Chaos et physique quantique: Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics
Saved in:
| Format: | Conference Proceeding Book |
|---|---|
| Language: | Undetermined |
| Published: |
Amsterdam u.a.
North-Holland
1991
|
| Series: | École d'Été de Physique Théorique <LesHouches>: Session
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Text engl. |
| Physical Description: | XXXIII, 795 S. Ill., graph. Darst. |
| ISBN: | 044489277X |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV004825974 | ||
| 003 | DE-604 | ||
| 005 | 19920513 | ||
| 007 | t | ||
| 008 | 920512s1991 ad|| |||| 10||| und d | ||
| 020 | |a 044489277X |9 0-444-89277-X | ||
| 035 | |a (OCoLC)165454227 | ||
| 035 | |a (DE-599)BVBBV004825974 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | |a und | ||
| 049 | |a DE-384 |a DE-12 |a DE-703 |a DE-355 |a DE-91G |a DE-19 |a DE-29T | ||
| 084 | |a UD 4847 |0 (DE-625)145533: |2 rvk | ||
| 084 | |a PHY 066f |2 stub | ||
| 245 | 1 | 0 | |a Chaos et physique quantique |b Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics |c éd. par M.-J. Giannoni ... |
| 246 | 1 | 1 | |a Chaos and quantum physics |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1991 | |
| 300 | |a XXXIII, 795 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a École d'Été de Physique Théorique <LesHouches>: Session |v 52 | |
| 500 | |a Text engl. | ||
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenchaos |0 (DE-588)4130849-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaos |0 (DE-588)4191419-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1989 |z Les Houches |2 gnd-content | |
| 689 | 0 | 0 | |a Quantenchaos |0 (DE-588)4130849-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Quantentheorie |0 (DE-588)4047992-4 |D s |
| 689 | 1 | 1 | |a Chaos |0 (DE-588)4191419-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Giannoni, Marie-Joya |e Sonstige |4 oth | |
| 711 | 2 | |a Ecole d'Eté de Physique Théorique |n 52 |d 1989 |c Les Houches |j Sonstige |0 (DE-588)5065953-4 |4 oth | |
| 830 | 0 | |a École d'Été de Physique Théorique <LesHouches>: Session |v 52 |w (DE-604)BV000022608 |9 52 | |
| 856 | 4 | 2 | |m Digitalisierung TU Muenchen |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002969048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002969048 | ||
Record in the Search Index
| _version_ | 1804118936608833536 |
|---|---|
| adam_text | CONTENTS
Lecturers
ix
Participants
xi
Préface
xv
Preface
xix
Contents
xxiii
General introduction, by N.L.
Balázs
1
1.
Introduction
2
2.
Classical dynamics
3
3.
Quantum mechanics
5
3.1.
Leading questions
5
4.
Models to study
7
References
9
Course
1.
Recent developments in classical mechanics,
by
1С.
Perchai
11
Introduction
15
1.
Basic theory and
integrable
systems
16
1.1.
Hamiltonian systems of
m
degrees of freedom
16
1.2.
Area preserving
17
1.3.
Canonical transformations and
Poisson
brackets
18
1.4.
Conservative systems of
1
degree of freedom
20
2.
Many degrees of freedom
22
2.1.
Independent mF systems
22
2.2.
Integrable
systems
24
2.3.
Fourier analysis and resonance analysis
26
2.4.
Linearity and nonlinearity
28
2.5.
Small perturbations of mF systems
29
3.
Variational principles and
cantori
32
3.1.
Variational principle and static model
32
3.2.
Discrete time
34
3.3.
Vertical pendulum and standard map
35
3.4.
Static models and
cantori
40
3.5.
Variational principles for mF invariant tori
43
3.6.
Stability
44
3.7.
Continued fractions
49
3.8.
Calculation of periodic orbits
51
3.9.
Periodic orbits and criticality
52
4.
Flux and transport
53
4.1.
Transport in area preserving maps
53
4.2.
Flux, barriers and turnstiles
57
5.
