The non-equilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N ) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N , the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate here the dynamics of an isolated quantum system represented by a scalar φ 4 theory after a global quench of the potential close to a dynamical critical point. We demonstrate that, within a pre-thermal regime, the time dependence of the relevant correlations is characterized by a short-time universal exponent, which we calculate at the lowest order in a dimensional expansion.

Extended quantum systems can be theoretically described in terms of the Schwinger-Keldysh functional integral formalism, whose action conveniently describes both dynamical and static properties. We show here that in thermal equilibrium, defined by the validity of fluctuation-dissipation relations, the action of a quantum system is invariant under a certain symmetry transformation and thus it is distinguished from generic systems. In turn, the fluctuation-dissipation relations can be derived as the Ward-Takahashi identities associated with this symmetry. Accordingly, the latter provides an efficient test for the onset of thermodynamic equilibrium and it makes checking the validity of fluctuation-dissipation relations unnecessary. In the classical limit, this symmetry reduces to the well-known one which characterizes equilibrium in the stochastic dynamics of classical systems coupled to thermal baths, described by Langevin equations. PACS numbers: 05.30.Jp,05.40.-a,05.70.Ln arXiv:1505.00912v2 [cond-mat.stat-mech] 10 Nov 2015

We investigate the effects of fluctuations on the dynamics of an isolated quantum system represented by a φ 4 field theory with O(N ) symmetry after a quench in d > 2 spatial dimensions. A perturbative renormalization-group approach involving a dimensional expansion in = 4 − d is employed in order to study the evolution within a prethermal regime controlled by elastic dephasing. In particular, we focus on a quench from a disordered initial state to the critical point, which introduces an effective temporal boundary in the evolution. At this boundary, the relevant fields acquire an anomalous scaling dimension, while the evolution of both the order parameter and its correlation and response functions display universal aging. Since the relevant excitations propagate ballistically, a light cone in real space emerges. At longer times, the onset of inelastic scattering appears as secularly growing self-generated dissipation in the effective Keldysh field theory, with the strength of the dissipative vertices providing an estimate for the time needed to leave the prethermal regime.

We study the prethermal dynamics of an interacting quantum field theory with a N -component order parameter and O(N ) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the non-equilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a non-perturbative large-N limit.Introduction -An isolated many-body system, suddenly brought out of equilibrium, can linger over a nonthermal quasi-steady state before thermalization occurs at later times triggered by inelastic scattering processes. This phenomenon, known as prethermalization, is ubiquitous in physics: first predicted in the context of heavy-ion collisions [1] and early-universe inflationary dynamics [2], it has been only recently recognized in condensed matter and cold-atoms physics [3].Prethermal states can host a novel class of critical phenomena, since the gap associated with these nonequilibrium (NEQ) states can vanish upon choosing properly the initial conditions and parameters of the system. Quenching a quantum many-particle system above or below the corresponding critical points results in qualitatively different NEQ dynamics [4,5]. For instance, in the case of an interacting bosonic quantum field, quenching above or below its dynamical critical point induces respectively an exponential relaxation of local observables or a coarsening dynamics of correlation functions [6][7][8]. By quenching, instead, close to the dynamical critical point, correlation functions display non-equilibrium dynamical scaling [5,[8][9][10] similar to critical aging in classical dissipative systems [11,12] with a consequent delay of thermalization and stabilization of the associated prethermal states. These NEQ dynamical critical points can both be of quantum and classical nature, depending on the strength of the quantum quench performed at initial times [9,10].Interestingly, a recent experiment [13] has observed the emergence of dynamical scaling in a one-dimensional twocomponent Bose gas quenched close to criticality. The correlation length of the order parameter displayed there a dynamical crossover between a short-time critical and a long-time non-critical regime. This suggests the possibility to explore the variety of the dynamical critical points occurring in the prethermal dynamics of a quantum many-body system via quantum quenches, which expose the temporal crossover between different scaling behaviours.In this work, we propose a minimal model in which it