Anyons in an exactly solved model and beyond

Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Statistical physics of social dynamics

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

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Berry phase effects on electronic properties

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

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CODATA Recommended Values of the Fundamental Physical Constants: 2006

It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may not be preserved but their sum is preserved.

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Homotopy and Quantization in Condensed Matter Physics

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

Bounds for the adiabatic approximation with applications to quantum computation

The viscosity of quantum fluids with an energy gap at zero temperature is related to the adiabatic curvature on the space parametrizing flat background metrics. For quantum Hall fluids on two-dimensional tori, the quantum viscosity is computed. It turns out to be isotropic, constant, and proportional to the magnetic field strength.

Viscosity of quantum Hall fluids.

The Index of a Pair of Projections

We describe a precise mathematical theory of the Laughlin argument for the quantization of the Hall conductance for general multiparticle Schr\"odinger operators with general background potentials. The quantization is a consequence of the geometric content of the conductance, namely, that it can be identified with an integral over the first Chern class. This generalizes ideas of Thouless et al., for noninteracting Bloch Hamiltonians to general (interacting and nonperiodic) ones.

Ruedi Seiler

Papers

Homotopy and Quantization in Condensed Matter Physics

Bounds for the adiabatic approximation with applications to quantum computation

Viscosity of quantum Hall fluids.

The Index of a Pair of Projections

Quantization of the Hall conductance for general, multiparticle Schrödinger Hamiltonians.