Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional fermionic system with open boundaries and subject to a finite duration quench of the inter-particle interaction. We provide analytical and asymptotic solutions to the unitary time evolution of the system, showing that both switching on and switching off the quench ramp create light-cone perturbations in the density. The post-quench dynamics is strongly affected by the interference between these two perturbations. In particular, we find that the discrepancy between the time-dependent density and the one obtained by a generalized Gibbs ensemble picture vanishes with an oscillatory behavior as a function of the quench duration, with local minima corresponding to a perfect overlap of the two light-cone perturbations. For adiabatic quenches, we also obtain a similar behavior in the approach of the generalized Gibbs ensemble density towards the one associated with the ground state of the final Hamiltonian.

The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a Generalized Gibbs Ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, non-monotonic response of steady state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the non-monotonous behaviour of observables. In continuum non-interacting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favour of the robustness of the phenomenon in the cases of non-sudden quenches and higher dimensionality.PACS numbers: 67.85. Lm, 05.70.Ln, 71.70.Ej, 05.30.Fk Non-equilibrium quantum physics is at the heart of most relevant applications of solid state physics, such as transistors and lasers [1][2][3] . More fundamentally, one of the main difficulties in studying many-body non-equilibrium quantum physics is represented by the unavoidable interactions that any quantum system has with its surroundings. This coupling is difficult to control and causes an effectively non-unitary evolution even on short time scales 4 . The recent advent of cold atom physics 5 allowed not only to access quantum systems characterized by weak coupling to the environment, but also to engineer Hamiltonians which show non-ergodic behavior 6,7 : the so called integrable systems 8 . Moreover, in the context of cold atom physics, it is possible to manipulate the parameters of the Hamiltonian in a time dependent and controllable fashion 7,9-12 . The combination of these three ingredients gave rise to a renewed interest in the physics of quantum quenches [13][14][15][16][17] , which led to the birth of a new thermodynamic ensemble, the Generalized Gibbs Ensemble (GGE) 1,[18][19][20][21]23 . Quantum quenches have been studied in a wide range of systems with the property that a change in a parameter of the Hamiltonian deeply affects the physical properties of the system itself. Interaction quenches in Luttinger liquids [24][25][26][27][28][29][30][31][32][33][34][35][36] and magnetic field quenches in the one-dimensional (1D) Ising model [37][38][39][40][41][42][43][44][45][46][47] are prominent examples in this direction. Furthermore, at the level of free fermions, quantum quenches between gapped phases characterized by different Chern numbers have also been studied [48][49][50][51] . However, not much attention has been devoted to the study of quantum quenches between gapless and gapped states. A notable exception is represented by quantum quenches from a Luttinger liquid to a sine-Gordon model [52][53][54][55][56][57][58][59][60][61] and quantum time mirrors 62 . However...

Understanding the properties of far-from-equilibrium quantum systems is becoming a major challenge of both fundamental and applied physics. For instance, the lack of thermalization in integrable and (many body) localized systems provides new insights in the understanding of the relaxation dynamics of quantum phases. On a more applicative side, the possibility of exploiting the properties of far-from-equilibrium states, for example in pump-probe experiments, opens unprecedented scenarios. The effort in providing a classification of far-from-equilibrium phases, in terms of local or topological order parameters, is hence intense. In this context, the concept of Dynamical Quantum Phase Transition (DQPT) has been introduced. A DQPT is (roughly) defined as a zero of the Loschmidt-Echo as a function of time and represents a natural non-equilibrium counterpart of a thermal phase transition. Here, we investigate the DQPTs occurring in the quantum xy chain subject to a quantum quench of finite duration. We show that the number of distinct DQPTs can vary as the duration of the quantum quench is varied. However, the parity of such number only depends on the pre-quench and post-quench Hamiltonians and is related to a topological invariant.