Purely chaotic systems
64
5.1.
Chaotic systems and symbolic dynamics
64
5.2.
Entropy and entropy rates
69
5.3.
Bernoulli maps and Lyapunov exponents
72
5.4.
Sawtooth and cat maps
74
6.
Convergence of perturbation series
78
6.1.
Continuous time
78
6.2.
Critical functions
80
References
83
Course
2.
Random matrix theories and chaotic dy¬
namics, by O. Bohigas
87
1.
Introduction
91
2.
The smooth part of the spectrum
94
3.
Characterisation of fluctuations
102
4.
Spectral fluctuations of the Wigner-Dyson ensembles
108
4.1.
Wigner
s
Gaussian ensembles 111
4.2.
Generalisations
122
4.3.
Fluctuation measures
123
4.4.
The Coulomb gas
129
4.5.
Dysons circular ensembles
132
4.6.
The Weyl Balian ensembles
134
5.
Theory vs. experiment, dynamical basis of
RMT
spectral fluctuations,
universalities
137
5.1.
RMT
predictions and nuclear resonance data
137
5.2.
Dynamical basis of spectral fluctuations; universalities
141
5.3.
More about symmetries
147
5.4.
Particular cases
151
5.5.
Breaking of the universality regime
156
5.6.
New experiments
162
6.
Breaking symmetries and induced spectral fluctuation transitions
166
6.1.
The GOE
-»
GUE
and GSE
—
GUE
transitions
169
6.2.
Dynamical basis of the GOE
->
GUE
transition
172
6.3.
More about magnetic fields (and rotations)
175
6.4.
Quantum-mechanical aspects of mixed phase space systems
183
Appendix A. Nearest-neighbour spacing distribution for Gaussian en¬
sembles (TV
= 2) 189
Appendix B.
η
-level cluster functions (large
N
limit)
189
Appendix C. Two-level cluster function
У^
and
related quantities (large
N
limit)
190
Appendix D. Superposition of several independent spectra
192
Appendix E. GOE
->
GUE
and GSE
-♦
GUE
transitions (large
N
limit)
194
References
196
Course
3.
The semi-classical quantization of chaotic
Hamiltonian systems, by M.C. Gutzwiller
201
1.
Introduction
205
2.
Feynman s path integral
207
3.
First and second variation of
ƒ
Ldt
210
4.
The quasi-classical propagator
213
5.
Green s function
216
6.
The classical Green s function
219
7.
The stationary phase approximation
222
8.
Application to
integrable
systems
226
9.
Hard chaos versus integrability
231
10.
The general trace formula
234
11.
The sum over periodic orbits
239
11.1.
Selberg s trace formula
240
11.2.
Coding the periodic orbits
241
11.3.
Discrete symmetries
243
11.4.
Oscillator strengths. Wigner functions, etc.
244
11.5.
Partial sums in the GTF
246
References
248
Course
4.
Some quantum-to-classical asymptotics,
by M. Berry
251
1.
Theories as limits of other theories
255
2.
The semiclassical limit
256
2.1.
Nonchaotic semiclassical nonanalyticities
256
2.2.
Long-time, small-ft
259
2.3.
Algorithmic complexity
260
2.4.
The challenge of quantum chaology
262
3.
Spectra
264
3.1.
Expectations
264
3.2.
Formalism
265
3.3.
Spectral asymptotics: principles
267
3.4.
Spectral asymptotics: formulae
270
4.
Long orbits (asymptotics of asymptotics)
273
4.1.
Gaussian random waves?
273
4.2.
Phase space democracy
274
4.3.
Energy-level statistics
278
4.4.
ApplicationC?) to the Riemann zeros
285
5.
Divergence and resurgence
288
5.1.
Making the periodic-orbit sum converge
288
5.2.
Resurgence
1:
exponentially small waves
292
5.3.
Resurgence
2:
Riemann-Siegel
295
5.4.
Resurgence
3:
bootstrapping the closed orbits
297
6.
Last words
299
References
299
Course
5.
