Integer Quantum Hall Transition and Random SU(N) Rotation

We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in this way allows us to obtain a new series of conservation laws for the equation describing the electron density evolution in the lowest Landau level. The resulting formalism is particularly well suited to numerical simulations, allowing us to obtain the critical exponent \nu numerically in a very simple way. We also suggest that if the number of nonzero generators is much less than N, the same model, in a certain intermediate time interval, describes percolating properties of a random incompressible steady two-dimensional flow. In other words, quantum Hall transition in a very smooth random potential inherits certain properties of percolation.Comment: 4 pages, 1 figur

Network Models of Quantum Percolation and Their Field-Theory Representations

We obtain the field-theory representations of several network models that are relevant to 2D transport in high magnetic fields. Among them, the simplest one, which is relevant to the plateau transition in the quantum Hall effect, is equivalent to a particular representation of an antiferromagnetic SU(2N) ($N\to 0$) spin chain. Since the later can be mapped onto a $\theta\ne 0$, $U(2N)/U(N)\times U(N)$ sigma model, and since recent numerical analyses of the corresponding network give a delocalization transition with $\nu\approx 2.3$, we conclude that the same exponent is applicable to the sigma model

Single electron magneto-conductivity of a nondegenerate 2D electron system in a quantizing magnetic field

We study transport properties of a non-degenerate two-dimensional system of non-interacting electrons in the presence of a quantizing magnetic field and a short-range disorder potential. We show that the low-frequency magnetoconductivity displays a strongly asymmetric peak at a nonzero frequency. The shape of the peak is restored from the calculated 14 spectral moments, the asymptotic form of its high-frequency tail, and the scaling behavior of the conductivity for omega -> 0. We also calculate 10 spectral moments of the cyclotron resonance absorption peak and restore the corresponding (non-singular) frequency dependence using the continuous fraction expansion. Both expansions converge rapidly with increasing number of included moments, and give numerically accurate results throughout the region of interest. We discuss the possibility of experimental observation of the predicted effects for electrons on helium.Comment: RevTeX 3.0, 14 pages, 8 eps figures included with eps

Keldysh Green's function approach to coherence in a non-equilibrium steady state: connecting Bose-Einstein condensation and lasing

Solid state quantum condensates often differ from previous examples of condensates (such as Helium, ultra-cold atomic gases, and superconductors) in that the quasiparticles condensing have relatively short lifetimes, and so as for lasers, external pumping is required to maintain a steady state. On the other hand, compared to lasers, the quasiparticles are generally more strongly interacting, and therefore better able to thermalise. This leads to questions of how to describe such non-equilibrium condensates, and their relation to equilibrium condensates and lasers. This chapter discusses in detail how the non-equilibrium Green's function approach can be applied to the description of such a non-equilibrium condensate, in particular, a system of microcavity polaritons, driven out of equilibrium by coupling to multiple baths. By considering the steady states, and fluctuations about them, it is possible to provide a description that relates both to equilibrium condensation and to lasing, while at the same time, making clear the differences from simple lasers

Scaling Theory of the Integer Quantum Hall Effect

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys