Muutke küpsiste eelistusi

E-raamat: Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos

Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 221,68 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of ChaosSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

The author poses the question: "...What are the signatures of quantum chaos?" In answer, he provides an advanced level tour of fingerprints of classical chaos systems in the quantum spectra via text examples, theorems, and equations. A sample of covered topics from mathematical physics and related fields includes random matrix theory, analytical number theory, scattering theory, and quantum ergodic systems. An especially intriguing experimental testing ground for chaos theory is the use of microwave billiards to study the transition from integrable to chaotic systems and its theoretical and engineering applications to mesoscopic systems. Annotation c. by Book News, Inc., Portland, Or.

4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.
Preface xiii
1 Signatures of Quantum Chaos
1(70)
1.1 Introduction
1(4)
1.2 Spectral Staircase
5(1)
1.3 Unfolding the Spectrum
6(1)
1.4 Hyperbolic Triangles: An Example
6(5)
1.4.1 Artin's Billiards
7(1)
1.4.2 Quaternion Algebras
8(1)
1.4.3 Arithmetic Groups
8(1)
1.4.4 Tiling Triangles
9(2)
1.4.5 Hecke Triangles
11(1)
1.5 Polygonal Billiard
11(1)
1.6 The Cardioid Billiard
11(1)
1.7 The Oval
11(4)
1.7.1 Circle Problem
13(2)
1.8 Torus
15(1)
1.9 Surface of Revolution
15(2)
1.10 Liouville Surface
17(1)
1.11 Scaling and Transition for Integrable Systems
17(4)
1.12 Zoll Surface
21(1)
1.13 Random Matrix Theory
21(1)
1.14 Short Range Correlation
22(1)
1.15 Integrable and Chaotic Systems: RMT Conjectures
23(1)
1.16 Number Variance
23(2)
1.17 Spectral Rigidity and Saturation
25(1)
1.18 Spectral Form Factor
25(1)
1.19 Exact Spectral Form Factor Theorem
26(1)
1.20 Berry's Semiclassical Theorem
27(2)
1.20.1 Degeneracy of Orbits
27(1)
1.20.2 Democracy: Classical Sum Rule
27(1)
1.20.3 Berry's Trick
27(2)
1.21 Example: Rectangular Billiards
29(1)
1.22 Saturation for Integrable Systems
30(1)
1.23 Saturation Values for GOE and GUE: Semiclassical Results
31(1)
1.24 Gaussian Fluctuation in RMT
31(1)
1.25 Selberg Trace Formula
32(1)
1.26 Gutzwiller's Trace Formula
33(1)
1.27 Gutzwiller for Plane Billiards
33(1)
1.28 Bolte's Semiclassical Statistics
34(1)
1.29 Selberg Trace Formula for Hyperbolic Plane Billiards
35(2)
1.29.1 Selberg Zeta Function
36(1)
1.29.2 Artin's Billiards and Venkov-Zograf Factorization
36(1)
1.29.3 Huber's Law
37(1)
1.29.4 Mean Multiplicity
37(1)
1.30 Riemann Zeta Function
37(4)
1.31 Mode-Fluctuation Distribution
41(1)
1.32 RMT Classes Revisited
42(3)
1.33 Triangles - Da Capo
45(1)
1.34 Montgomery-Dyson Hypothesis
45(1)
1.35 L-Functions
46(3)
1.35.1 L-Functions Encore
48(1)
1.36 Selberg's Moment Theorem for L-Functions
49(1)
1.37 Dyson's Autocorrelation Conjecture
50(1)
