Quantum Chaos and Quantum Dots

Quantum Chaos and Quantum Dots
Author: Katsuhiro Nakamura
Publisher:
Total Pages: 228
Release: 2004
Genre: Mesoscopic phenomena (Physics).
ISBN: 9780198525899

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Dynamics of billiard balls and their role in physics have received wide attention since the monumental lecture by Lord Kelvin at the turn of the 19th century. Billiards can nowadays be created as quantum dots in the microscopic world enabling one to envisage the so-called quantum chaos, i.e.quantum manifestation of chaos of billiard balls. In fact, owing to recent progress in advanced technology, nanoscale quantum dots, such as chaotic stadium and antidot lattices analogous to the Sinai Billiard, can be fabricated at the interface of semiconductor heterojunctions. This book begins itsexploration of the effect of chaotic electron dynamics on ballistic quantum transport in quantum dots with a puzzling experiment on resistance fluctuations for stadium and circle dots. Throughout the text, major attention is paid to the semiclassical theory which makes it possible to interpretquantum phenomena in the language of the classical world. Chapters one to four are concerned with the elementary statistical methods (curvature, Lyapunov exponent, Kolmogorov-Sinai entropy and escape rate), which are needed for a semiclassical description of transport in quantum dots. Chapters fiveto ten discuss the topical subjects in the field, including the ballistic weak localization, Altshuler-Aronov-Spivak oscillation, partial time-reversal symmetry, persistent current, Arnold diffusion and Coulomb blockade.

Quantum Chaos and Quantum Dots

Quantum Chaos and Quantum Dots
Author: Katsuhiro Nakamura
Publisher:
Total Pages: 0
Release: 2004
Genre: Mesoscopic phenomena (Physics)
ISBN:

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Quantum Chaos Y2K

Quantum Chaos Y2K
Author: Karl-Fredrik Berggren
Publisher: World Scientific
Total Pages: 288
Release: 2001
Genre: Science
ISBN: 9789812811004

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Spectral twinkling: A new example of singularity-dominated strong fluctuations (summary) / M. Berry -- Quantum chaos in GaAs/AlxGa1-x As microstructures / A. M. Chang -- Ground state spin and Coulomb blockade peak motion in chaotic quantum dots / J. A. Folk ... [et al.] -- Quantum chaos and transport phenomena in quantum dots / A. S. Sachrajda -- Conductance of a ballistic electron billiard in a magnetic field: Does the semiclassical approach apply? / T. Blomquist and I. Zozoulenko -- Semiconductor billiards - a controlled environment to study fractals / R. P. Taylor ... [et al.] -- Experimental signatures of wavefunction scarring in open semiconductor billiards / J. P. Bird, R. Akis, and D. K. Ferry -- Chaos in quantum ratchets / H. Linke ... [et al.] -- Statistics of resonances in open billiards / H. Ishio -- The exterior and interior edge states of magnetic billiards: Spectral statistics and correlations / K. Hornberger and U. Smilansky -- Non-universality of chaotic classical dynamics: implications for quantum chaos / M. Wilkinson -- Chaos and interactions in quantum dots / Y. Alhassid -- Stochastic aspects of many-body systems: The embedded Gaussian ensembles / H. A. Weidenmuller -- Quantum-classical correspondence for isolated systems of interacting particles: Localization and ergodicity energy space / F. M. Izrailev -- Effect of symmetry breaking on statistical distributions / G. E. Mitchell and J. F. Shriner, Jr. -- Quantum chaos and quantum computers / D. L. Shepelyansky -- Disorder and quantum chronodynamics - non-linear [symbol] models / T. Guhr and T. Wilke -- Correlations between periodic orbits and their role in spectral statistics / M. Sieber and K. Richeter -- Quantum spectra and wave functions in terms of periodic orbits for weakly chaotic systems / R. E. Prange, R. Narevich and O. Zaitsev -- Bifurcation of periodic orbit as semiclassical origin of superdeformed shell structure / K. Matsuyanagi -- Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics / M. Brack, M. Sieber and S. M. Reimann -- Neutron stars and quantum billiards / A. Bulgac and P. Magierski -- Scars and other weak localization effects in classically chaotic systems / E. J. Heller -- Tunneling and chaos / S. Tomsovic -- Relaxation and fluctuations in quantum chaos / G. Casati -- Rydberg electrons in crossed fields: A paradigm for nonlinear dynamics beyond two degrees of freedom / T. Uzer -- Classical analysis of correlated multiple ionization in strong fields / B. Eckhardt and K. Sacha -- Classically forbidden processes in photoabsorption spectra / J. B. Delos ... [et al.] -- Quantum Hall effect breakdown steps due to an instability of laminar flow against electron-hole pair formation / L. Eaves -- Dynamical and wave chaos in the Bose-Einstein condensate / W. P. Reinhardt and S. B. McKinney -- Wave dynamical chaos: An experimental approach in billiards / A. Richter -- Acoustic chaos / C. Ellegaard, K. Schaadt and P. Bertelsen -- Ultrasound resonances in a rectangular plate described by random matrices / K. Schaadt, G. Simon and C. Ellegaard -- Quantum correlations and classical resonances in an open chaotic system / W. T. Lu ... [et al.] -- Why do an experiment, if theory is exact, and any experiment can at best approximate theory? / H.-J. Stockmann -- Wave-Chaotic optical resonators and lasers / A. D. Stone -- Angular momentum localization in oval billiards / J. U. Nockel -- Chaos and time-reversed acoustics / M. Fink -- Single-mode delay time statistics for scattering by a chaotic cavity / K. J. H. van Bemmel, H. Schomerus and C. W. J. Beenakker.

