Efimov-DNA phase diagram: Three stranded DNA on a cubic lattice.

Abstract: The determination in 1953 of the structure of deoxyribonucleic acid (DNA), with its two entwined helices and paired organic bases, was a tour de force in X-ray crystallography. But more significantly, it also opened the way for a deeper understanding of perhaps the most important biological process. In the words of Watson and Crick: "It has not escaped our notice that the specific pairing that we have postulated immediately suggests a possible copying mechanism for the genetic material." [Obituary of Francis Crick:

Abstract: Resonant two-body forces are shown to give rise to a series of levels in three-particle systems. The number of such levels may be very large. Possibility of the existence of such levels in systems of three α-particles ( 12 C nucleus) and three nucleons ( 3 H) is discussed.

Abstract: Particles with short-range interactions and a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-body sector, the universal properties are familiar and depend only on the scattering length a. In the 3-body sector for identical bosons, the universal properties include the existence of a sequence of shallow 3-body bound states called “Efimov states” and log-periodic dependence of scattering observables on the energy and the scattering length. The spectrum of Efimov states in the limit a → ± ∞ is characterized by an asymptotic discrete scaling symmetry that is the signature of renormalization group flow to a limit cycle. In this review, we present a thorough treatment of universality for the system of three identical bosons and we summarize the universal information that is currently available for other 3-body systems. Our basic tools are the hyperspherical formalism to provide qualitative insights, Efimov's radial laws for deriving the constraints from unitarity, and effective field theory for quantitative calculations. We also discuss topics on the frontiers of universality, including its extension to systems with four or more particles and the systematic calculation of deviations from universality.

Abstract: In the bizarre world of quantum physics, three interacting particles can form a loosely bound system even if the two-particle attraction is too weak to allow for the binding of a pair. This exotic trimer state was predicted 35 years ago by Russian physicist Vitali Efimov, who found a remarkable and counterintuitive solution to the notoriously difficult quantum-mechanical three-body problem. Efimov's well known result was a landmark in theoretical few-body physics, but until now these exotic states had not been demonstrated experimentally. Now that has been achieved, in an ultracold gas of caesium atoms. The existence of this gas confirms key predictions and opens up few-body quantum systems to further experiment. The first experimental observation of Efimov's prediction confirms key theoretical predictions and represents a starting point from which to explore the universal properties of resonantly interacting few-body systems. Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov's prediction1,2 of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics3,4,5,6,7,8. However, the observation of Efimov quantum states has remained an elusive goal3,5. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss9,10 when the strength of the two-body interaction is varied. We also detect a minimum9,11,12 in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems7. While Feshbach resonances13,14 have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter15 to the world of few-body quantum phenomena.

Abstract: A renormalization group transformation is introduced with the help of which critical properties of infinite systems can be related to finite systems. As a numerical example the method is applied to the two-dimensional Ising model. The critical point and critical point exponent are computed in addition to the amplitude of the logarithmic singularity in the specific heat.