1.38 N-Level Correlation: Semiclassical Calculations
50(1)
1.39 The Hardy-Littlewood Conjecture
51(1)
1.40 Zeros of Principal L-Functions
52(1)
1.41 Modular Billiards: Two Point Correlation Form Factor
53(1)
1.42 Geometrically Finite Spaces
53(3)
1.42.1 Exponent of Convergence
53(2)
1.42.2 Lattice Point Problem
55(1)
1.43 Geometric Structure
56(1)
1.44 STF for Geometrically Finite Spaces
56(3)
1.45 Length Spectra for Hyperbolic Surfaces
59(1)
1.46 Hyperbolic 3-Orbifold
59(3)
1.47 Slow Oscillations
62(1)
1.48 Chaos in Electronic Band Structure
63(1)
1.49 Magnetization and Susceptibility
63(2)
1.50 Gutzwiller Scattering Model
65(1)
1.51 Experimental Work
66(5)
1.51.1 Microwave Cavities
66(3)
1.51.2 Mesoscopic Devices
69(2)
2 Billiards: Polygonal and Others
71(18)
2.1 Introduction
71(1)
2.2 Rational Billiards
71(1)
2.3 Entropy and Mixing
72(1)
2.4 Billiard Groups
72(1)
2.5 Billiard Motion
72(1)
2.6 Periodic Orbits
73(2)
2.7 Regular Polygons and Zeta Function
75(1)
2.8 Veech Polygons
76(1)
2.9 Fermat Curves
77(1)
2.10 Monodromy Map
77(1)
2.11 Numerical Results: Quantum Billiards
78(1)
2.11.1 Rational and Irrational Billiards
78(1)
2.11.2 Staircase Billiards
78(1)
2.11.3 Pure Rhombus Billiard
79(1)
2.12 II/4 Right Triangles
79(1)
2.13 Richens' Truncated Triangle
80(1)
2.14 GWW Models
81(1)
2.15 Pseudo-integrable L-shaped Billiard
81(1)
2.16 Length Spectra for Pseudo-Integrable Billiards
82(1)
2.17 Sinai Billiards
83(1)
2.18 Point Sinai Billiard
84(1)
2.19 Bunimovich Stadium
85(1)
2.20 Spectral Autocorrelation and Survival Probability
85(1)
2.21 Cardioid Billiard
86(2)
2.22 Hyperbola
88(1)
3 Quantum Transition Amplitudes
89(36)
3.1 Introduction
89(6)
3.2 Distributions of Matrix Elements
95(4)
3.3 Quantum Ergodic Systems
99(2)
3.4 Random Eigenfunctions
101(3)
3.5 Trapping
104(2)
3.6 Coulombic Periodic Potentials
106(1)
3.7 Quantized Hyperbolic Toral Automorphisms
107(4)
3.8 Correlations
111(1)
3.9 Hyperbolic Toral Automorphisms
112(3)
3.10 Equidistribution Results
115(1)
3.11 Prime Geodesic Theorem
116(3)
3.12 Billiards Flow
119(1)
3.13 Rate of Quantum Ergodicity
119(1)
3.14 Ratner's Central Limit Theorem
120(1)
3.15 Recent Results on Tori
121(1)
3.16 Trace Formula for the Quantized Cat Map
121(1)
3.17 Appendix
122(3)
4 Variance of Quantum Matrix Elements
125(8)
4.1 Introduction
125(1)
4.2 Variance of Quantum Matrix Elements
125(1)
4.3 Berry's Trick and the Hyperbolic Case
126(2)
4.4 Nonhyperbolic Case
128(1)
4.5 Random Matrix Theory
128(1)
4.6 Baker's Map and Other Systems
129(1)
4.7 Appendix: Baker's Map
129(4)
5 Error Terms
133(8)
5.1 Introduction
133(2)
5.2 The Riemann Zeta Function in Periodic Orbit Theory
135(2)
5.3 Form Factor for Primes
137(1)
5.4 Error Terms in Periodic Orbit Theory: Co-compact Case
138(1)
5.5 Binary Quadratic Forms as a Model
139(2)
6 Co-Finite Model for Quantum Chaology
141(12)
6.1 Introduction
141(1)
6.2 Co-finite Models
141(3)
6.3 Geodesic Triangle Spaces
144(1)
6.4 L-Functions
