tive theories developed by humankind, allow for extraordinarily accurate calculations of the properties of individual and small collections of particles.

Nature, however, confronts us with materials consisting of unimaginably large numbers of particles. For example, there are many more electrons in a copper penny than there are stars in the known universe. It is therefore not surprising that condensed-matter and materials physicists regularly discover phenomena that neither were foreseen nor are easily understood. These phenomena emerge as collective aspects of the material at hand. Emergent phenomena are properties of a system of many interacting parts that are not properties of the individual microscopic constituents. It is often not readily possible to understand such collective properties in terms of the motion of individual constituent particles. Emergent phenomena occur at all scales, from the microscopic to the everyday to the astronomical, and from the precincts of quantum mechanics to the world known to Newton and Maxwell. The infinite diversity of emergent phenomena ensures that the beauty, excitement, and deep practical utility of condensed-matter and materials physics comprise an inexhaustible resource.

Emergent phenomena are not merely academic curiosities. Some, like the emergence of life from biomolecules, define our very existence. Others, like the regular arrangements of atoms in crystals, are simply so familiar that we rarely even pause to wonder at them anymore. There are countless examples of this kind. At the same time, the discovery and study of emergent phenomena often lead to immensely important practical applications. Superconductivity, discovered almost 100 years ago, is a good example. While Dutch physicist Kamerlingh Onnes did envision producing magnetic fields using solenoids wound from superconducting wire, he could never have foreseen superconducting magnets big enough to surround a human, nor that such a magnet would be the heart of a technological marvel (magnetic resonance imaging; see Figure 1.1 in Chapter 1) that would revolutionize medicine. Looking ahead, one can imagine that the recently discovered high-temperature superconductors, which have so far seen limited application, might ultimately play a major role in reducing world energy consumption by allowing lossless transmission of electrical power over long distances. Unlike superconductors, which took many decades to see large-scale application, there is the very recent dramatic example of giant magnetoresistive materials, which came to dominate hard disk data storage in just a few years. Liquid crystalline materials, in which large numbers of asymmetric molecules in solution exhibit a dizzying variety of emergent phases, are used in everyday electronics like cellular telephones and laptop computers. Jamming of granular materials (discussed below), perhaps unfamiliar to the average citizen, is an emergent phenomenon with real economic consequences in the mining, pharmaceutical, and other industries. And the list goes on.

Emergent phenomena are so widespread that a comprehensive review is both



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