Abstract
Jean-Marie Stephan, Institut Camille Jordan, Lyon, CNRS
Inhomogeneous quantum quenches
I consider a simple non-equilibrium problem, where a critical one-dimensional quantum system is prepared in a state with two different particle densities on the left and on the right, and let evolve with a Hamiltonian that conserves the number of particles. A typical example would be a fermionic system prepared with different left/right chemical potentials. After such a quench the system can remain strongly inhomogeneous, with for example a density of particles that varies with position. For free fermions a lot can, and has been understood by making use of a semiclassical picture, in which particles carrying a momentum k propagate ballistically with velocity v(k). Generalization to interacting systems is very much an active subject of research.
I will discuss attempts at understanding such dynamics using (conformal) field theory. In such an approach, the systemÕs inhomogeneity enters the field theory action through parameters that vary with position. In particular, the metric itself varies, resulting in a field theory in curved space. I will present a few simple examples where such an approach can be carried out to get exact results for correlation functions, or more complicated observables such as entanglement entropies.
References: arXiv:1507.08132 arXiv:1512.02872 arXiv:1606.04401