Decoherence and the quantum-to-classical transition:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | Corr. 2. print. |
| Series: | The frontiers collection
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [383] - 407 |
| Physical Description: | XV, 416 S. Ill., graph. Darst. |
| ISBN: | 9783540357735 |
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Record in the Search Index
| _version_ | 1804138924068569088 |
|---|---|
| adam_text | Contents
1
Introducing Decoherence
................................. 1
2 The Basic
Formalism and Interpretation of Decoherence
.. 13
2.1
The Concept and Interpretation of Quantum States
......... 14
2.1.1
Classical Versus Quantum States
................... 14
2.1.2
The Probabilistic Nature of Quantum States
......... 16
2.1.3
The Ontological Status of Quantum States
.......... 18
2.2
The Superposition Principle
............................. 20
2.2.1
The Interpretation of Superpositions
................ 20
2.2.2
Experimental Verification of Superpositions
.......... 21
2.2.3
The Scope of the Superposition Principle
............ 26
2.3
Quantum Entanglement
................................. 28
2.3.1
Quantum Versus Classical Correlations
.............. 30
2.3.2
Quantification of Entanglement and Distinguishability
32
2.4
The Concept and Interpretation of Density Matrices
........ 33
2.4.1
Pure-State Density Matrices and the Trace Operation
. 34
2.4.2
Mixed-State Density Matrices
...................... 36
2.4.3
Quantifying the Degree of Mixedness
............. 39
2.4.4
The Basis Ambiguity of Mixed-State Density Matrices
41
2.4.5
Mixed-State Density Matrices
Versus Physical Ensembles
......................... 43
2.4.6
Reduced Density Matrices
......................... 44
2.5
The Measurement Problem
and the Quantum-to-Classical Transition
.................. 49
2.5.1
The
Von
Neumann Scheme
for Ideal Quantum Measurement
................... 50
2.5.2
The Problem of the Preferred Basis
................. 53
2.5.3
The Problem of the Nonobservability of Interference
. . 55
2.5.4
The Problem of Outcomes
......................... 57
2.6
Which-Path Information and Environmental Monitoring
..... 60
2.6.1
The Double-Slit Experiment,
Which-Path Information, and Complementarity
...... 60
2.6.2
The Description of the Double-Slit Experiment
in Terms of Entanglement
......................... 63
2.6.3
The Environment as a Which-Path Monitor
......... 65
XII Contents
2.7
Decoherence and the Local Damping of Interference
......... 68
2.8
Environment-Induced Superselection
...................... 71
2.8.1
Pointer States in the Quantum-Measurement Limit
... 76
2.8.2
Pointer States in the Quantum Limit of Decoherence
.. 81
2.8.3
General Methods for Determining the Pointer States
.. 81
2.8.4
Selection of Quasiclassical Properties
............... 83
2.9
Redundant Encoding of Information in the Environment
and Quantum Darwinism
.............................. 85
2.10
A Simple Model for Decoherence
......................... 88
2.11
Decoherence Versus Dissipation
.......................... 93
2.12
Decoherence Versus Classical Noise
....................... 95
2.13
Virtual Decoherence and Quantum Erasure
.............. 98
2.14
Resolution into Subsystems
..............................101
2.15
Formal Tools and Their Interpretation
....................103
2.15.1
The Schmidt Decomposition
.......................104
2.15.2
The Wigner Representation
........................106
2.15.3
Purifying the Environment
......................109
2.15.4
The Operator-Sum Formalism
.....................110
2.16
Summary
..............................................112
3
Decoherence Is Everywhere:
Localization Due to Environmental Scattering
............115
3.1
The Scattering Model
...................................119
3.2
Calculating the Decoherence Factor
.......................122
3.3
Full Versus Partial Which-Path Resolution
.................128
3.3.1
The Short-Wavelength Limit
.......................128
3.3.2
The Long-Wavelength Limit
.......................130
3.4
Decoherence Due to Scattering of Thermal Photons
and Air Molecules
......................................132
3.4.1
Photon Scattering
................................132
3.4.2
Scattering of Air Molecules
........................136
3.4.3
Comparison with Experiments
.....................138
3.5
Dlustrating the Dynamics of Decoherence
..................139
3.6
Summary
..............................................150
4
Master-Equation Formulations of Decoherence
............153
4.1
General Formalism
.....................................154
4.2
The Born-Markov Master Equation
.......................155
4.2.1
Structure of the Born-Markov Master Equation
......156
4.2.2
Derivation of the Born-Markov Master Equation
.....158
4.3
Master Equations in the
Lindblad
Form
...................165
4.4
Non-Markovian Dynamics
...............................
