Recent research has focused on various aspects of the quantum- classical correspondence problem. To see why this is not trivial, consider, for instance, that there are (infinitely) many more states possible for a quantum particle than for a classical particle (e.g., a quantum particle could, fairly literally, be in two different places at once!). This means that an infinite number of possible states must disappear in the classical limit. How, then, is the clas-sical dynamics to be recovered from the quantum dynamics?

For macroscopic systems, the answer appears to lie in the fact that the coupling to the environment (which is unavoidable for very large systems) destroys very rapidly the coherence between any macroscopically distinct branches of the wavefunction. Most nonclassical states and all macroscopically entangled states then become incoherent mixtures, which can no longer be interpreted as describing an individual system. This decoherence process would be the key to the classical limit.

Decoherence would play an important (and destructive) role in certain devices which have been proposed recently called quantum computers. In a quantum computer, each binary register would not necessarily have to be in one of the two states 0 and 1, but could exist in a coherent superposition of the two. Quantum computers could, in principle, perform certain calculations much faster than classical computers; however, it is essential that the coherence should be maintained for the whole duration of the calculation. Some of the current work is devoted to looking at coherence-destroying mechanisms in quantum computers, and, in particular, at how these effects scale with the size of the computer and the length of the calculation.

A recently-completed project is a study of the so-called quantum chaos problem. Consider a system which, when treated classically, exhibits chaotic behavior. Does this classical chaos leave a trace in the mesoscopic quantum world, and, if so, what is it? It has been suggested that quantum computers could be used to simulate the behavior of classically chaotic systems. It might be very interesting to study what one has then. Would the behavior of the quantum computer be recognizable as chaotic from a classical point of view, or would the quantum nature of the system inhibit the chaotic evolution?