Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos

We study heat transport in a nonequilibrium steady state of a quantum interacting spin chain. We provide clear numerical evidence of the validity of Fourier law. The regime of normal conductivity is shown to set in at the transition to quantum chaos.Comment: 4 pages, 5 figures, RevTe

Reconstructing Fourier's law from disorder in quantum wires

The theory of open quantum systems is used to study the local temperature and heat currents in metallic nanowires connected to leads at different temperatures. We show that for ballistic wires the local temperature is almost uniform along the wire and Fourier's law is invalid. By gradually increasing disorder, a uniform temperature gradient ensues inside the wire and the thermal current linearly relates to this local temperature gradient, in agreement with Fourier's law. Finally, we demonstrate that while disorder is responsible for the onset of Fourier's law, the non-equilibrium energy distribution function is determined solely by the heat baths

Thermal rectification in carbon nanotube intramolecular junctions: Molecular dynamics calculations

We study heat conduction in (n, 0)/(2n, 0) intramolecular junctions by using molecular dynamics method. It is found that the heat conduction is asymmetric, namely, heat transports preferably in one direction. This phenomenon is also called thermal rectification. The rectification is weakly dependent on the detailed structure of connection part, but is strongly dependent on the temperature gradient. We also study the effect of the tube radius and intramolecular junction length on the rectification. Our study shows that the tensile stress can increase rectification. The physical mechanism of the rectification is explained

Third Order Renormalization Group applied to the attractive one-dimensional Fermi Gas

We consider a Callan-Symanzik and a Wilson Renormalization Group approach to the infrared problem for interacting fermions in one dimension with backscattering. We compute the third order (two-loop) approximation of the beta function using both methods and compare it with the well known multiplicative Gell-Mann Low approach. We point out a previously unnoticed qualitative dependence of the third order fixed point on an arbitrary dimensionless parameter, which strongly suggest the spurious nature of the fixed point.Comment: 16 pages, Revised version, added comment

Normal heat conduction in one dimensional momentum conserving lattices with asymmetric interactions

The heat conduction behavior of one dimensional momentum conserving lattice systems with asymmetric interparticle interactions is numerically investigated. It is found that with certain degree of interaction asymmetry, the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit, in clear contrast to the well accepted viewpoint that Fourier's law is generally violated in low dimensional momentum conserving systems. It suggests in nonequilibrium stationary states the mass gradient resulted from the asymmetric interactions may provide an additional phonon scattering mechanism other than that due to the nonlinear interactions.Comment: 4 pages, 4 figure

Thermal conductivity of the Toda lattice with conservative noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$

Heat conduction induced by non-Gaussian athermal fluctuations

We study the properties of heat conduction induced by non-Gaussian noises from athermal environments. We find that new terms should be added to the conventional Fourier law and the fluctuation theorem for the heat current, where its average and fluctuation are determined not only by the noise intensities but also by the non-Gaussian nature of the noises. Our results explicitly show the absence of the zeroth law of thermodynamics in athermal systems.Comment: 15 pages, 4 figures, PRE in pres

Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size $\sqrt{N}$ (where $N$ is the chain length), that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page