Ig9
Contents XIII
A World of Spins and Oscillators:
Canonical Models for Decoherence
........................171
5.1
Mapping onto Canonical Models
..........................173
5.1.1
Mapping of the Central System
....................173
5.1.2
Mapping of the Environment
......................174
5.2
Quantum Brownian Motion
..............................178
5.2.1
Derivation of the Born-Markov Master Equation
.....178
5.2.2
Harmonic Oscillator as the Central System
..........182
5.2.3
Ohmic Decoherence and Dissipation
................188
5.2.4
The Caldeira-Leggett Master Equation
.............191
5.2.5
Dynamics of Quantum Brownian Motion
............194
5.2.6
Limitations of the Quantum Brownian Motion
and Caldeira-Leggett Models
......................203
5.2.7
Exact Master Equation
...........................206
5.3
The Spin-Boson Model
..................................207
5.3.1
Simplified Spin-Boson Model Without Tunneling
.....208
5.3.2
Born-Markov Master Equation
for the Spin-Boson Model
.........................218
5.4
Spin-Environment Models
...............................222
5.4.1
A Simple Dynamical Spin-Spin Model
..............223
5.4.2
Spin-Environment Models in the Weak-Coupling
Limit: Mapping to Oscillator Environments
..........228
5.4.3
Beyond Markov:
Solving General Spin-Environment Models
...........237
5.5
Summary
..............................................237
Of Buckey Balls and SQUIDs:
Observing Decoherence in Action
.........................243
6.1
The First Milestone: Atoms in a Cavity
...................244
6.1.1
Atom-Field Interactions and
Rabi
Oscillations
.......246
6.1.2
Creating the Cat State
............................247
6.1.3
Observing the Gradual Action of Decoherence
.......251
6.1.4
Bringing
Schrödinger
Cats Back to Life
.............255
6.2
Interferometry
with C70 Molecules
........................258
6.2.1
The Double-Slit Experiment with Electrons
..........258
6.2.2
Experimental Setup
..............................259
6.2.3
Confirming the Wave Nature of Massive Molecules
.... 262
6.2.4
Which-Path Information and Decoherence
...........263
6.2.5
Decoherence Due to Emission of Thermal Radiation
.. 265
6.2.6
Beyond Buckey Balls
.............................267
6.3
SQUIDs and Other Superconducting Qubits
...............270
6.3.1
Superconductivity and Supercurrents
............... 271
6.3.2
Basic Physics of SQUIDs
..........................272
6.3.3
Superposition States and Coherent Oscillations
in SQUIDs
......................................275
XIV Contents
6.3.4
Observing and Quantifying Decoherence
.............279
6.4
Other Experimental Domains
............................282
6.4.1
Decoherence in Bose-Einstein Condensates
..........282
6.4.2
Decoherence in Quantum-Electromechanical Systems
. 284
6.5
Outlook
...............................................289
7
Decoherence and Quantum Computing
...................293
7.1
A Brief Overview of Quantum Computing
.................294
7.1.1
The Power of Quantum Computing
.................294
7.1.2
Reading Out a Quantum Computer
.................297
7.1.3
Simulating Physical Systems
.......................298
7.1.4
Examples of Famous Quantum Algorithms
..........300
7.1.5
Physical Realizations of Quantum Computers
........300
7.2
Decoherence Versus Controllability in Quantum Computers
.. 301
7.3
Decoherence Versus Classical Fluctuations
.................302
7.4
Quantum Error Correction
..............................304
7.4.1
Classical Versus Quantum Error Correction
..........305
7.4.2
Representing the Influence of Decoherence
by Discrete Errors
................................307
7.4.3
Undoing Decoherence in a Quantum Computer
.....311
7.4.4
When Does an Error-Correcting Code Exist?
........314
7.4.5
Importance of Redundant Encoding
and the Three-Bit Code for Phase Errors
............315
7.4.6
Apparatus-Induced Decoherence and Fault Tolerance
. 320
7.5
Quantum Computation on Decoherence-Free Subspaces
.....321
7.5.1
What Does a Decoherence-Free Subspace Look Like?
