Focusing on semiclassical systems, we show that the parametrically long exponential growth of outof-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in an integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

We study nonlinear optical responses in superconducting systems with inversion (I) symmetrybreaking order parameters. We first show that any superconducting system with I and time-reversal (T ) symmetries requires an I-breaking order parameter to support optical transitions between particle-hole pair bands. We then use a 1D toy model of an I-breaking superconductor to numerically calculate linear and nonlinear conductivities, including shift current and second harmonic generations (SHG) responses. We find that the magnitude of the signal is significantly larger in shift current/SHG response compare to the linear response due to the matrix element effect. We also present various scaling behaviors of the SHG signal, which may be relevant to the recent experimental observation of SHG in cuprates [1]. Finally, we confirm the generality of our observations regarding nonlinear responses of I-breaking superconductors, by analyzing other models including a 1D three-band model and 2D square lattice model.

It has become widely accepted that particles with long-range hopping do not undergo Anderson localization. However, several recent studies demonstrated localization of particles with long-range hopping. In particular, it was recently shown that the effect of long-range hopping in 1D lattices can be mitigated by cooperative shielding, which makes the system behave effectively as one with short-range hopping. Here, we show that cooperative shielding, demonstrated previously for 1D lattices, extends to 3D lattices with isotropic long-range r −α hopping, but not to 3D lattices with dipolar-like anisotropic long-range hopping. We demonstrate the presence of localization in 3D lattices with uniform (α = 0) isotropic long-range hopping and the absence of localization with uniform anisotropic long-range hopping by using the scaling behaviour of eigenstate participation ratios. We use the scaling behaviour of participation ratios and energy level statistics to show that the existence of delocalized, non-ergodic extended, or localized states in the presence of disorder depends on both the exponents α and the isotropy of the long-range hopping amplitudes.

We study how time-and angle-resolved photoemission (tr-ARPES) reveals the dynamics of BCStype, s-wave superconducting systems with time-varying order parameters. Approximate methods are discussed, based on previous approaches to either optical conductivity or quantum dot transport, to enable computationally efficient prediction of photoemission spectra. One use of such predictions is to enable extraction of the underlying order parameter dynamics from experimental data, which is topical given the rapidly growing use of tr-ARPES in studying unconventional superconductivity. The methods considered model the two-time lesser Green's functions with an approximated lesser self-energy that describes relaxation by coupling of the system to two types of baths. The approach primarily used here also takes into consideration the relaxation of the excited states into equilibrium by explicitly including the level-broadening of the retarded and advanced Green's functions. We present equilibrium and non-equilibrium calculations of tr-ARPES spectrum from our model and discuss the signatures of different types of superconducting dynamics. arXiv:1809.09204v3 [cond-mat.supr-con]

We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t 1 ∼ s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.

Abstract. We briefly review the theory for electromagnetic reactions in light nuclei based on the coupled-cluster formulation of the Lorentz integral transform method. Results on photodisintegration reactions of 22 O and 40 Ca are reported and preliminary calculations on the Coulomb sum rule for 4 He are discussed.

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