Collective vibrations in a crystal, called phonons, are a type of Nambu-Goldstone boson. UC Berkeley physicists have proved that counting the number of bosons in a material, whether a solid crystal, a magnet, or a superfluid, tells you what type of behavior the material will have at low temperatures where symmetry is spontaneously broken. Credit: Haruki Watanabe/UC Berkeley.
Matter exhibits weird properties at very cold temperatures. Take superfluids, for example: discovered in 1937, they can flow without resistance forever, spookily climbing the walls of a container and dripping onto the floor.
In the past 100 years, 11 Nobel Prizes have been awarded to nearly two dozen people for the discovery or theoretical explanation of such cold materials - superconductors and Bose-Einstein condensates, to name two - yet a unifying theory of these extreme behaviors has eluded theorists.
University of California, Berkeley, physicist Hitoshi Murayama and graduate student Haruki Watanabe have now discovered a commonality among these materials that can be used to predict or even design new materials that will exhibit such unusual behavior. The theory, published online June 8 by the journal Physical Review Letters, applies equally to magnets, crystals, neutron stars and cosmic strings.
"This is a particularly exciting result because it concerns pretty much all areas of physics; not only condensed matter physics, but also astrophysics, atomic, particle and nuclear physics and cosmology," said Murayama, the MacAdams Professor of Physics at UC Berkeley, a faculty senior scientist at Lawrence Berkeley National Laboratory and director of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo. "We are putting together all of them into a single theoretical framework."
The theorem Watanabe and Murayama proved is based on the concept of spontaneous symmetry breaking, a phenomenon that occurs at low temperatures and leads to odd behavior. This produces superconductors, which allow electric currents to flow without resistance; or Bose-Einstein condensates, which have such low energy that every atom is in the same quantum state.
By describing the symmetry breaking in terms of collective behavior in the material - represented by so-called Nambu-Goldstone bosons - Murayama and Watanabe found a simple way to classify materials’ weirdness. Boson is the name given to particles with zero or integer spin, as opposed to fermions, which have half-integer spin.
"Once people tell me what symmetry the system starts with and what symmetry it ends up with, and whether the broken symmetries can be interchanged, I can work out exactly how many bosons there are and if that leads to weird behavior or not," Murayama said. "We’ve tried it on more than 10 systems, and it works out every single time."
Anthony Leggett of the University of Illinois at Urbana Champaign, who won the 2003 Nobel Prize in Physics for his pioneering work on superfluids, pointed out that "it has long been appreciated that an important consequence of the phenomenon of spontaneously broken symmetry, whether occurring in particle physics or in the physics of condensed matter, is the existence of the long-wavelength collective excitations known as Nambu-Goldstone bosons.
"In their paper, Watanabe and Maruyama have now derived a beautiful general relation... (involving) Nambu Goldstone bosons... (that) reproduces the relevant results for all known cases and gives a simple framework for discussing any currently unknown form of ordering which may be discovered in the future."
"Surprisingly, the implications of spontaneous symmetry breaking on the low energy spectrum had not been worked out, in general, until the paper by Watanabe and Murayama," wrote Hirosi Ooguri, a professor of physics and mathematics at Caltech. "I expect that there will be a wide range of applications of this result, from condensed matter physics to cosmology. It is a wonderful piece of work in mathematical physics."
Symmetry has been a powerful concept in physics for nearly 100 years, allowing scientists to find unifying principles and build theories that describe how elementary particles and forces interact now and in the early universe. The simplest symmetry is rotational symmetry in three dimensions: a sphere, for example, looks the same when you rotate it arbitrarily in any direction. A cylinder, however, has a single rotational symmetry around its axis.
Some interactions are symmetric with respect to time, that is, they look the same whether they proceed forward or backward in time. Others are symmetric if a particle is replaced by its antiparticle.