145(1)
6.5 Zelditch's Prime Geodesic Theorem
146(1)
6.6 Zelditch's Pseudo Differential Operators
147(1)
6.7 Weyl's Law Generalized
148(2)
6.8 Equidistribution Theory
150(3)
7 Landau Levels and L-Functions
153(26)
7.1 Introduction
153(1)
7.2 Landau Model: Mechanics on the Plane and Sphere
153(2)
7.3 Landau Model: Mechanics on the Half-Plane
155(2)
7.4 Selberg's Spectral Theorem
157(1)
7.5 Pseudo Billiards
158(1)
7.6 Landau Levels on a Compact Riemann Surface
159(1)
7.7 Automorphic Forms
160(2)
7.8 Maass-Selberg Trace Formula
162(1)
7.9 Degeneracy by Selberg
163(1)
7.10 Hecke Operators
163(4)
7.11 Selberg Trace Formula for Hecke Operators
167(2)
7.12 Eigenvalue Statistics on X
169(1)
7.13 Mesoscopic Devices
170(1)
7.14 Hall Conductance on Leaky Tori
170(1)
7.15 L-Functions, One More Time
171(2)
7.16 Maass Cusp Forms
173(2)
7.17 Equidistribution and Quantum Ergodicity
175(2)
7.18 Alternative Zeta Functions
177(1)
7.19 Infinite Volume Case
178(1)
8 Wigner Time Delay
179(18)
8.1 Introduction
179(1)
8.2 Gutzwiller Model
179(1)
8.2.1 Example: Artin Surface
179(1)
8.3 Time Delay Function
180(2)
8.3.1 Example: Artin Surface
180(1)
8.3.2 Example: Gutzwiller Model
181(1)
8.4 Phase Shift Asymptotics
182(1)
8.4.1 Example: Gutzwiller Model
182(1)
8.5 Resonances and Poles of the Scattering Matrix
183(1)
8.6 Density of Riemann Zeros
183(1)
8.7 Correlation Function of XXX(k)
184(2)
8.8 Gutzwiller Model in a Magnetic Field
186(1)
8.9 Winding Number
187(1)
8.10 Muller's Admissable Surfaces
188(2)
8.11 Scattering Determinants for Congruence Groups
190(1)
8.12 Semiclassical Expansion
191(2)
8.13 Semiclassical Results for the Wigner Time Delay
193(2)
8.14 Appendix
195(2)
9 Scattering Theory for Leaky Tori
197(14)
9.1 Introduction
197(1)
9.2 Muller's Admissable Surfaces
197(2)
9.3 Scattering Operators
199(2)
9.4 Weyl's Law for Mesoscopic Systems
201(2)
9.5 Muller's Trace Formula
203(1)
9.6 Scattering Theory on Hyperbolic Half-Cylinders
203(1)
9.7 Hyperbolic Half-Cylinders
204(1)
9.8 Poschl-Teller Hamiltonians
204(1)
9.9 Scattering Theory on Hyperbolic Half Cylinders
205(1)
9.10 Scattering Theory for Two Strictly Convex Bodies
206(1)
9.11 Diffraction and Resonances
207(4)
10 Dissolving Bound States
211(16)
10.1 Introduction
211(1)
10.2 Quantum Mechanics on Leaky Tori
212(2)
10.3 Eisenstein Series and Scattering Matrices
214(2)
10.3.1 Modular Group
215(1)
10.3.2 Gutzwiller's Leaky Tori
216(1)
10.4 Congruence Subgroups
216(1)
10.5 Lattice Deformations
217(2)
10.6 Fermi Golden Rule
219(1)
10.7 Essentially Cuspidal
220(3)
10.8 Deformation of Character
223(2)
10.9 Length Spectra of Mesoscopic Systems
225(1)
10.10 Upper Bounds on the Number of Resonances
226(1)
10.11 Conclusions
226(1)
11 Dissolving Eigenvalues
227(8)
11.1 Introduction
227(2)
11.2 The Bottom of the Continuous Spectrum
229(1)
11.3 Dissolving Degenerate Eigenvalues
230(1)
11.4 Small Eigenvalues
231(4)
12 Half-Integral Forms
235(18)
12.1 Introduction
