Narrow Results

We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint starting with [1-3]. We show, in particular, the existence and finiteness of the conductivity measure μ_Σ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, μ_Σ converges in the weak*-topology to the trivial measure in the case of perfect insulators (strong disorder, complete localization), whereas in the limit of perfect conductors (absence of disorder) it converges to an atomic measure concentrated at frequency ν = 0. However, the AC-conductivity μ_Σ|_ℝ\{0} does not vanish in general: We show that μ_Σ(ℝ\{0}) > 0, at least for large temperatures and a certain regime of small disorder.

It is shown that black holes in a quark gluon plasma (QGP) obeying minimum viscosity bounds exhibit a Schwarzschild radius in close match with the range of interaction of the strong force. For such black holes, an evaporation time of about $10^{16}$ s is estimated, indicating that they would survive by far the quark-gluon plasma era, namely between $10^{-10}$ and $10^{-6}$ s after the big bang. On the assumption that the big-bang generated unequal amounts of quark and antiquarks, this suggests that such unbalance might have survived to this day in the form of excess antiquark nuggets hidden to all but gravitational interactions. A connection with the saturon picture, whereby minimum viscosity regimes would associate with the onset coherent quantum field structures with maximum storage properties, is also established.

By means of the Ford–Kac–Mazur formalism, the heat current and local kinetic energy of a dielectric chain with Fermi–Pasta–Ulam–β nonlinear interactions are derived out in the stationary equilibrium and analyzed numerically. We find that the anharmonicity reduces the heat current for repulsive interactions and enhances the heat current for attractions. The magnitudes of heat current are relevant strong at low frequencies, while the local kinetic energy is bigger in the high-frequency regime. The local kinetic energy displays a periodic oscillation due to the interference of the thermal waves. In particular, the transmission matrix exhibits oscillations due to scattering of phonons for the imperfect contacts. In general, the thermal transport is qualitatively altered by the differences of temperature between reservoirs, nonlinear interactions and the size of chain as well as the contacts.

Here, we introduce a statistical approach derived from dynamics, for the study of the geophysical fluid dynamics phenomena characterized by a weak interaction among the variables of interest and the rest of the system. The approach is reminiscent of the one developed some years ago [M. Bianucci, R. Mannella, P. Grigolini and B. J. West, Phys. Rev. E51, 3002 (1995)] to derive statistical mechanics of macroscopic variables on interest starting from Hamiltonian microscopic dynamics. However, in the present work, we are interested to generalize this approach beyond the context of the foundation of thermodynamics, in fact, we take into account the cases where the system of interest could be non-Hamiltonian (dissipative) and also the interaction with the irrelevant part can be of a more general type than Hamiltonian. As such example, we will refer to a typical case from geophysical fluid dynamics: the complex ocean–atmosphere interaction that gives rise to the El Niño Southern Oscillation (ENSO). Here, changing all the scales, the role of the “microscopic” system is played by the atmosphere, while the ocean (or some ocean variables) plays the role of the intrinsically dissipative macroscopic system of interest. Thus, the chaotic and divergent features of the fast atmosphere dynamics remains in the decaying properties of the correlation functions and of the response function of the atmosphere variables, while the exponential separation of the perturbed (or close) single trajectories does not play a direct role. In the present paper, we face this problem in the frame of a not formal Langevin approach, limiting our discussion to physically based rather than mathematics arguments. Elsewhere, we obtain these results via a much more formal procedure, using the Zwanzing projection method and some elements from the Lie Algebra field.

We have investigated the thermal conductivity of defective fullerene (C${}_{60})$ by using the nonequilibrium molecular dynamics (MD) method. It is found that the thermal conductivity of C${}_{60}$ with one defect is lower than the thermal conductivity of perfect C${}_{60}$. However, double defects in C${}_{60}$ have either positive or negative influence on the thermal conductivity, which depends on the positions of the defects. The phonon spectra of perfect and defective C${}_{60}$ are also provided to give corresponding supports. Our results can be extended to long C${}_{60}$ chains, which is helpful for the thermal management of C${}_{60}$.

We rigorously prove the existence of directed transport for a certain class of ac-driven nonlinear one-dimensional systems, namely the generation of transport with a preferred direction in the absence of a net driving force.

We study the dynamics of interacting lattice fermions with random hopping amplitudes and random static potentials, in presence of time-dependent electromagnetic fields. The interparticle interaction is short-range and translation invariant. Electromagnetic fields are compactly supported in time and space. In the limit of infinite space supports (macroscopic limit) of electromagnetic fields, we derive Ohm and Joule's laws in the AC-regime. An important outcome is the extension to interacting fermions of the notion of macroscopic AC-conductivity measures, known so far only for free fermions with disorder. Such excitation measures result from the second law of thermodynamics and turn out to be Lévy measures. As compared to the Drude (Lorentz–Sommerfeld) model, widely used in Physics, the quantum many-body problem studied here predicts a much smaller AC-conductivity at large frequencies. This indicates (in accordance with experimental results) that the relaxation time of the Drude model, seen as an effective parameter for the conductivity, should be highly frequency-dependent. We conclude by proposing an alternative effective description — using Lévy processes in Fourier space — of the phenomenon of electrical conductivity.

Through simulations of quantum coherent transport on disordered molecular networks, we show that three dimensional structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations. Furthermore, configurations that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.