Hyperbolic geometry in two dimensions and
trace formulas, by Y. Colin
de Verdiére
305
1.
Introduction
309
2.
The models of hyperbolic geometry
309
2.1.
Description of the
Poincaré
half-plane model
309
2.2.
Classification of the positive isometries
311
2.3.
The Gauss-Bonnet formula
311
3.
Discrete groups
312
3.1.
The triangle groups rp.q.r
312
3.2.
The arithmetic groups
314
3.3.
The surface groups
314
4.
Classical chaos
315
4.1.
Examples
315
5.
Quantization
316
5.1.
The free case
318
5.2.
The quotient case
318
5.2.1.
The groups
Гр,ч,г
318
5.2.2.
The surface groups
319
5.2.3.
The spectrum
319
5.2.4.
The Weyl formula
319
6.
The trace formula formalism
319
6.1.
The heat equation
319
6.2.
Short time asymptotics of the heat equation
321
6.3.
The
Poisson
formula in one dimension
322
6.4.
The Selberg trace formula
323
6.4.1.
Interpretation
325
6.5.
The general case: the regularized eigenvalue density
325
6.6.
Relation to the Feynman path integral
326
7.
Asymptotic behaviour of eigenmodes
326
7.1.
Example: the 2-dimensional sphere with the usual metric
327
7.2.
Example: the torus R2
/Г
327
7.3.
Shnirelman s conjecture
328
References
329
Course
6.
Quantum and classical properties of some
billiards on the hyperbolic plane,
by
С
Schmit
331
1.
Introduction
335
1.1.
Numerical methods
336
2.
Results
341
2.1.
Tesselating triangle
341
2.2.
Non-tiling triangle
349
2.3.
From quantum to classical properties (tessellating triangle)
354
2.4.
Summary and conclusions
363
Appendix
1. 363
Appendix
2. 365
References
368
Course
7.
The classical and quantum theory of chaotic
scattering, by U. Smilansky
371
1.
Introduction and background
375
2.
Classical dynamics
382
2.1.
General concepts and definitions
382
2.2.
Chaotic scattering
387
2.2.1.
The model
389
2.2.2.
Construction of the invariant set
392
2.2.3.
Symbolic dynamics
396
2.2.4.
Properties of the invariant set
399
2.2.5.
Reaction functions and other
observables
401
2.2.6.
The transition to chaos
404
3.
Quantum mechanics
408
3.1.
General concepts and definitions
408
3.2.
The semi-classical approximation
409
3.3.
Random matrix theory for the 5-matrix
411
3.4.
Numerical tests of the
RMT
hypothesis
420
4.
Experiments and possible applications
429
5.
Summary
433
Appendix A. Semi-classical quantization of canonical transformations
435
Appendix B. A classical sum rule (Hannay and Ozorio
de
Almeida
[61]) 438
References
439
Course
8.
Time-dependent quantum systems,
byB.V.Chirikov
443
1.
Introduction: a personal view of dynamical chaos
447
1.1.
Philosophy
447
1.2.
A simple example, and the origin of chaos
448
1.3.
The basic model
452
2.
A brief review of the classical chaos
454
2.1.
The basic model and physical problem
454
2.2.
Nonlinear resonances and their interaction
457
2.3.
Local instability and chaos
460
2.4.
Regular, or familiar, chaos
464
2.5.
Critical phenomena in dynamics: beyond any order
468
3.
Quantum dynamics and the classical limit
471
3.1.
The correspondence principle
471
3.2.
Quantization of maps
473
3.3.
Quasienergy eigenstates
476
3.4.
Quantum resonance
477
4.
Quantum stability: perturbative. or extreme, localization
479
4.1.
Resonant perturbation
479
4.2.
Nonresonant
perturbation and chaos
482
5.
Dynamically stable quantum diffusion
483
5.1.
The correspondence principle and quantum diffusion
483
5.2.
Relaxation time scale and quantum steady state
484
5.3.
Motion stability in quantum diffusion
487
5.4.
An example of true chaos in quantum mechanics
490
6.