235(1)
12.2 The Shimura Correspondence
236(3)
12.2.1 Fourier Coefficients
237(1)
12.2.2 Iwaniec's Estimate for Fourier Coefficients of Half Integral Forms
238(1)
12.3 Shintani's Map
239(2)
12.3.1 Kohnen-Zagier Example Again
240(1)
12.4 Maass Forms
241(1)
12.5 Maass Forms of Half Integral Weight
242(1)
12.6 Shimura's Correspondence for Maass Forms
243(1)
12.7 Spectra of Landau States
244(1)
12.8 Fourier Coefficients of Maass Forms
245(1)
12.9 Distribution of Closed Geodesics on PSL(2, R)\XXX
246(1)
12.10 Conclusion
246(1)
12.11 Appendix
247(6)
12.11.1 Theta Series
247(2)
12.11.2 Niwa's Construction
249(1)
12.11.3 General Shintani Map
249(2)
12.11.4 Newforms and Oldforms
251(1)
12.11.5 Number of Inequivalent Cusps
252(1)
13 Isometric and Isospectral Manifolds
253(10)
13.1 Introduction
253(1)
13.2 Lattices and Spectra
254(1)
13.3 Hyperbolic Spaces
254(1)
13.4 Isospectral Deformations
255(1)
13.5 Sunada's and Berard's Theorems
255(1)
13.6 Schrodinger Operators
256(1)
13.7 Heisenberg Manifolds
256(1)
13.8 Spectra of Heisenberg Manifolds
257(1)
13.9 Length Spectra of Heisenberg Manifolds
257(1)
13.10 Poisson Formula for Heisenberg Manifolds
258(1)
13.11 Two Problems of Zelditch
259(2)
13.12 Sarnak's Conjecture
261(1)
13.13 Appendix
261(2)
14 Mesoscopic Structures
263(34)
14.1 Introduction
263(3)
14.2 Scattering Matrix
266(1)
14.3 Probability Distribution of the XXX's and Level Repulsion
267(1)
14.4 Eigenvalue Statistics
268(1)
14.5 Dyson-Mehta Formula and Beenakker's Generalization
269(1)
14.6 Dyson-Beenakker Integral Equation
269(1)
14.7 Beenakker's Variance Formula
270(1)
14.8 Applications of the Dyson-Mehta-Beenakker Formula
271(3)
14.8.1 Conductance
271(1)
14.8.2 Shot Noise Power
272(1)
14.8.3 Suppression of Shot Noise Power
272(1)
14.8.4 Normal - Superconductor Interface
273(1)
14.8.5 Quantum Point Contact
274(1)
14.8.6 Josephson Junction
274(1)
14.9 Diffusion Equation Approach
274(2)
14.9.1 Inelastic Scattering
276(1)
14.10 Disordered Metallic Wires
276(2)
14.11 Dyson's Large-N Expansion
278(1)
14.12 Universality of Weak Localization
278(1)
14.13 Applications to Quantum Dots
279(3)
14.13.1 Probability Distribution of the XXX's
279(2)
14.13.2 Conductance of a Quantum Dot
281(1)
14.13.3 Ballistic Shot-Noise for Quantum Dot
281(1)
14.13.4 Normal-Superconductor Interface
282(1)
14.14 Small-N Results
282(1)
14.15 Conductance Distribution for Quantum Dot
283(1)
14.16 Resonance Statistics
284(1)
14.16.1 Mesoscopic Resonance Width
284(1)
14.16.2 Microwave Cavity Resonance Statistics
285(1)
14.17 Disordered Metals
285(1)
14.18 Parametric Correlations
286(3)
14.19 Semiclassical Results
289(2)
14.20 Quantum Hall Effect
291(1)
14.21 Testing for Chaos
292(1)
14.22 Quantum Point Contacts: In-Plane Gate Devices
293(1)
14.23 Some Concluding Remarks
293(2)
14.24 Appendix
295(2)
15 References
297(32)
Index 329
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97894015879212e.html
Märksõnad: