Some aspects and applications of σ-models in particle and condensed matter physics are briefly reviewed. ∗Contribution to Salamfest, 8 -12 March 1993, Trieste 1

The spatial observation of a Bose condensate is reported. Dispersive light scattering was used to observe the separation between the condensed and normal components of the Bose gas inside a magnetic trap. This technique is nondestructive, and about a hundred images of the same condensate can be taken. The width of the angular distribution of scattered light increased suddenly at the phase trans...

The phenomenon of Anderson localization in the quantum kicked rotator is analyzed by means of concepts which were originally introduced in condensed matter physics. A diagrammatic language similar to the impurity diagram technique employed in the theory of disordered conductors is developed. The method is applied to a calculation of the quantum return probability and leads to results which coin...

A new condensed form of the Fukui function, the natural orbital Fukui function (NOFF), is proposed and derived from natural bond orbital occupancy. It is defined as the change in natural bond orbital occupancy upon electronic perturbation (electron addition to, or depletion from, a molecular system). Applying NOFF to a series of cycloaddition reactions (e.g., [4 + 2] and [2 + 1] cycloadditions)...

We present an argument for assigning a definite phase to an assembly of Bose-Einstein Condensed atoms. This relies on the demonstration that a coherent state of the condensed system is a robust state in the presence of interactions between the condensate and its environment.

A nonperturbative study of field theories with a complex action, such as QCD at finite baryon density, is difficult due to the sign problem. We show that the relativistic Bose gas at finite chemical potential has a sign and "silver blaze" problem, similar to QCD. We then apply stochastic quantization and complex Langevin dynamics to study this theory with nonperturbative lattice simulations. In...

We briefly review some of the connections between symmetry breaking in condensed matter physics and in particle physics, assisting, in particular, our current understanding of the origin of mass.

Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we pro...

We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between ent...