Superdiffusion Of Energy Research Articles

Energy super-diffusion in 1d deterministic nonlinear lattices with broken standard momentum

The property of total momentum conservation is a key issue in determining the energy diffusion behavior for 1d nonlinear lattices. The super-diffusion of energy has been found for 1d momentum conserving nonlinear lattices with the only exception of 1d coupled rotator model. However, for all the other 1d momentum non-conserving nonlinear lattices studied so far, the energy diffusion is normal. Here we investigate the energy diffusion in a 1d nonlinear lattice model with inverse couplings. For the standard definition of momentum, this 1d inverse coupling model does not preserve the total momentum while it exhibits energy super-diffusion behavior. In particular, with a parity transformation, this 1d inverse coupling model can be mapped into the well-known 1d FPU-β model although they have different phonon dispersion relations. In contrary to the 1d FPU-β model where the long-wave length phonons are responsible for the super-diffusion behavior, the short-wave length phonons contribute to the super-diffusion of energy in the 1d inverse coupling model.

Diffusion behaviors of energy and momentum for 1D single-walled carbon nanotubes

The single-walled carbon nanotube (CNT) is a quasi-1D material with ultra high thermal conductivity. It is known that the heat conduction is closely related with the energy diffusion and the information of heat conduction can be obtained by examining the energy diffusion behavior. The correlated energy distribution CE(i,t) calculated in diffusion process gives the whole spatial distribution of energy spreading at every correlation time which is much better than the traditional heat conduction method where only a number of thermal conductivity is provided. In previous study the anomalous super-diffusion of energy has been reported for CNT via a non-equilibrium diffusion method. Here we apply the more sophisticate equilibrium diffusion method to investigate the energy diffusion behavior in CNT with much longer length up to m with much higher accuracy. At room temperature, the super-diffusion of energy described by the mean square displacement of energy is found to be not far away from ballistic diffusion which is consistent with the experimentally measured ultra high thermal conductivity for CNT. With the equilibrium diffusion method, the diffusion of momentum has also been performed for CNT and ballistic diffusion is found which can be viewed as a support for anomalous super energy diffusion. The momentum diffusion can also give accurate information of sound velocity which is determined as m s−1 at room temperature. In particular, the very weak temperature coefficient of sound velocity can be obtained as m (. The normalized temperature coefficient of sound velocity can be related with the normalized temperature coefficient of Raman frequency shifts experimentally measured as . The obtained value via the momentum diffusion method is consistent with the experimental measurements.

Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence

In [2] it has been proved that a linear Hamiltonian lattice field perturbed by a conservative stochastic noise belongs to the 3/2-L\'evy/Diffusive universality class in the nonlinear fluctuating theory terminology [15], i.e. energy superdiffuses like an asymmetric stable 3/2-L\'evy process and volume like a Brownian motion. According to this theory this should remain valid at zero tension if the harmonic potential is replaced by an even potential. In this work we consider a quartic anharmonicity and show that the result obtained in the harmonic case persists up to some small critical value of the anharmonicity.

Confining interparticle potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems

We provide molecular dynamics simulation of heat transport and energy diffusion in one-dimensional molecular chains with different interparticle pair potentials at zero and non-zero temperature. We model the thermal conductivity (TC) and energy diffusion (ED) in the chain of coupled rotators and in the Lennard-Jones chain either without or with the confining parabolic interparticle potential. The considered chains without the confining potential have normal TC and ED at non-zero temperature, while the corresponding chains with the confining potential are characterized by anomalous (diverging with the system length) TC and superdiffusion of energy. Similar effect is produced by the anharmonic quartic confining pair potential. We confirm in such a way that, surprisingly, the confining pair potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems. We show that the normal TC is always accompanied by the normal ED in the thermalized anharmonic chains, while the superdiffusion of energy occurs in the thermalized chains with only anomalous heat transport.

Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise

We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation $${\partial_t u = -|\Delta|^{3/4}u}$$ . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126–1142, 2014).

From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit

We consider a harmonic chain perturbed by an energy conserving noise depending on a parameter $\gamma$. When $\gamma$ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $\gamma=0$, the energy superdiffuses according to a 3/4 fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $\gamma$.

Anomalous Fluctuations for a Perturbed Hamiltonian System with Exponential Interactions

A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained