Crossover time in quantum boson and spin systems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1994
|
| Series: | Lecture notes in physics
M, Monographs ; 21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 268 S. graph. Darst. |
| ISBN: | 3540580115 0387580115 |
Staff View
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| 100 | 1 | |a Berman, Gennadij P. |d 1946- |e Verfasser |0 (DE-588)1067172203 |4 aut | |
| 245 | 1 | 0 | |a Crossover time in quantum boson and spin systems |c Gennady P. Berman ; Evgeny N. Bulgakov ; Darryl D. Holm |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a XI, 268 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in physics : M, Monographs |v 21 | |
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CONTENTS
1
INTRODUCTION
1
2
METHOD
OF
COHERENT
STATES
4
2.1
INTRODUCTION
TO
THE
COHERENT
STATES
.
4
2.2
SOME
PROPERTIES
OF
BOSON
COHERENT
STATES
.
8
2.3
SOME
PROPERTIES
OF
SPIN
COHERENT
STATES
.
13
3
THE
EXACT
C-NUMBER
EQUATION
FOR
TIME-DEPENDENT
EXPECTATION
VALUES
IN
COHERENT
STATES
16
3.1
EXACT
C-NUMBER
EQUATION
FOR
QUANTUM
EXPECTATION
VALUES:
TIME-INDEPENDENT
BOSON
HAMILTONIANS
IN
COHERENT
STATES
.
17
3.2
GENERALIZATION
FOR
THE
CASE
OF
ANY
NUMBER
OF
DEGREES
OF
FREEDOM
.
20
3.3
EXAMPLE:
DYNAMICS
OF
EXPECTATION
VALUES
FOR
A
NONLINEAR
QUANTUM
OSCILLATOR
.
21
3.4
NONLINEAR
REPRESENTATION
OF
EXPECTATION-VALUE
DYNAMICS
.
24
3.5
EXACT
C-NUMBER
EQUATION
FOR
QUANTUM
EXPECTATION
VALUES:
TIME-INDEPENDENT
SPIN
HAMILTONIANS
IN
COHERENT
STATES
.
26
3.6
EXACT
C-NUMBER
EQUATION
FOR
QUANTUM
TIME-DEPENDENT
EXPECTATION
VALUES
FOR
BOSON-SPIN
HAMILTONIANS
WITH
ARBITRARY
NUMBER
OF
DEGREES
OF
FREEDOM
.
28
3.7
DYNAMICS
OF
QUANTUM
CORRELATION
FUNCTIONS
.
30
3.8
GENERALIZATION
OF
C-NUMBER
EQUATIONS
IN
THE
CASE
OF
TIME-DEPENDENT
HAMILTONIANS
.
30
4
QUASICLASSICAL
PERTURBATION
THEORY
FOR
TIME-DEPENDENT
EXPECTATION
VALUES
WITH
QUANTUM
NONLINEAR
HAMILTONIANS
32
4.1
QUASICLASSICAL
DYNAMICAL
PERTURBATION
THEORY
FOR
LINEAR
C-NUMBER
EQUATIONS
.
32
VII
4.2
NONLINEAR
DYNAMICAL
PERTURBATION
THEORY
FOR
TIME-DEPENDENT
EXPECTATION
VALUES
.
35
5
THE
CHARACTERISTIC
TIMES
OF
VIOLATION
OF
QUASICLASSICAL
APPROXIMATION
FOR
INTEGRABLE
BOSON
AND
SPIN
SYSTEMS
40
5.1
THE
CHARACTERISTIC
TIMES
OF
VIOLATION
OF
QUASICLASSICAL
APPROXIMATION
FOR
INTEGRABLE
BOSON
SYSTEMS
.
41
5.2
VIOLATION
OF
QUASICLASSICAL
APPROXIMATION
UPON
TAKING
INTO
ACCOUNT
AN
ADDITIONAL
AVERAGING
OVER
THE
INITIAL
DENSITY
MATRIX
.
46
5.3
TIME-BEHAVIOR
OF
QUANTUM
CORRELATION
FUNCTIONS
.
5.4
THE
CHARACTERISTIC
TIMES
OF
VIOLATION
OF
QUASICLASSICAL
APPROXIMATION
FOR
INTEGRABLE
QUANTUM
NONLINEAR
SPIN
SYSTEMS
.