Quantum stability: diffusion localization
492
6.1.
Localization principle for quantum chaos
492
6.2.
A sketch of the quantum steady state
497
6.3.
Quasienergy eigenfunctions
500
6.4.
Addendum: the impact of noise and of measurement
504
7. Diffusion
localization:
alternative
explanations
505
7.1. Quantum
corrections in the quasiclassical region
505
7.2.
Anderson s localization mechanism
506
7.3.
Two-level statistical approximation
507
7.4.
Localization and cantori
509
7.5.
Classical model for quantum dynamics
511
8.
Statistical properties of chaotic eigenstates
513
8.1.
Quantum ergodicity and level repulsion
513
8.2.
Localization and intermediate statistics
519
8.3.
Level repulsion and diffusion suppression
521
8.4.
Spatial fluctuations in eigenfunctions
523
9.
Diffusive photoelectric effect in hydrogen
525
9.1.
Classical ionization in
Rydberg
atoms
525
9.2.
Quantum suppression of diffusive excitation
530
9.3.
Two freedoms in the atom and two frequencies in the field
536
9.4.
First laboratory observations of quantum chaos in hydrogen
537
10.
Conclusion: questions, problems, conjectures
... 539
References
543
Course
9.
Wavepacket dynamics and quantum chaol-
ogy, by E.J. Heller
547
Introduction
551
1.
Phase space pictures of semiolassical amplitudes
553
1.1.
Probability and Van Vleck determinants
553
1.2.
Diagrams
555
1.3.
Stationary phase points
557
1.4.
Accuracy of the semiclassical Green s function
559
1.5.
Gaussiane in
phase space
561
1.6.
Dynamics via phase space pictures
564
2.
Linearized dynamics and the stability of trajectories
565
2.1.
The stability (monodromy) matrix
565
2.2.
Stability of periodic orbits
567
2.3.
Linearized Green
s
function and wavepacket propagation
569
2.4.
Special cases of wavepacket propagation
574
2.5.
Eigenstates by Fourier transform of dynamics
577
3.
Spectra of unstable periodic orbits
581
3.1.
Spectrum-dynamics connections
581
3.2.
Photodissociation
of a molecule
584
3.3.
Spectrum of a resonance affecting a periodic orbit: transition from
stable to unstable motion
590
4.
Quantum spectra, ergodicity. and the nature of eigenstates
603
4.1.
Dynamical and spectral complexity
603
4.2.
Phase
space
volume
swept by dynamics
605
4.3.
Rate of exploration of phase space
606
4.4.
Recurrences and the spectral intensities
615
4.5.
Implications for the eigenstates
616
5.
Random waves
620
6.
Numerical method and results
624
6.1.
Method
624
6.2.
Results
626
7.
Theory for the eigenstates
629
7.1.
Localized states
629
7.2.
Weakly localized states
633
7.3.
Scarred eigenstates
636
7.4.
How wide are scars?
645
7.5.
Bogomolny s theory for scars in coordinate space
646
7.6.
Time dependent Green s function theory
650
8.
Speculations
657
8.1.
Order within chaos
657
8.2.
Nonlinear manifolds
658
8.3.
Assigning chaotic spectra
659
8.4.
Acoustics
660
References
661
Course
10.
Chaos in atomic and molecular physics,
by D.
Delande
665
1.
Introduction
669
1.1.
Finding out a real chaotic system
669
1.2.
Atoms in external fields
672
2.
The hydrogen atom
675
2.1.
Equations of motion. Constants
675
2.2.
Symmetry group of the hydrogen atom
677
2.3.
Equivalence with a harmonic oscillator
679
3.
The hydrogen atom in a magnetic field: the classical dynamics
682
3.1.
Hamiltonian of the system
-
Equivalence with coupled harmonic
oscillators
682
3.2.
The weak field behavior
684
3.3.
The strong field behavior
688
4.
The hydrogen atom in a magnetic field: the weak field behavior
692
4.1.
Equivalence with coupled harmonic oscillators
692
4.2.
