Quantum Breathing of an Impurity in a One-dimensional Bath of   Interacting Bosons
  By means of time-dependent density-matrix renormalization-group (TDMRG) we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode, which is found to be well-described by a single oscillation frequency and a damping rate. If the impurity is very weakly coupled to the bath, a Luttinger-liquid description is valid and the impurity suffers an Abraham-Lorentz radiation-reaction friction. For a large portion of the explored parameter space, the TDMRG results fall well beyond the Luttinger-liquid paradigm. 
Sebastiano Peotta, Davide Rossini, Marco Polini, Francesco Minardi,   Rosario Fazio
cond-mat.quant-gas cond-mat.stat-mech