Quantum Chaos

Quantum Chaos
Author: Hans-Jürgen Stöckmann
Publisher: Cambridge University Press
Total Pages: 386
Release: 1999-10-13
Genre: Science
ISBN: 0521592844

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Discusses quantum chaos, an important area of nonlinear science.

Quantum Chaos and Mesoscopic Systems

Quantum Chaos and Mesoscopic Systems
Author: N.E. Hurt
Publisher: Springer Science & Business Media
Total Pages: 362
Release: 1997-02-28
Genre: Mathematics
ISBN: 9780792344599

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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.

Single Quantum Dots

Single Quantum Dots
Author: Peter Michler
Publisher: Springer Science & Business Media
Total Pages: 370
Release: 2003-12-09
Genre: Science
ISBN: 9783540140221

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Special focus is given to the optical and electronic properties of single quantum dots due to their potential applications in devices operating with single electrons and/or single photons. This includes quantum dots in electric and magnetic fields, cavity-quantum electrodynamics, nonclassical light generation, and coherent optical control of excitons.

Dissipative Quantum Chaos and Decoherence

Dissipative Quantum Chaos and Decoherence
Author: Daniel Braun
Publisher: Springer
Total Pages: 139
Release: 2003-07-01
Genre: Science
ISBN: 3540409165

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This overview of the state of the art of research in an exciting field mainly emphasizes the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems.

Electrical Control and Quantum Chaos with a High-Spin Nucleus in Silicon

Electrical Control and Quantum Chaos with a High-Spin Nucleus in Silicon
Author: Serwan Asaad
Publisher: Springer Nature
Total Pages: 212
Release: 2021-10-19
Genre: Science
ISBN: 3030834735

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Nuclear spins are highly coherent quantum objects that were featured in early ideas and demonstrations of quantum information processing. In silicon, the high-fidelity coherent control of a single phosphorus (31-P) nuclear spin I=1/2 has demonstrated record-breaking coherence times, entanglement, and weak measurements. In this thesis, we demonstrate the coherent quantum control of a single antimony (123-Sb) donor atom, whose higher nuclear spin I = 7/2 corresponds to eight nuclear spin states. However, rather than conventional nuclear magnetic resonance (NMR), we employ nuclear electric resonance (NER) to drive nuclear spin transitions using localized electric fields produced within a silicon nanoelectronic device. This method exploits an idea first proposed in 1961 but never realized experimentally with a single nucleus, nor in a non-polar crystal such as silicon. We then present a realistic proposal to construct a chaotic driven top from the nuclear spin of 123-Sb. Signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors, hybrid spin-mechanical quantum systems, and quantum-computing elements using all-electrical controls.