We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. Scaling relationships are uncovered for the slow evolution of heterogeneities at all time scales.

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution in these systems: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators obtained for a given noise realization. We explain why the noise-averaged correlators describe the fingerprint of quenched disorder when it exists, while the coarse-grained correlators are linked to noise-induced mesoscopic fluctuations. We predict constraints on the distribution of the fluctuations of the coarse-grained quantities. In particular, we show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. A symmetry of the underlying theory, namely invariance under reparametrizations of the time coordinates, underlies these results. We establish a connection between the probabilities of spatial distributions of local coarse-grained quantities and the theory of dynamic random manifolds. We define, and discuss the behavior of, a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We characterize the fluctuations in the system in terms of their fractal properties. For concreteness, we present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.

We show that the generating functional describing the slow dynamics of spin-glass systems is invariant under reparametrizations of the time. This result is general and applies for both infinite and short-range models. It follows simply from the assumption that a separation between short time scales and long time scales exists in the system, and from the constraints of causality and unitarity. Global-time reparametrization invariance suggests that the low action excitations in a spin-glass may be smoothly spatially varying time reparametrizations. These Goldstone modes may provide the basis for an analytic dynamical theory of short-range spin glasses.

T he metallic state of high-temperature copper-oxide superconductors, characterized by unusual and distinct temperature dependences in the transport properties 1-4 , is markedly different from that of textbook metals. Despite intense theoretical efforts 5-11 , our limited understanding is impaired by our inability to determine experimentally the temperature and momentum dependence of the transport scattering rate. Here, we use a powerful magnetotransport probe to show that the resistivity and the Hall coefficient in highly doped Tl 2 Ba 2 CuO 6+δ originate from two distinct inelastic scattering channels. One channel is due to conventional electronelectron scattering; the other is highly anisotropic, has the same symmetry as the superconducting gap and a magnitude that grows approximately linearly with temperature. The observed form and anisotropy place tight constraints on theories of the metallic state. Moreover, in heavily doped non-superconducting La 2−x Sr x CuO 4 , this anisotropic scattering term is absent 12 , suggesting an intimate connection between the origin of this scattering and superconductivity itself.The in-plane properties of layered metals can sometimes be obtained from measurements of out-of-plane quantities. For example, angular magnetoresistance oscillations (AMRO), which are angular variations in the interlayer resistivity ρ ⊥ induced by rotating a magnetic field H in a polar plane relative to the conducting layers, can provide detailed information on the shape of the in-plane Fermi surface (FS) in layered metals. Here we resolve for the first time, the momentum (k) and energy (ω or T) dependence of the in-plane transport lifetime τ in an overdoped cuprate Tl 2 Ba 2 (Ca 0 )Cu 1 O 6+δ (Tl2201) through advances, both experimental and theoretical, in the AMRO technique. Experimentally, we extend the temperature range of previous AMRO measurements on overdoped Tl2201 13 (with a superconducting transition temperature T c = 15 K) by more than one order of magnitude. Theoretically, we derive a new general analytical expression for the interlayer conductivity σ ⊥ in a tilted H that incorporates basal-plane anisotropy. For T > 4 K, the AMRO can only be explained by inclusion of an anisotropic scattering rate 1/τ whose anisotropy grows with T. Significantly, the anisotropy in 1/τ and its T dependence up to 55 K can quantitatively account for both the robust linear-in-T component to the in-plane resistivity ρ ab and the T-dependent Hall coefficient R H over the same temperature range 14,15 . These anomalous behaviours are not characteristic of a simple Fermi liquid, which is often the starting point for modelling overdoped cuprates. We discuss the consequences of these findings for our understanding of the normal-state transport in cuprates.As described in the Supplementary Information, detailed azimuthal and polar-angle-dependent AMRO data were taken at 4.2 K and 45 T and fitted to the Shockley-Chambers tube integral form of the Boltzmann transport equation, modified for a quasitwo-dimensional (quasi...