Stationary phase and macrovariable: from wave to particle
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Kyoto
Progress of Theoretical Physics
2009 [erschienen] 2010
|
| Series: | Progress of theoretical physics supplement
182 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 208 S. |
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| 100 | 1 | |a Fukuda, Reijiro |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stationary phase and macrovariable |b from wave to particle |c by Reijiro Fukuda |
| 264 | 1 | |a Kyoto |b Progress of Theoretical Physics |c 2009 [erschienen] 2010 | |
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| 490 | 1 | |a Progress of theoretical physics supplement |v 182 | |
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| 650 | 4 | |a Quantentheorie | |
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| 830 | 0 | |a Progress of theoretical physics supplement |v 182 |w (DE-604)BV002573679 |9 182 | |
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Record in the Search Index
| _version_ | 1804141234371952640 |
|---|---|
| adam_text | Contents
1.
Introduction; macrovariable
and ordinary life
4
2.
Macrovariable
and stationary phase
7
2.1.
Motion as a whole
............................. 7
2.2.
Path integral and the stationary phase
.................. 7
2.3.
Properties of the stationary phase
.................... 8
3.
Separable case; center of mass
11
3.1.
Froin wave to particle
—
X becomes point-like particle
—....... 12
3.2.
Quantum density becomes classical local density
............ 17
3.3.
Momentum as
macrovariable
....................... 19
3.4.
Mixed state and density matrix
......,.............. , 23
3.5.
Macrovariables
in operator form
,.................... 26
3.6.
Numerical studies
...........,....,............ 27
3.7.
Presence of external force
......................... 28
3.8.
Momentum operator
............................31
4.
Theory of measurement
37
4.1.
Measurement by macrovariabl«
...................... 37
4.2.
Model I
—
center of mass as X-
—.................... 41
4.3.
Model II a
—
measurement by field theory
—.............. 46
4.4.
Model lib
—
ionization model by field theory
—■........... . 51
4.5.
Many detectors
. ..,........................... 55
2
R. Fukuda
5. Higher
orders in 1/N; correction to the ideal measurement
56
5.1.
Expansion scheme
............................. 56
5.2.
Expansion by off diagonal elements of Ho
................ 58
5.3.
The signal function
............................ 60
5.4.
Summary up to
2nd
order
......................... 65
5.5.
Numerical estimates
............................ 67
5.6.
Physical interpretation
........................... 68
6.
Determinism in new time scale
—
from particle to wave
— 69
6.1.
Starting observations
........................... 70
6.2.
Time scale and the definition of the wave function
Ψ
. ......... 71
6.3.
Summary of the theory of measurement by
macrovariable
....... 73
6.4.
Structure of Xst and the branch selection
................ 75
6.5.
Density of points, coherence and the state vector
............ 76
6.6.
Derivation of Ln/L
=>
с^ 2
........................ 79
6.7.
Time average picture
............................ 80
7.
Non-separable case
81
7.1.
Methods of treating non-separable case
................. 81
7.2.
Model
1;
Χ = Σί Χϊ/Ν
..........................
83
7.3.
Model
2;
External field
.......................... 85
7.4.
Model
3;
2-level atoms
.......................... 86
8.
Field theory I; Hermite field
91
8.1.
Model Lagrangian
.......................:.....91
8.2.
Extensive quantity and
macrovariable
..................92
8.3.
Energy eigenstate
.............................94
8.4.
Necessary theorem
.............................102
8.5.
Macrovariable
and Hilbert space
.............
;
........105
8.6.
Operator changing the macroscopic state
................
Ill
8.7.
Time evolution
...............................112
8.8.
Approximate stationary phase
......................114
9.
Field theory II; non-Hermite field
120
9.1.
Non-Hermite field
.............................121
9.2.
Macrovariable
...............................121
9.3.
The kernel has the form cF with
F
=
O(V)
...............126
9.4.
Order
paranieter
and stationary phase
..................132
10.
iV-particle system
141
10.1:
Theorems and assumptions
........................141
10.2.
Extensive quantity and
macrovariable
.................. 143
10.3.
Proof of the statement
........................... 148
10.4.
External confining potential
....................... 158
11.
Dissipation and the
macrovariable
161
11.1.
Case
1 —
Bosonic field
ф(х)
as
a macrovariable
■ —.......... 162
11.2.
Case
2 - -
normal system and adiabatic expansion
—..........168
11.3.
Order considerations for large
N ,....................172
11.4.
Stationarity and the double path effective action
. ........... 173
11.5.
Measurement in the presence of environment
......■....... . 176
Stationary Phase and
Macrovariable
--
From Wave to Particle
— 3
12.
Discussion
176
Appendix
A. Method of Steepest Descent and Stationary Phase
177
B. The Kernel
К
for Harmonic plus Linear Potential
180
C. Regularizing
л/б (ж)
181
D. Perturbative Formula
of the Kernel
К
182
E. Hermite
Field
186
F.
Κβ)
by X Integration First
190
G.
Connected Graphs and the Exponentiation
191
H. Stationarity of the
Macrovariable
in
(8-70) 193
I. Path Integral by Coherent State Representation
195
J. Non-Equilibrium Feynman Rule with Initial Equilibrium
199
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:12:38Z |
| institution | BVB |
| language | English |
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| physical | 208 S. |
| publishDate | 2009 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Progress of Theoretical Physics |
| record_format | marc |
| series | Progress of theoretical physics supplement |
| series2 | Progress of theoretical physics supplement |
| spelling | Fukuda, Reijiro Verfasser aut Stationary phase and macrovariable from wave to particle by Reijiro Fukuda Kyoto Progress of Theoretical Physics 2009 [erschienen] 2010 208 S. txt rdacontent n rdamedia nc rdacarrier Progress of theoretical physics supplement 182 Mathematische Physik Quantentheorie Mathematical physics Quantum theory Progress of theoretical physics supplement 182 (DE-604)BV002573679 182 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019015130&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fukuda, Reijiro Stationary phase and macrovariable from wave to particle Progress of theoretical physics supplement Mathematische Physik Quantentheorie Mathematical physics Quantum theory |
| title | Stationary phase and macrovariable from wave to particle |
| title_auth | Stationary phase and macrovariable from wave to particle |
| title_exact_search | Stationary phase and macrovariable from wave to particle |
| title_full | Stationary phase and macrovariable from wave to particle by Reijiro Fukuda |
| title_fullStr | Stationary phase and macrovariable from wave to particle by Reijiro Fukuda |
| title_full_unstemmed | Stationary phase and macrovariable from wave to particle by Reijiro Fukuda |
| title_short | Stationary phase and macrovariable |
| title_sort | stationary phase and macrovariable from wave to particle |
| title_sub | from wave to particle |
| topic | Mathematische Physik Quantentheorie Mathematical physics Quantum theory |
| topic_facet | Mathematische Physik Quantentheorie Mathematical physics Quantum theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019015130&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002573679 |
| work_keys_str_mv | AT fukudareijiro stationaryphaseandmacrovariablefromwavetoparticle |