Classical and quantum dissipative systems:
"Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they sho...
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| Edition: | Second edition |
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| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Summary: | "Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potentials models of nuclear reactions are considered and solved. Readership: Researchers and graduate students in applied mathematics and theoretical physics"... |
| Physical Description: | xvi, 576 Seiten Diagramme |
| ISBN: | 9789813207905 9813207906 9789813207912 9813207914 |
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| adam_text | CLASSICAL AND QUANTUM DISSIPATIVE SYSTEMS
/ RAZAVY, MOHSENYYEAUTHOR
: 2017
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PHENOMENOLOGICAL EQUATIONS OF MOTION FOR DISSIPATIVE SYSTEMS
LAGRANGIAN FORMULATION
HAMILTONIAN FORMULATION
HAMILTON-JACOBI FORMULATION
MOTION OF A CHARGED DAMPED PARTICLE IN AN EXTERNAL ELECTROMAGNETIC FIELD
NOETHER AND NON-NOETHER SYMMETRIES AND CONSERVATION LAWS
DISSIPATIVE FORCES DERIVED FROM MANY-BODY PROBLEMS
DAMPED MOTION OF THE CENTRAL PARTICLE
CLASSICAL MICROSCOPIC MODELS OF DISSIPATION AND MINIMAL COUPLING RULE
QUANTIZATION OF DISSIPATIVE SYSTEMS
QUANTIZATION OF EXPLICITLY TIME-DEPENDENT HAMILTONIANS
COHERENT STATE FORMULATION OF DAMPED SYSTEMS
DENSITY MATRIX AND THE WIGNER DISTRIBUTION FUNCTION
PATH INTEGRAL FORMULATION OF A DAMPED HARMONIC OSCILLATOR
QUANTIZATION OF THE MOTION OF AN INFINITE CHAIN
THE HEISENBERG EQUATIONS OF MOTION FOR A PARTICLE COUPLED TO A HEAT BATH
QUANTUM MECHANICAL MODELS OF DISSIPATIVE SYSTEMS
DISSIPATION ARISING FROM THE MOTION OF THE BOUNDARIES
THE OPTICAL POTENTIAL
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
Titel: Classical and quantum dissipative systems
Autor: Razavy, Mohsen
Jahr: 2017
Contents
Preface to the Second Edition vii
Preface to the First Edition ix
Introduction 1
1 Phenomenological Equations of Motion for Dissipative Systems 5
1.1 Frictional Forces Depending on Velocity.............. 5
1.2 Drag Force on a Sphere Moving through Viscous Fluid...... 8
1.3 Raleigh s Oscillator.......................... 13
1.4 Frictional Forces Quadratic in Velocity............... 13
1.5 Non-Newtonian and Nonlocal Dissipative Forces ......... 16
1.6 One-Dimensional Dissipative Motion and the Problem of
Harmonically Bound Electron.................... 17
1.7 Abraham-Lorentz-Dirac Equation for Radiating Electron..... 20
1.8 The Abraham-Lorentz-Dirac Equations of Motion for a Charged
Particle................................ 21
1.9 A Method for Solving Abraham-Lorentz-Dirac Equation..... 26
1.10 The Classical Theory of Line Width................ 29
1.11 Dynamical Systems Expressible as Linear Difference Equations . 30
1.12 The Fermi Accelerator......................... 32
2 Lagrangian Formulation 47
2.1 Dissipative Functions of Rayleigh, Lur e and Sedov........ 48
2.2 The Inverse Problem of Analytical Dynamics........... 53
2.3 Some Examples of the Lagrangians for Dissipative Systems ... 63
2.4 Non-Uniqueness of the Lagrangian................. 66
2.5 Acceptable Lagrangians for Dissipative Systems.......... 69
2.6 Complex or Leaky Spring Constant................. 71
2.7 A Fractional Derivative Approach to the Lagrangian for the
Damped Motion........................... 72
xi
xii Classical and Quantum Dissipative Systems
3 Hamiltonian Formulation 79
3.1 Inverse Problem for the Hamiltonian................ 79
3.2 Nonuniqueness of the Hamiltonian for Dissipative Motions in the
Coordinate Space and in the Phase Space............. 82
3.3 Ostrogradsky s Method ....................... 86
3.4 Dekker s Complex Coordinate Formulation ............ 88
3.5 Hamiltonian Formulation of the Motion of a Particle with
Variable Mass............................. 89
3.6 Variable Mass Oscillator....................... 90
3.7 Bateman s Damped-Amplified Harmonic Oscillators ....... 92
3.8 Group-Theoretical Approach to the Solution of the Damped
Harmonic Oscillator......................... 98
3.9 Dissipative Forces Quadratic in Velocity.............. 101
3.10 Resistive Forces Proportional to Arbitrary Powers of Velocity . . 102
3.11 Constrained Lagrangian and Hamiltonian Formulation of Damped
Systems................................ 103
3.12 Hamiltonian Formulation in Phase Space of A^-Dimensions. . . . 106
3.13 Classical Brackets for Damped Systems .............. 109
3.14 Dynamical Matrix Formulation of the Classical Hamiltonian and