52
5.5
APPLICATION
OF
THE
DYNAMICAL
PERTURBATION
THEORY
IN
DERIVING
THE
TIME-SCALE
T
K
.
58
5.6
THE
TIME-SCALE
TR
FOR
THE
ONE-DIMENSIONAL
EINSTEIN
GAS
.
GL
5.7
CONCLUSION
.
CN
TIME-SCALE
TX
FOR
A
KICKED
QUANTUM
NONLINEAR
OSCILLATOR
64
6.1
QUANTUM
MAP
FOR
C-NUMBER
EXPECTATION
VALUES
.
.
66
6.2
CLASSICAL
LIMIT
.
6.3
THE
TIME-SCALE
R
H
OF
APPLICABILITY
OF
CLASSICAL
CHAOTIC
MOTION
.
6.4
QUANTUM
BOUNDARY
OF
STOCHASTICITY
.
6.5
ADDITIONAL
AVERAGING
OVER
THE
INITIAL
DENSITY
MATRIX
.
7
THE
TIME
OF
APPLICABILITY
OF
THE
QUASICLASSICAL
APPROACH
IN
A
BOSON
SYSTEM
OF
TWO
INTERACTING
QUANTUM
NONLINEAR
RESONANCES
7.1
THE
MAIN
EQUATIONS
.
79
80
VIII
7.2
CLASSICAL
LIMIT
.
83
7.3
THE
RESULTS
OF
NUMERICAL
SIMULATIONS
OF
QUANTUM
DYNAMICS
.
84
7.4
CONCLUSION
.
88
8
TWO
INTERACTING
QUANTUM
NONLINEAR
RESONANCES
IN
A
SPIN
SYSTEM
89
8.1
INTRODUCTION
.
89
8.2
TIME-INDEPENDENT
HAMILTONIAN
AND
CLOSED
C-NUMBER
EQUATIONS
.
90
8.3
THE
APPROXIMATION
OF
CONSTANT
AMPLITUDE
OF
THE
EXTERNAL
FIELD
.
92
8.4
TIME-DEPENDENT
QUANTUM
CORRELATION
FUNCTIONS
.
94
8.5
QUANTUM
PERTURBATION
THEORY
.
95
9
QUANTIZATION
OF
A
STOCHASTIC
WEB
103
9.1
INTRODUCTION
.
103
9.2
QUANTUM
MAP
.
104
9.3
CLASSICAL
LIMIT
.
105
9.4
EQUATION
FOR
THE
GENERATING
FUNCTION
.
107
9.5
THE
REGION
OF
PARAMETERS
FOR
QUASICLASSICAL
CONSIDERATION
.
109
9.6
TIME-SCALE
OF
QUASICLASSICAL
DESCRIPTION
FOR
STRONG
CHAOS
.
112
9.7
QUANTUM
DYNAMICS
IN
THE
REGION
OF
WEAK
CHAOS
.
.
114
9.7.1
TIME-SCALE
TIH
FOR
QUANTUM
MAP
.
114
9.7.2
THE
INFLUENCE
OF
THE
INITIAL
CONDITIONS
.
117
9.8
CONCLUSION
.
127
10
CHARACTERISTIC
TIMES
FOR
CHAOTIC
DYNAMICS
IN
WIGNER
REPRESENTATION
129
10.1
INTRODUCTION
.
129
10.2
THE
S-ORDERED
QUANTUM
DENSITY
MATRIX
.
130
10.3
WIGNER
REPRESENTATION
IN
"
ACTION-ANGLE
"
VARIABLES
.
135
10.4
EVOLUTION
OF
THE
QUANTUM
KICKED
ROTATOR
IN
THE
WIGNER
REPRESENTATION
.
138
IX
10.5
QUANTUM
EQUATIONS
OF
MOTION
10.6
CLASSICAL
MODEL
OF
QUANTUM
STOCHASTICITY
10.7
DISCUSSION
.
11
QUANTUM
CHAOS
OF
ATOMS
IN
A
RESONANT
CAVITY
11.1
INTRODUCTION
.
11.2
QUANTUM
EQUATIONS
OF
MOTION
.
11.3
CLOSED
EQUATIONS
OF
MOTION
FOR
THE
QUANTUM-MECHANICAL
EXPECTATION
VALUES
.
11.4
QUANTUM
CORRELATION
FUNCTIONS
11.5
BREAKING
THE
SEMICLASSICAL
APPROXIMATION
11.6
RESULTS
OF
NUMERICAL
ANALYSIS
11.7
CONCLUSION
.
