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.

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.

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

In this volume, six review articles which cover a broad range of topics of current interest in modern optics are included. The first article by S. Saltiel, A.A. Sukhorukov and Y.S. Kivshar presents an overview of various types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic non-linear media, the so-called multi-step parametric interactions. The second article by H.E. Tureci, H.G.L. Schwefel, Ph. Jacquod and A.D. Stone reviews the progress that has been made in recent years in the understanding of modes in wave-chaotic systems. The next article by C.P. Search and P. Meystre reviews some important recent developments in non-linear optics and in quantum optics. The fourth article by E. Hasman, G. Biener, A. Niv and V. Kleiner discusses space-variant polarization manipulation. The article reviews both theoretical analysis and experimental techniques. The article which follows, by A.S. Desyatnikov, L. Torner and Y.S. Kivshar presents an overview of recent researches on optical vortices and phase singularities of electromagnetic waves in different types of non-linear media, with emphasis on the properties of vortex solitons. The concluding article by K. Iwata presents a review of imaging techniques with X-rays and visible light in which phase of the radiation that penetrates through a transparent object plays an important part.

Provides a grounding in random matrix techniques applied to analytic number theory.

The 2001 Spring Meeting of the 65th Deutsche Physikalische Gesellschaft was held together with the 65. Physikertagung, in Hamburg, during the pe riod March 26 30 2001. With more than 3500 conference attendees, a record has again been achieved after several years of stabilisation in participation. This proves the continuing and now even increasing, attraction of solid state physics, especially for young colleagues who often discuss for the first time their scientific results in public at this meeting. More than 2600 scientific pa pers were presented orally, as well as posters, among them about 120 invited lectures from Germany and from abroad. This Volume 41 of "Advances in Solid State Physics" contains the written versions of half of the latter. We nevertheless hope that the book truly reflects the current state of the field. Amazingly enough, the majority of the papers as well as the discussions at the meeting, concentrated on the nanostructured solid state. This re flects the currently extremely intensive quest for developing the electronic and magnetic device generations of the future, which stimulates science be sides the challenge of the unknown as has always been the case since the very beginning of Solid State Physics about 100 years ago.

Comprises a comprehensive reference source that unifies the entire fields of atomic molecular and optical (AMO) physics, assembling the principal ideas, techniques and results of the field. 92 chapters written by about 120 authors present the principal ideas, techniques and results of the field, together with a guide to the primary research literature (carefully edited to ensure a uniform coverage and style, with extensive cross-references). Along with a summary of key ideas, techniques, and results, many chapters offer diagrams of apparatus, graphs, and tables of data. From atomic spectroscopy to applications in comets, one finds contributions from over 100 authors, all leaders in their respective disciplines. Substantially updated and expanded since the original 1996 edition, it now contains several entirely new chapters covering current areas of great research interest that barely existed in 1996, such as Bose-Einstein condensation, quantum information, and cosmological variations of the fundamental constants. A fully-searchable CD- ROM version of the contents accompanies the handbook.