the Generalized Poisson Bracket .................. 114
3.15 Symmetric Phase Space Formulation of the Damped Harmonic
Oscillator............................... 117
3.16 Hamiltonian Formulation of Dynamical Systems Expressible as
Difference Equations......................... 118
3.17 Fractional Derivatives in the Hamiltonian Formulation of Damped
Motion................................. 119
4 Hamilton-Jacobi Formulation 127
4.1 The Hamilton-Jacobi Equation for Linear Damping........ 128
4.2 Classical Action for an Oscillator with Leaky Spring Constant . . 130
4.3 More About the Hamilton-Jacobi Equation for the
Damped Motion ........................... 131
4.4 The Hamilton-Jacobi Equation with Fractional Derivative .... 133
5 Motion of a Charged Damped Particle in an
External Electromagnetic Field 137
6 Noether and Non-Noether Symmetries and
Conservation Laws 143
6.1 Non-Noether Symmetries and Conserved Quantities....... 150
6.2 Noether s Theorem for a Scalar Field................ 152
7 Dissipative Forces Derived from Many-Body Problems 157
7.1 The Schrödinger Chain........................ 157
7.2 A Particle Coupled to a Chain................... 159
7.3 Dynamics of a Non-Uniform Chain................. 161
Contents xiii
7.4 Mechanical System Coupled to a Heat Bath............164
7.5 Euclidean Lagrangian........................171
7.6 Hamiltonian Formulation of a Tuned Circuit Coupled to a
Transmission Line..........................172
8 The Equation of Motion for an Oscillator Coupled to a Field 179
8.1 Harmonically Bound Radiating Electron..............179
8.2 An Oscillator Coupled to a String of Finite Length........181
8.3 An Oscillator Coupled to an Infinite String............186
9 Damped Motion of the Central Particle 191
9.1 Diagonalization of the Quadratic Hamiltonian...........191
10 Classical Microscopic Models of Dissipation and Minimal
Coupling Rule 201
11 Quantization of Dissipative Systems 205
11.1 Early Attempts to Quantize the Damped Oscillator....... 206
11.2 Tarasov s Conditions for a Self-Consistent Quantum-Mechanical
Formulation of Dissipative Systems................ 209
11.3 Yang-Feldman Method of Quantization.............. 214
11.4 Heisenberg s Equations of Motion for Dekker s Formulation . . 216
11.5 Quantization of the Bateman Hamiltonian............ 217
11.6 Quantization of Pseudo-Hermitian Hamiltonian for a Damped
Harmonic Oscillator......................... 223
11.7 Fermi s Nonlinear Equation for Quantized Radiation Reaction . 226
11.8 Attempts to Quantize Systems with a Dissipative Force
Quadratic in Velocity........................ 229
11.9 Solution of the Wave Equation for Linear and Newtonian
Damping Forces........................... 231
11.10 Quantization of a Damped Hamiltonian Given by a Dynamical
Matrix................................ 234
11.11 Embedding a Damped Motion in a Volume-Preserving
Dynamical System......................... 239
11.12 Lagrangians and Hamiltonians for Velocity-Dependent Forces . 245
11.13 Quadratic Damping as an Externally Applied Force....... 250
11.14 Motion in a Viscous Field of Force Proportional to an Arbitrary
Power of Velocity.......................... 252
11.15 The Classical Limit and the Van Vleck Determinant ...... 253
11.16 Fractional Derivatives and the Wave Equation with
Linear Damping........................... 254
12 Quantization of Explicitly Time-Dependent Hamiltonians 259
12.1 Wave Equation for the Caldirola-Kanai Hamiltonian ......259
12.2 Quantization of a System with Variable Mass..........266
xiv Classical and Quantum Dissipative Systems
12.3 Evolution Operator Method for the Variable Mass
Harmonic Oscillator.........................269
12.4 The Schrödinger-Langevin Equation for a Charged Particle
Moving in an External Electromagnetic Field ..........272
12.5 Extensions of the Madelung Hydrodynamical Formulation of
Wave Mechanics...........................275
12.6 Quantization of a Modified Hamilton-Jacobi Equation for
Damped Systems..........................282
12.7 Exactly Solvable Cases of the Schrödinger-Langevin Equation . 287
12.8 Harmonically Bound Radiating Electron and the Schrödinger-
Langevin Equation.........................290
12.9 Other Phenomenological Nonlinear Potentials for
Dissipative Systems.........................292
12.10 Scattering in the Presence of Frictional Forces..........294
12.11 Application of the Noether Theorem: Linear and Nonlinear
Wave Equations for Dissipative Systems.............296
12.12 Wave Equation for Impulsive Forces Acting at Certain Intervals 298
