Igor V. Lerner – författare

This volume provides a representitive overview of recent progress in the theories of quantum disordered and chaotic systems, and an introduction to the underlying concepts and techniques.

Advances in material technology and low temperature techniques have led to the discovery of new physical phenomena. Situations are now routinely achieved in which the electronic system is so dominated by interactions that the old concepts of a Fermi liquid are no longer necessarily a good starting point, particularly so in the theory of low-dimensional systems. Disorder is often an unavoidable complication in such systems, leading to a host of rich physical phenomena, which has pushed the forefront of fundamental research to the point where the interplay between many-body correlations and quantum interference enhanced by disorder has become the key to understanding novel phenomena.The topics included in this volume cover surprises found in novel nanostructures and low-dimensional devices of submicron size, including quantum interference and electron-electron interactions in transport in metals, semiconductors and superconductors, theories of the Luttinger liquid of electrons in carbon nanotubes, Wigner crystals in 2-D electronic systems, the Kondo effect in quantum dots in the Coulomb blockade regime, quantum chaos in ballistic and disordered microstructures, and mesoscopic effects in superconductors. Experimental papers cover the physics of the Kondo effect in 0-D devices, transport in 1-D nanotubes, magneto-optics of skyrmions and composite fermions in the quantum Hall regime, and a possible metal-insulator transition in 2-D electron and hole gases.

Advances in material technology and low temperature techniques have led to the discovery of new physical phenomena. Situations are now routinely achieved in which the electronic system is so dominated by interactions that the old concepts of a Fermi liquid are no longer necessarily a good starting point, particularly so in the theory of low-dimensional systems. Disorder is often an unavoidable complication in such systems, leading to a host of rich physical phenomena, which has pushed the forefront of fundamental research to the point where the interplay between many-body correlations and quantum interference enhanced by disorder has become the key to understanding novel phenomena.The topics included in this volume cover surprises found in novel nanostructures and low-dimensional devices of submicron size, including quantum interference and electron-electron interactions in transport in metals, semiconductors and superconductors, theories of the Luttinger liquid of electrons in carbon nanotubes, Wigner crystals in 2-D electronic systems, the Kondo effect in quantum dots in the Coulomb blockade regime, quantum chaos in ballistic and disordered microstructures, and mesoscopic effects in superconductors. Experimental papers cover the physics of the Kondo effect in 0-D devices, transport in 1-D nanotubes, magneto-optics of skyrmions and composite fermions in the quantum Hall regime, and a possible metal-insulator transition in 2-D electron and hole gases.

Mesoscopic physics deals with effects at submicron and nanoscales where the conventional wisdom of macroscopic averaging is no longer applicable. A wide variety of new devices have recently evolved, all extremely promising for major novel directions in technology, including carbon nanotubes, ballistic quantum dots, hybrid mesoscopic junctions made of different type of normal, superconducting and ferromagnetic materials. This, in turn, demands a profound understanding of fundamental physical phenomena on mesoscopic scales. As a result, the forefront of fundamental research in condensed matter has been moved to the areas where the interplay between electron-electron interactions and quantum interference of phase-coherent electrons scattered by impurities and/or boundaries is the key to such understanding. An understanding of decoherence as well as other effects of the interactions is crucial for developing future electronic, photonic and spintronic devices, including the element base for quantum computation.

Mesoscopic physics deals with effects at submicron and nanoscales where the conventional wisdom of macroscopic averaging is no longer applicable. A wide variety of new devices have recently evolved, all extremely promising for major novel directions in technology, including carbon nanotubes, ballistic quantum dots, hybrid mesoscopic junctions made of different type of normal, superconducting and ferromagnetic materials. This, in turn, demands a profound understanding of fundamental physical phenomena on mesoscopic scales. As a result, the forefront of fundamental research in condensed matter has been moved to the areas where the interplay between electron-electron interactions and quantum interference of phase-coherent electrons scattered by impurities and/or boundaries is the key to such understanding. An understanding of decoherence as well as other effects of the interactions is crucial for developing future electronic, photonic and spintronic devices, including the element base for quantum computation.

Mesoscopic physics deals with effects at submicron and nanoscales where the conventional wisdom of macroscopic averaging is no longer applicable. A wide variety of new devices have recently evolved, all extremely promising for major novel directions in technology, including carbon nanotubes, ballistic quantum dots, hybrid mesoscopic junctions made of different type of normal, superconducting and ferromagnetic materials. This, in turn, demands a profound understanding of fundamental physical phenomena on mesoscopic scales. As a result, the forefront of fundamental research in condensed matter has been moved to the areas where the interplay between electron-electron interactions and quantum interference of phase-coherent electrons scattered by impurities and/or boundaries is the key to such understanding. An understanding of decoherence as well as other effects of the interactions is crucial for developing future electronic, photonic and spintronic devices, including the element base for quantum computation.

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec­ tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel­ oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec­ tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel­ oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.