First-order perturbation theory
693
4.2.1.
Semi-classical approximation
694
4.2.2.
Symmetry properties of the eigenstates
695
4.2.3.
Phase-space distributions
696
4.2.4.
Wavefunctions
696
4.2.5.
Nodal
structure
697
4.3.
Regular
regime
698
4.3.1.
Numerical
simulation
of the spectrum
699
4.3.2.
Energy spectrum
700
4.3.3.
Statistical properties of energy levels
701
4.4.
Experimental results
702
4.4.1.
Experimental set-up
702
4.4.2.
Results
703
5.
The hydrogen atom in a magnetic field: the strong field behavior
705
5.1.
Energy spectrum
706
5.1.1.
Statistical properties of energy levels
707
5.1.2.
Experimental results
710
5.2.
Non-generic features in the energy spectrum
713
5.3.
Eigenstates
719
References
724
Course
11.
Random matrix theory applied to electrons
in small metal particles, by B.
Mühlschlegel 727
1.
Introduction
731
2.
Thennodynamic properties
732
2.1.
Canonical excitations
732
2.2.
Level statistics
735
3.
Dynamical properties
738
References
741
Seminar
1.
Quantised maps, by N.L.
Balázs
743
1.
Classical maps
744
2.
The quantum version
745
2.1.
Snapshots, quantised
746
2.1.1.
The alternating oscillator
747
2.1.2.
The alternating quartic oscillator
748
2.2.
A canonical map with no Hamiltonian
749
2.2.1.
Results
756
3.
Conclusion
758
References
758
Seminar
2.
Quantum localization and
ñuctuations,
bv G.
Casati
761
Seminar
3.
Statistical properties of quantum chaos,
by F.M. Izrailev
771
1.
Introduction
772
2.
The model of the kicked rotator on the torus
775
3.
Maximal quantum chaos
776
4.
Localized chaotic states
778
5.
Intermediate level statistics
779
6.
Scaling properties of intermediate quantum chaos
786
7.
Scaling properties of Band Random Matrices
788
References
790
Seminar
4.
Quantum localization of dynamical chaos,
by
D.h.
Shepelyansky
793
Seminars presented at the Summerschool, but not published in these
proceedings:
Quantori in the discrete Frenkel-Kontorova model,
by F. Borgonovi (co-authors:
I. Guarnen,
D. Shepelyan-
sky)
Ruelle
zeta
functions, by J.-P.
Eckmann
Shell structure in terms of periodic orbits, by H. Frisk
Short talks related to random matrix theories,
by F.M. Izrailev, B. Dietz, T. Dittrich, G.
Lenz,
T.
Mar¬
tin,
L. Molinari
The semiclassical structure of wave functions and the co¬
herent state representation, by P. Leboeuf (co-authors:
J.
Kurchan, M.
Saraceno)
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV004825974 |
| classification_rvk | UD 4847 |
| classification_tum | PHY 066f |
| ctrlnum | (OCoLC)165454227 (DE-599)BVBBV004825974 |
| discipline | Physik |
| format | Conference Proceeding Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02007nam a2200457 cb4500</leader><controlfield tag="001">BV004825974</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19920513 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">920512s1991 ad|| |||| 10||| und d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">044489277X</subfield><subfield code="9">0-444-89277-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)165454227</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004825974</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">und</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UD 4847</subfield><subfield code="0">(DE-625)145533:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 066f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Chaos et physique quantique</subfield><subfield code="b">Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics</subfield><subfield code="c">éd. par M.-J. Giannoni ...</subfield></datafield><datafield tag="246" ind1="1" ind2="1"><subfield code="a">Chaos and quantum physics</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam u.a.</subfield><subfield code="b">North-Holland</subfield><subfield code="c">1991</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXXIII, 795 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">École d'Été de Physique Théorique <LesHouches>: Session</subfield><subfield code="v">52</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Text engl.