.
142
.
146
.
156
157
.
157
.
160
.
163
.
168
.
169
.
171
.
177
12
QUANTUM
CHAOS
OF
ATOMS
IN
A
RESON
AN
T
CAVITY
DRIVEN
BY
AN
EXTERNAL
RESONANT
FIELD
178
12.1
INTRODUCTION
.
JYG
12.2
THE
FORMULATION
OF
THE
MODEL
.
180
12.3
TIME-INDEPENDENT
HAMILTONIAN
FOR
SLOW
DYNAMICS
.
184
12.4
CLOSED
C-NUMBER
EQUATIONS
FOR
QUANTUM
EXPECTATION
VALUES
IN
COHERENT
STATES
186
12.5
SEMICLASSICAL
APPROXIMATION
AND
CHAOTIC
DYN
AMI
CS
.
190
12.6
THE
PECULIARITIES
OF
QUANTUM
DYNAMICS
IN
THE
REGIME
OF
STRONG
SEMICLASSICAL
CHAOS
.
195
12.7
ADDITIONAL
AVERAGING
OVER
THE
INITIAL
DENSITY
MATRIX
.
20Q
12.8
CONCLUSION
.
2Q2
13
VIOLATION
OF
THE
SEMICLASSICAL
APPROXIMATION
AND
QUANTUM
CHAOS
IN
A
PARAMAGNETIC
SPIN
SYSTEM
13.1
INTRODUCTION
.
13.2
DESCRIPTION
OF
THE
PARAMAGNETIC
SPIN
MODEL
13.3
SLOW
DYNAMICS
AND
ITS
TIME-INDEPENDENT
HAMILTONIAN
.
13.4
CONCLUSION
.
204
204
205
211
212
X
14
WEAK
QUANTUM
CHAOS
IN
A
SYSTEM
OF
N
ATOMS
IN
A
RESONANT
CAVITY
INTERACTING
WITH
AN
EXTERNAL
RESONANT
FIELD
214
14.1
THE
NONSINGULAR
REPRESENTATION
IN
THE
VICINITY
OF
SEPARATRIX
.
216
14.2
EQUATIONS
FOR
QUANTUM
EXPECTATION
VALUES
.
218
14.3
SEMICLASSICAL
CONSIDERATION
.
219
14.4
DYNAMICS
OF
EXPECTATION
VALUES
AND
QUANTUM
CORRELATION
FUNCTIONS
IN
THE
INTEGRABLE
LIMIT
.
219
14.5
NUMERICAL
CALCULATIONS
OF
WEAK
QUANTUM
CHAOS
.
.
232
14.6
CONCLUSION
.
235
15
QUANTUM
DYNAMICS
IN
STATIONARY
COHERENT
STATES
(SCS)
236
15.1
INTRODUCTION
.
236
15.2
STATIONARY
COHERENT
STATES.
BASIC
EQUATIONS
.
237
15.3
DYNAMICAL
CHAOS
IN
SCS
.
240
15.4
STABILITY
OF
SCS
.
243
15.5
DIFFUSION
IN
SCS
.
243
15.6
STRANGE
ATTRACTOR
IN
SCS
.
244
16
DISCUSSION
247
APPENDIX
A
.
251
APPENDIX
B
.
255
APPENDIX
C
.
256
REFERENCES
.
