Reviews of Modern Physics – January - March 2005
Volume 77, Issue 1

This review of the fundamental constants provides recommended values and the associated uncertainties, updating the last review of 1998. Since that time, new methods have become competitive for the determination of Planck's constant h and the fine-structure constant α, and there has been a dramatic improvement in the measurement of Newton's gravitational constant G.

The phenomenon of Andreev–Saint James reflection, usually referred to as Andreev reflection, has emerged as an important probe of superconductivity, yielding results for both the electronic excitations and the nature of the condensate. This work surveys the basic features of the phenomenon and discusses experimental results on the most widely investigated high-temperature superconductors in the context of some current theories.

Synchronization phenomena in large populations of interacting elements are the subject of intense research effort in physical, biological, chemical, and social systems. The Kuramoto model, a model of oscillators coupled through the sine of their phase differences, captures the essential features of synchronization in a broad range of systems. This review presents the mathematical analysis of the model, numerical methods, and applications of the model in various contexts.

Galaxy clusters are the largest bound objects in the universe. Large clusters can comprise 12 10 solar masses of stars in hundreds of galaxies, with these galaxies embedded in 10 13 solar masses of hot gas and 10 14 solar masses of nonbaryonic dark matter. Their sheer size makes them rich laboratories for studies of the evolution of the universe and estimates of fundamental cosmological parameters.

In the decade since its inception, the density-matrix renormalization group has been shown to be a precise and reliable tool for numerical analysis of many-body systems of low dimensionality. This review covers the key aspects of the method, including time-dependent and nonequilibrium generalizations, and its applications to one- and two-dimensional quantum systems, quantum chemistry, nuclear physics, and small particles.

Helium crystals are model systems for the general study of crystal surfaces. They also show unique quantum properties. This review summarizes contemporary research in the field, especially on surface roughening, crystal steps, the role of quantum and thermal fluctuations, the growth dynamics and various instabilities. Relevant experiments are presented together with their theoretical interpretation. Experimental techniques and open questions in the field are also discussed.

Nanoclusters—containing a number of particles ranging from ten to a million—are the building blocks of nanoscience. Living at the boundary between the microscopic and macroscopic, they have properties that are different from those of infinite solids. This review presents an overview of their thermodynamic properties and growth kinetics, with applications to a variety of clusters including different elements and fullerene molecules. Properties discussed are the stability, melting, and solid-solid phase transitions, all of which depend on cluster size.