Self-Consistent Mode-Coupling Approach to 1D Heat Transport

In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario to accomodate the known results obtained so far for this problem. More precisely, we conjecture that the universality class is determined by the leading order of the nonlinear interaction potential. Moreover, our analysis allows us determining the memory kernel, whose expression puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.Comment: Submitted to Physical Review

Anomalous kinetics and transport from 1D self--consistent mode--coupling theory

We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion

A simulation study of energy transport in the Hamiltonian XY-model

The transport properties of the planar rotator model on a square lattice are analyzed by means of microcanonical and non--equilibrium simulations. Well below the Kosterlitz--Thouless--Berezinskii transition temperature, both approaches consistently indicate that the energy current autocorrelation displays a long--time tail decaying as t^{-1}. This yields a thermal conductivity coefficient which diverges logarithmically with the lattice size. Conversely, conductivity is found to be finite in the high--temperature disordered phase. Simulations close to the transition temperature are insted limited by slow convergence that is presumably due to the slow kinetics of vortex pairs.Comment: Submitted to Journal of Statistical Mechanics: theory and experimen

Nonequilibrium Invariant Measure under Heat Flow

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic Fermi-Pasta-Ulam chain

In vivo evaluation of DSAEK interface with scanning-laser confocal microscopy

{BACKGROUND:} Descemet Stripping Automated Endothelial Keratoplasty ({DSAEK)} allows selective replacement of the endothelium. Post-operative haze and particles can affect the interface quality and, ultimately, visual outcome. In this study, we evaluated {DSAEK} interface with in vivo laser confocal microscopy ({LCM)} in order to: (i) correlate interface status with best corrected visual acuity, and (ii) with time from surgery; (iii) correlate interface particle number with best corrected visual acuity. Host-donor interface was imaged and graded using a published reflectivity scale. Particles at the interface were counted. {METHODS:} 18 eyes of 16 patients (6 males and 10 females); mean age: 74 ± 8.3 years which underwent {DSAEK} were examined by means of in vivo laser confocal microscopy between 1 and 24 months after surgery. Host-donor interface was imaged and graded using a published reflectivity scale. Particles present at the interface were counted. {RESULTS:} Interface reflectivity was 2.17 ± 1.2 and significantly correlated with visual acuity (Spearman correlation coefficient -0.83; P {\textless} 0.001), and with time after surgery (Spearman correlation coefficient -0.87; P {\textless} 0.001). Visual acuity was 0.67 ± 0.27. The number of particles was 205 ± 117.8; no correlation was found between this number and visual acuity (Spearman correlation coefficient -0.41; P = 0.15). {CONCLUSION:} {DSAEK} interface imaged with {LCM} is helpful in diagnosing poor host-donor interface quality in {DSAEK} surgery. A good quality interface is related to a better visual acuity. Moreover, the quality of the interface appears to improve as time passes from the surgery. Interface quality is related with visual acuity and improves with time from surgery. {LCM} should be considered as an added tool in post-{DSAEK} follow-up of patients. Finally, our study shows that the presence of particles does not influence visual outcome