We study the time evolution of the entanglement entropy of a one-dimensional nonintegrable spin chain, starting from random nonentangled initial pure states. We use exact diagonalization of a nonintegrable quantum Ising chain with transverse and longitudinal fields to obtain the exact quantum dynamics. We show that the entanglement entropy increases linearly with time before finite-size saturation begins, demonstrating a ballistic spreading of the entanglement, while the energy transport in the same system is diffusive. Thus, we explicitly demonstrate that the spreading of entanglement is much faster than the energy diffusion in this nonintegrable system.

We ask whether the eigenstate thermalization hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, every eigenstate is thermal. We examine expectation values of few-body operators in highly excited many-body eigenstates and search for "outliers," the eigenstates that deviate the most from ETH. We use exact diagonalization of two one-dimensional nonintegrable models: a quantum Ising chain with transverse and longitudinal fields, and hard-core bosons at half-filling with nearest- and next-nearest-neighbor hopping and interaction. We show that even the most extreme outliers appear to obey ETH as the system size increases and thus provide numerical evidences that support ETH in this strong sense. Finally, periodically driving the Ising Hamiltonian, we show that the eigenstates of the corresponding Floquet operator obey ETH even more closely. We attribute this better thermalization to removing the constraint of conservation of the total energy.

Motivated by the findings of logarithmic spreading of entanglement in a many-body localized system, we more closely examine the spreading of entanglement in the fully many-body localized phase, where all many-body eigenstates are localized. Performing full diagonalizations of an XXZ spin model with random longitudinal fields, we identify two factors contributing to the spreading rate: the localization length (ξ), which depends on the disorder strength, and the final value of entanglement per spin (s∞), which primarily depends on the initial state. We find that the entanglement entropy grows with time as ∼ ξ × s∞ log t, providing support for the phenomenology of many-body localized systems recently proposed by Huse and Oganesyan [arXiv:1305.4915v1].

We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple "hydrodynamic" mode due to energy diffusion. Then, we examine some properties of the nontrivial slow operators. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain; this system is hydrodynamically "trivial", with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.

We explore the dynamics of the entanglement entropy near equilibrium in highly entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.

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Early postoperative enteral feeding has been demonstrated to improve the outcome of patients who underwent surgery for gastrointestinal (GI) malignancies, trauma, perforation, and/or obstruction. Thus, this study was conducted to assess the efficacy of early postoperative enteral nutrition (EN) after emergency surgery in patients with GI perforation or strangulation.The medical records of 484 patients, admitted between January 2007 and December 2012, were reviewed retrospectively. Patients were divided into 2 groups: the early EN (EEN, N = 77) group and the late EN (LEN, N = 407) group. The morbidity, mortality, length of hospital, and intensive care unit (ICU) stays were compared between the 2 groups. Propensity score matching was performed in order to adjust for any baseline differences.Patients receiving EEN had reduced in-hospital mortality rates (EEN 4.5% vs LEN 19.4%; P = 0.008), pulmonary complications (EEN 4.5% vs LEN 19.4%; P = 0.008), lengths of hospital stay (median: 14.0, interquartile range: 8.0–24.0 vs median: 17.0, interquartile range: 11.0–26.0, P = 0.048), and more 28-day ICU-free days (median: 27.0, interquartile range: 25.0–27.0 vs median: 25.0, interquartile range: 22.0–27.0, P = 0.042) than those receiving LEN in an analysis using propensity score matching. The significant difference in survival between the 2 groups was also shown in the Kaplan–Meier survival curve (P = 0.042). In a further analysis using the Cox proportional hazard ratio after matching on the propensity score, EEN was associated with reduced in-hospital mortality (hazard ratio, 0.03; 95% confidence interval, 0.01–0.49; P = 0.015).EEN is associated with beneficial effects, such as reduced in-hospital mortality rates, pulmonary complications, lengths of hospital stay, and more 28-day ICU-free days, after emergency GI surgery.