12.13 Classical Limit for the Time-Dependent Problems........299
13 Coherent State Formulation of Damped Systems 305
13.1 First Integral of Motion and Quantum Description of an
Oscillator with Variable Frequency.................305
13.2 Wave Function and the Coherent State Representation for the
Time-Dependent Harmonic Oscillator ...............309
13.3 First Integrals of Motion and the Creation and Annihilation
Operators...............................311
13.4 Coherent State for the Central Oscillator .............315
13.5 Coherent States for Harmonic Oscillator with Time-Dependent
Frequency...............................317
14 Density Matrix and the Wigner Distribution Function 323
14.1 Classical Distribution Function for Nonconservative Motions . . . 323
14.2 The Density Matrix ......................... 326
14.3 Phase Space Quantization of Dekker s Hamiltonian........ 329
14.4 Density Operator and the Fokker-Planck Equation for Dekker s
Hamiltonian.............................. 331
14.5 Squeezed State of a Damped Harmonic Oscillator......... 333
14.6 A Different Formulation of the Problem of Time-Dependence of
the Squeezed State.......................... 338
14.7 Density Matrix Formulation of a Solvable Model......... 340
14.8 Wigner Distribution Function for the Damped Oscillator..... 344
14.9 Density Operator for a Particle Coupled to a Heat Bath..... 346
Contents xv
15 Path Integral Formulation of a Damped Harmonie Oscillator 351
15.1 Propagator for the Damped Harmonic Oscillator......... 352
15.2 Path Integral Quantization of a Harmonic Oscillator with
Complex Spring Constant...................... 358
15.3 Other Formulations of Classical Actions and the Corresponding
Propagators for the Damped Harmonic Oscillator......... 361
15.4 Path Integral Formulation of a System Coupled to a Heat Bath . 365
16 Quantization of the Motion of an Infinite Chain 371
16.1 Quantum Mechanics of a Uniform Chain..............371
16.2 Ground State of the Central Particle................374
16.3 Wave Equation for a Non-Uniform Chain.............376
16.4 Connection with Other Phenomenological Frictional Forces . . . 378
16.5 Fokker-Planck Equation for the Probability Density .......379
17 The Heisenberg Equations of Motion for a Particle Coupled
to a Heat Bath 383
17.1 Heisenberg Equations for a Damped Harmonic Oscillator .... 383
17.2 Heisenberg-Langevin Equations for a Damped Harmonic
Oscillator: Quantized Noise Operator............... 388
17.3 Quantization of the Motion of an Oscillator Coupled to
a String ............................... 393
17.4 Quantized Motion of a Spring Attached to a Finite String . . . 399
17.5 Senitzky s Model.......................... 401
17.6 Density Matrix for the Motion of a Particle Coupled to
a Field................................ 403
17.7 Commutation Relations for the Motion for the
Central Particle........................... 406
17.8 Wave Equation for the Motion of the Central Particle...... 407
17.9 Motion of the Center-of-Mass in a Viscous Medium....... 414
17.10 Invariance Under Galilean Transformation............ 417
17.11 Velocity Coupling and Coordinate Coupling........... 418
18 Quantum Mechanical Models of Dissipative Systems 421
18.1 General Properties of the Decay Modes of Quantum
Mechanical Systems.........................421
18.2 Forced Vibration of a Chain of Oscillators with Damping .... 427
18.3 A Spin System Coupled to a Tuned Circuit Coupled to a
Transmission Line..........................430
18.4 Coupling of a Quantum System to a Dissipative
Classical Motion...........................440
18.5 The Wigner-Weisskopf Model...................446
18.6 Equation of Motion for a Harmonically Bound
Radiating Electron.........................450
xvi Classical and Quantum Dissipative Systems
18.7 Path Integral Approach to the Spectrum of Harmonically
Bound Oscillator..........................455
18.8 More about the Quantum-Mechanical Formulation of the
Abraham-Lorentz-Dirac Equation.................459
18.9 Quantum Theory of Line Width..................463
18.10 Spin-Boson System: Another Model of Dissipative Two-Level
Quantum System..........................469
18.11 Gisin s Nonlinear Wave Equation.................474
18.12 Gisin s Formulation of Dissipation for Systems Periodic
in Time...............................477
18.13 Nonlinear Generalization of the Wave Equation.........483
18.14 Decaying States in a Many-Boson System ............491
19 Dissipation Arising from the Motion of the Boundaries 503
19.1 Dissipative Forces Arising from Vacuum Fluctuations.......510