260
XI |
| any_adam_object | 1 |
| author | Berman, Gennadij P. 1946- Bulgakov, Evgenij N. Holm, Darryl D. 1947- |
| author_GND | (DE-588)1067172203 (DE-588)114074275 |
| author_facet | Berman, Gennadij P. 1946- Bulgakov, Evgenij N. Holm, Darryl D. 1947- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Physik |
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| id | DE-604.BV009620323 |
| illustrated | Illustrated |
| indexdate | 2024-08-18T00:19:16Z |
| institution | BVB |
| isbn | 3540580115 0387580115 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006358301 |
| oclc_num | 488818915 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-384 DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | XI, 268 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics : M, Monographs |
| spelling | Berman, Gennadij P. 1946- Verfasser (DE-588)1067172203 aut Crossover time in quantum boson and spin systems Gennady P. Berman ; Evgeny N. Bulgakov ; Darryl D. Holm Berlin [u.a.] Springer 1994 XI, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics : M, Monographs 21 Bosons Chaotic behavior in systems Nonlinear theories Nuclear spin Quantum field theory Quantum theory Quantentheorie Quantenphysik (DE-588)4266670-3 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Zeitverhalten (DE-588)4238464-3 gnd rswk-swf Quasiklassische Näherung (DE-588)4296820-3 gnd rswk-swf Gültigkeit (DE-588)4484674-5 gnd rswk-swf Spinsystem (DE-588)4182338-2 gnd rswk-swf Cross-over Kritisches Phänomen (DE-588)4303440-8 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Boson (DE-588)4146396-1 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 s Cross-over Kritisches Phänomen (DE-588)4303440-8 s DE-604 Boson (DE-588)4146396-1 s Spinsystem (DE-588)4182338-2 s Quantenchaos (DE-588)4130849-9 s Quasiklassische Näherung (DE-588)4296820-3 s Gültigkeit (DE-588)4484674-5 s Approximation (DE-588)4002498-2 s 1\p DE-604 Quantenphysik (DE-588)4266670-3 s 2\p DE-604 Zeitverhalten (DE-588)4238464-3 s 3\p DE-604 Bulgakov, Evgenij N. Verfasser aut Holm, Darryl D. 1947- Verfasser (DE-588)114074275 aut Lecture notes in physics M, Monographs ; 21 (DE-604)BV021852221 21 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358301&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berman, Gennadij P. 1946- Bulgakov, Evgenij N. Holm, Darryl D. 1947- Crossover time in quantum boson and spin systems Lecture notes in physics Bosons Chaotic behavior in systems Nonlinear theories Nuclear spin Quantum field theory Quantum theory Quantentheorie Quantenphysik (DE-588)4266670-3 gnd Approximation (DE-588)4002498-2 gnd Zeitverhalten (DE-588)4238464-3 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Gültigkeit (DE-588)4484674-5 gnd Spinsystem (DE-588)4182338-2 gnd Cross-over Kritisches Phänomen (DE-588)4303440-8 gnd Quantenchaos (DE-588)4130849-9 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Boson (DE-588)4146396-1 gnd |
| subject_GND | (DE-588)4266670-3 (DE-588)4002498-2 (DE-588)4238464-3 (DE-588)4296820-3 (DE-588)4484674-5 (DE-588)4182338-2 (DE-588)4303440-8 (DE-588)4130849-9 (DE-588)4300046-0 (DE-588)4146396-1 |
| title | Crossover time in quantum boson and spin systems |
| title_auth | Crossover time in quantum boson and spin systems |
| title_exact_search | Crossover time in quantum boson and spin systems |
| title_full | Crossover time in quantum boson and spin systems Gennady P. Berman ; Evgeny N. Bulgakov ; Darryl D. Holm |
| title_fullStr | Crossover time in quantum boson and spin systems Gennady P. Berman ; Evgeny N. Bulgakov ; Darryl D. Holm |
| title_full_unstemmed | Crossover time in quantum boson and spin systems Gennady P. Berman ; Evgeny N. Bulgakov ; Darryl D. Holm |
| title_short | Crossover time in quantum boson and spin systems |
| title_sort | crossover time in quantum boson and spin systems |
| topic | Bosons Chaotic behavior in systems Nonlinear theories Nuclear spin Quantum field theory Quantum theory Quantentheorie Quantenphysik (DE-588)4266670-3 gnd Approximation (DE-588)4002498-2 gnd Zeitverhalten (DE-588)4238464-3 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Gültigkeit (DE-588)4484674-5 gnd Spinsystem (DE-588)4182338-2 gnd Cross-over Kritisches Phänomen (DE-588)4303440-8 gnd Quantenchaos (DE-588)4130849-9 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Boson (DE-588)4146396-1 gnd |
| topic_facet | Bosons Chaotic behavior in systems Nonlinear theories Nuclear spin Quantum field theory Quantum theory Quantentheorie Quantenphysik Approximation Zeitverhalten Quasiklassische Näherung Gültigkeit Spinsystem Cross-over Kritisches Phänomen Quantenchaos Quantenmechanisches System Boson |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358301&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021852221 |
| work_keys_str_mv | AT bermangennadijp crossovertimeinquantumbosonandspinsystems AT bulgakovevgenijn crossovertimeinquantumbosonandspinsystems AT holmdarryld crossovertimeinquantumbosonandspinsystems |