 286
18.4
The Optical Potential
. 291
18.5
Gisin's Nonlinear Wave Equation
. 295
18.6
Nonlinear Generalization of the Wave
Equation
. 298
18.7
Dissipation Arising from the Motion of the Boundaries
. 301
18.8
Decaying States in a Many-Boson System
. 308
19
More on the Concept of Optical Potential
315
19.1
The Classical Analogue of the Nonlocal Interaction
. 315
19.2
Minimal and/or Maximal Coupling
. 319
19.3
Damped Harmonic Oscillator and Optical Potential
. 323
19.4
Quantum Mechanical Analogue of the
Raleigh Oscillator
. 326
Index
331 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Razavy, Mohsen |
| author_facet | Razavy, Mohsen |
| author_role | aut |
| author_sort | Razavy, Mohsen |
| author_variant | m r mr |
| building | Verbundindex |
| bvnumber | BV021629793 |
| callnumber-first | Q - Science |
| callnumber-label | QC173 |
| callnumber-raw | QC173.458.E53 |
| callnumber-search | QC173.458.E53 |
| callnumber-sort | QC 3173.458 E53 |
| callnumber-subject | QC - Physics |
| classification_rvk | UL 2000 |
| classification_tum | PHY 054f PHY 060f |
| ctrlnum | (OCoLC)66385422 (DE-599)BVBBV021629793 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
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| id | DE-604.BV021629793 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:56:40Z |
| indexdate | 2024-07-09T20:40:19Z |
| institution | BVB |
| isbn | 1860945252 1860945309 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014844717 |
| oclc_num | 66385422 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-29T DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 |
| physical | XV, 334 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Razavy, Mohsen Verfasser aut Classical and quantum dissipative systems Mohsen Razavy London Imperial College Press 2005 XV, 334 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dissipation d'énergie Mecânica quântica larpcal Théorie quantique Quantentheorie Energy dissipation Mechanics Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Fluktuations-Dissipations-Theorem (DE-588)4306911-3 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Dissipatives System (DE-588)4209641-8 s DE-604 Fluktuations-Dissipations-Theorem (DE-588)4306911-3 s Quantentheorie (DE-588)4047992-4 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014844717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Razavy, Mohsen Classical and quantum dissipative systems Dissipation d'énergie Mecânica quântica larpcal Théorie quantique Quantentheorie Energy dissipation Mechanics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Fluktuations-Dissipations-Theorem (DE-588)4306911-3 gnd Dissipatives System (DE-588)4209641-8 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4306911-3 (DE-588)4209641-8 |
| title | Classical and quantum dissipative systems |
| title_auth | Classical and quantum dissipative systems |
| title_exact_search | Classical and quantum dissipative systems |
| title_exact_search_txtP | Classical and quantum dissipative systems |
| title_full | Classical and quantum dissipative systems Mohsen Razavy |
| title_fullStr | Classical and quantum dissipative systems Mohsen Razavy |
| title_full_unstemmed | Classical and quantum dissipative systems Mohsen Razavy |
| title_short | Classical and quantum dissipative systems |
| title_sort | classical and quantum dissipative systems |
| topic | Dissipation d'énergie Mecânica quântica larpcal Théorie quantique Quantentheorie Energy dissipation Mechanics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Fluktuations-Dissipations-Theorem (DE-588)4306911-3 gnd Dissipatives System (DE-588)4209641-8 gnd |
| topic_facet | Dissipation d'énergie Mecânica quântica Théorie quantique Quantentheorie Energy dissipation Mechanics Quantum theory Fluktuations-Dissipations-Theorem Dissipatives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014844717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT razavymohsen classicalandquantumdissipativesystems |