. 322
7.5.2
Experimental Realizations
of Decoherence-Free Subspaces
.....................325
7.5.3
Environment Engineering and Dynamical Decoupling
. 326
7.6
Summary and Outlook
..................................327
8
The Role of Decoherence in Interpretations
of Quantum Mechanics
...................................329
8.1
The Standard and Copenhagen Interpretations
.............330
8.1.1
The Problem of Outcomes
.........................331
8.1.2
Observables,
Measurements,
and Environment-Induced Superselection
............333
8.1.3
The Concept of Classicality
in the Copenhagen Interpretation
..................335
8.2
Relative-State Interpretations
............................336
8.2.1
Everett Branches and the Preferred-Basis Problem
... 337
8.2.2
Probabilities in Relative-State Interpretations
........339
8.2.3
The Existential Interpretation
....................343
8.3
Modal Interpretations
...................................344
Contents
XV
8.3.1
Property Assignment Based on
Environment-Induced Superselection
................345
8.3.2
Property Assignment Based on
Instantaneous Schmidt Decompositions
..............345
8.3.3
Property Assignment Based on
Decompositions of the Decohered Density Matrix
.....346
8.4
Physical Collapse Theories
...............................347
8.4.1
The Preferred-Basis Problem
......................349
8.4.2
Simultaneous Presence of Decoherence
and Spontaneous Localization
......................350
8.4.3
The Tails Problem
................................351
8.4.4
Connecting Decoherence and Collapse Models
........352
8.4.5
Experimental Tests of Collapse Models
..............353
8.5
Bohmian Mechanics
....................................354
8.5.1
Particles as Fundamental Entities
..................355
8.5.2
Bohmian Trajectories and Decoherence
..............356
8.6
Summary
..............................................357
9
Observations, the Quantum Brain, and Decoherence
......359
9.1
The Role of the Observer in Quantum Mechanics
...........359
9.2
Quantum Observers and the
Von
Neumann Chain
..........361
9.3
Decoherence in the Brain:
The Brain as a Quantum Computer?
......................365
9.3.1
Decoherence Timescales for Superposition States
in Neurons
......................................368
9.3.2
Decoherence Timescales for Superposition States
in Microtubules
..................................371
9.4
Subjective Resolutions of the Measurement Problem
......375
Appendix: The Interaction Picture
...........................379
References
....................................................383
Index
.........................................................409
|
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| id | DE-604.BV035466786 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:55Z |
| institution | BVB |
| isbn | 9783540357735 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017386533 |
| oclc_num | 255093473 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-188 DE-706 |
| owner_facet | DE-355 DE-BY-UBR DE-188 DE-706 |
| physical | XV, 416 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | The frontiers collection |
| spelling | Schlosshauer-Selbach, Maximilian 1976- Verfasser (DE-588)133567796 aut Decoherence and the quantum-to-classical transition Maximilian Schlosshauer Corr. 2. print. Berlin [u.a.] Springer 2008 XV, 416 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The frontiers collection Literaturverz. S. [383] - 407 Quantenmechanik - Kohärenz Quantentheorie Coherence (Nuclear physics) Quantum theory Kohärenz (DE-588)4139923-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Kohärenz (DE-588)4139923-7 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017386533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schlosshauer-Selbach, Maximilian 1976- Decoherence and the quantum-to-classical transition Quantenmechanik - Kohärenz Quantentheorie Coherence (Nuclear physics) Quantum theory Kohärenz (DE-588)4139923-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4139923-7 (DE-588)4047989-4 |
| title | Decoherence and the quantum-to-classical transition |
| title_auth | Decoherence and the quantum-to-classical transition |
| title_exact_search | Decoherence and the quantum-to-classical transition |
| title_full | Decoherence and the quantum-to-classical transition Maximilian Schlosshauer |
| title_fullStr | Decoherence and the quantum-to-classical transition Maximilian Schlosshauer |
| title_full_unstemmed | Decoherence and the quantum-to-classical transition Maximilian Schlosshauer |
| title_short | Decoherence and the quantum-to-classical transition |
| title_sort | decoherence and the quantum to classical transition |
| topic | Quantenmechanik - Kohärenz Quantentheorie Coherence (Nuclear physics) Quantum theory Kohärenz (DE-588)4139923-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenmechanik - Kohärenz Quantentheorie Coherence (Nuclear physics) Quantum theory Kohärenz Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017386533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schlosshauerselbachmaximilian decoherenceandthequantumtoclassicaltransition |