We discuss a 1+1 dimensional Galilean invariant model recently introduced in connection with ultracold quantum gases. After showing its relation to a nonrelativistic 2+1 Chern-Simons matter system, we identify the generators of the supersymmetry and its relation with the existence of self-dual equations
We calculate the time evolution of a far-from-equilibrium initial state of a non-relativistic ultracold Bose gas in one spatial dimension. The non-perturbative approximation scheme is based on a systematic expansion of the two-particle irreducible ef
fective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory and off-shell effects that are not captured in mean-field theory.
We review the imaginary time path integral approach to the quench dynamics of conformal field theories. We show how this technique can be applied to the determination of the time dependence of correlation functions and entanglement entropy for both g
lobal and local quenches. We also briefly review other quench protocols. We carefully discuss the limits of applicability of these results to realistic models of condensed matter and cold atoms.
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomen
on of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
The possibility that particle production in high-energy collisions is a result of two asymmetric hydrodynamic flows is investigated, using the Khalatnikov form of the 1+1-dimensional approximation of hydrodynamic equations. The general solution is di
scussed and applied to the physically appealing generalized in-out cascade where the space-time and energy-momentum rapidities are equal at initial temperature but boost-invariance is not imposed. It is demonstrated that the two-bump structure of the entropy density, characteristic of the asymmetric input, changes easily into a single broad maximum compatible with data on particle production in symmetric processes. A possible microscopic QCD interpretation of asymmetric hydrodynamics is proposed.
We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the mo
mentum distribution of the density and spin response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the density response function signals the transition between a BEC and a BCS regimes, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC to BCS crossover. Also, we predict spin rotational symmetry-breaking in this system.