In this paper, we use the Feingold-Peres model, a well-known paradigm of quantum chaos, as an example. Using semiclassical analysis and numerical simulations, we investigate the statistical properties of observables in few-body systems with chaotic classical limits and the emergence of random-matrix-theory universality. More specifically, we focus on (1) the applicability of the eigenstate thermalization hypothesis in few-body systems and the dependence of its form on the effective Planck constant and (2) the existence of a universal random-matrix-theory description of observables when truncated to a small microcanonical energy window. Our results provide insights into the established field of few-body quantum chaos and help bridge it to modern perspectives, such as the general eigenstate thermalization hypothesis.
We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high energy physics and many-body theory. We discuss developments in the effective field theory of spontaneous symmetry breaking, of hydrodynamics and non-equilibrium dynamics more generally, fracton phases of matter, and dualities between 2+1 dimensional field theories. We furthermore discuss the application of effective field theory to non-Fermi liquids, the dynamics of entanglement entropy and to condensed matter aspects of cosmology.
The discovery of ultracold dilute liquids has significantly elevated our interest in various phenomena which go under the name of beyond-mean-field (BMF) physics. In these lecture notes we give an elementary introduction to the quantum stabilization and liquefaction of a collapsing weakly interacting Bose-Bose mixture. A detailed derivation of the leading BMF correction, also known as the Lee-Huang-Yang (LHY) term, in this system is presented in a manner suitable for further generalizations and extensions. Although the LHY term is a nonanalytic function of the density
n, under certain conditions the leading BMF correction becomes analytic and can be expanded in integer powers of
n, effectively introducing three-body and higher-order interactions. We discuss why and how well the Bogoliubov approach can predict these few-body observables.