</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantentheorie</subfield><subfield code="0">(DE-588)4047992-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantenchaos</subfield><subfield code="0">(DE-588)4130849-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Chaos</subfield><subfield code="0">(DE-588)4191419-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="y">1989</subfield><subfield code="z">Les Houches</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Quantenchaos</subfield><subfield code="0">(DE-588)4130849-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Quantentheorie</subfield><subfield code="0">(DE-588)4047992-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Chaos</subfield><subfield code="0">(DE-588)4191419-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Giannoni, Marie-Joya</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="711" ind1="2" ind2=" "><subfield code="a">Ecole d'Eté de Physique Théorique</subfield><subfield code="n">52</subfield><subfield code="d">1989</subfield><subfield code="c">Les Houches</subfield><subfield code="j">Sonstige</subfield><subfield code="0">(DE-588)5065953-4</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">École d'Été de Physique Théorique <LesHouches>: Session</subfield><subfield code="v">52</subfield><subfield code="w">(DE-604)BV000022608</subfield><subfield code="9">52</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung TU Muenchen</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002969048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002969048</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift 1989 Les Houches gnd-content |
| genre_facet | Konferenzschrift 1989 Les Houches |
| id | DE-604.BV004825974 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:18:13Z |
| institution | BVB |
| institution_GND | (DE-588)5065953-4 |
| isbn | 044489277X |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002969048 |
| oclc_num | 165454227 |
| open_access_boolean | |
| owner | DE-384 DE-12 DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T |
| owner_facet | DE-384 DE-12 DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T |
| physical | XXXIII, 795 S. Ill., graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | North-Holland |
| record_format | marc |
| series | École d'Été de Physique Théorique <LesHouches>: Session |
| series2 | École d'Été de Physique Théorique <LesHouches>: Session |
| spelling | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics éd. par M.-J. Giannoni ... Chaos and quantum physics Amsterdam u.a. North-Holland 1991 XXXIII, 795 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier École d'Été de Physique Théorique <LesHouches>: Session 52 Text engl. Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1989 Les Houches gnd-content Quantenchaos (DE-588)4130849-9 s DE-604 Quantentheorie (DE-588)4047992-4 s Chaos (DE-588)4191419-3 s Giannoni, Marie-Joya Sonstige oth Ecole d'Eté de Physique Théorique 52 1989 Les Houches Sonstige (DE-588)5065953-4 oth École d'Été de Physique Théorique <LesHouches>: Session 52 (DE-604)BV000022608 52 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002969048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics École d'Été de Physique Théorique <LesHouches>: Session Quantentheorie (DE-588)4047992-4 gnd Quantenchaos (DE-588)4130849-9 gnd Chaos (DE-588)4191419-3 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4130849-9 (DE-588)4191419-3 (DE-588)1071861417 |
| title | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics |
| title_alt | Chaos and quantum physics |
| title_auth | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics |
| title_exact_search | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics |
| title_full | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics éd. par M.-J. Giannoni ... |
| title_fullStr | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics éd. par M.-J. Giannoni ... |
| title_full_unstemmed | Chaos et physique quantique Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics éd. par M.-J. Giannoni ... |
| title_short | Chaos et physique quantique |
| title_sort | chaos et physique quantique les houches session lii 1 31 aout 1989 chaos and quantum physics |
| title_sub | Les Houches, session LII, 1 - 31 août 1989 = Chaos and quantum physics |
| topic | Quantentheorie (DE-588)4047992-4 gnd Quantenchaos (DE-588)4130849-9 gnd Chaos (DE-588)4191419-3 gnd |
| topic_facet | Quantentheorie Quantenchaos Chaos Konferenzschrift 1989 Les Houches |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002969048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022608 |
| work_keys_str_mv | AT giannonimariejoya chaosetphysiquequantiqueleshouchessessionlii131aout1989chaosandquantumphysics AT ecoledetedephysiquetheoriqueleshouches chaosetphysiquequantiqueleshouchessessionlii131aout1989chaosandquantumphysics AT giannonimariejoya chaosandquantumphysics AT ecoledetedephysiquetheoriqueleshouches chaosandquantumphysics |