19.2 Frictional Force on an Atom Moving with Constant Velocity above
a Planar Surface...........................515
19.3 Motion of the Boundaries and Production of Particles in Two-
Dimensional Space-Time.......................519
19.4 Dissipative Force Acting on a Spherical Mirror Moving
in Vacuum...............................529
20 The Optical Potential 537
20.1 The Classical Analogue of a Nonlocal Interaction.........544
20.2 Minimal and/or Maximal Coupling when the Potential is Real
and Nonlocal.............................547
20.3 Optical Potential and the Classical Velocity-Dependent Frictional
Force..................................551
20.4 A Solvable Model Showing the Energy Transfer from the
Collective to Intrinsic Degrees of Freedom.............556
20.5 Damped Harmonic Oscillator and Optical Potential........563
20.6 Quantum Mechanical Analogue of the Raleigh Oscillator.....567
Index 570
|
| any_adam_object | 1 |
| author | Razavy, Mohsen |
| author_GND | (DE-588)143888528 |
| author_facet | Razavy, Mohsen |
| author_role | aut |
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| callnumber-label | QC173 |
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| classification_rvk | UL 2000 |
| ctrlnum | (OCoLC)994197712 (DE-599)BVBBV044422955 |
| 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 |
| edition | Second edition |
| format | Book |
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Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potentials models of nuclear reactions are considered and solved. 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| id | DE-604.BV044422955 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:52:33Z |
| institution | BVB |
| isbn | 9789813207905 9813207906 9789813207912 9813207914 |
| language | English |
| lccn | 016058647 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029824515 |
| oclc_num | 994197712 |
| open_access_boolean | |
| owner | DE-11 DE-29T DE-91G DE-BY-TUM |
| owner_facet | DE-11 DE-29T DE-91G DE-BY-TUM |
| physical | xvi, 576 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Razavy, Mohsen (DE-588)143888528 aut Classical and quantum dissipative systems Mohsen Razavy, University of Alberta, Canada Second edition New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2017] © 2017 xvi, 576 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier "Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potentials models of nuclear reactions are considered and solved. Readership: Researchers and graduate students in applied mathematics and theoretical physics"... Quantentheorie Energy dissipation Quantum theory Mechanics Fluktuations-Dissipations-Theorem (DE-588)4306911-3 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Quantentheorie (DE-588)4047992-4 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 LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029824515&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029824515&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Razavy, Mohsen Classical and quantum dissipative systems Quantentheorie Energy dissipation Quantum theory Mechanics Fluktuations-Dissipations-Theorem (DE-588)4306911-3 gnd Dissipatives System (DE-588)4209641-8 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4306911-3 (DE-588)4209641-8 (DE-588)4047992-4 |
| title | Classical and quantum dissipative systems |
| title_auth | Classical and quantum dissipative systems |
| title_exact_search | Classical and quantum dissipative systems |
| title_full | Classical and quantum dissipative systems Mohsen Razavy, University of Alberta, Canada |
| title_fullStr | Classical and quantum dissipative systems Mohsen Razavy, University of Alberta, Canada |
| title_full_unstemmed | Classical and quantum dissipative systems Mohsen Razavy, University of Alberta, Canada |
| title_short | Classical and quantum dissipative systems |
| title_sort | classical and quantum dissipative systems |
| topic | Quantentheorie Energy dissipation Quantum theory Mechanics Fluktuations-Dissipations-Theorem (DE-588)4306911-3 gnd Dissipatives System (DE-588)4209641-8 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Quantentheorie Energy dissipation Quantum theory Mechanics Fluktuations-Dissipations-Theorem Dissipatives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029824515&sequence=000001&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=029824515&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT razavymohsen classicalandquantumdissipativesystems |
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