Thermal Rectification in Graded Materials

In order to identify the basic conditions for thermal rectification we investigate a simple model with non-uniform, graded mass distribution. The existence of thermal rectification is theoretically predicted and numerically confirmed, suggesting that thermal rectification is a typical occurrence in graded systems, which are likely to be natural candidates for the actual fabrication of thermal diodes. In view of practical implications, the dependence of rectification on the asymmetry and system's size is studied.Comment: 5 pages, 4 figure

Non-integrability and the Fourier heat conduction law

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics

One-Dimensional Self-organization and Nonequilibrium Phase Transition in a Hamiltonian System

平衡态相变依赖于系统的维数。自上世纪五十年代起，人们就已认识到一般情况下一维系统中不会发生平衡态相变。另一方面，非平衡态相变也广泛存在于二、三维耗散系统，从未在一维非耗散系统中被发现过。最近，厦门大学物理系王矫教授与意大利因苏布里亚大学Giulio Casati教授合作，在一个一维哈密顿系统中发现了自组织及非平衡态相变。该工作不仅表明一维非耗散、具有确定性动力学的系统能够发生非平衡态相变和自组织，也指出有必要将传统的基于线性响应理论对一维输运问题的研究推广到超出线性响应理论的范围，为一维输运问题研究打开了一个新的探索方向，有望发现全新的物质与能量输运机制。【Abstract】Self-organization and nonequilibrium phase transitions are well known to occur in two- and three- dimensional dissipative systems. Here, instead, we provide numerical evidence that these phenomena also occur in a one-dimensional Hamiltonian system. To this end, we calculate the heat conductivity by coupling the two ends of our system to two heat baths at different temperatures. It is found that when the temperature difference is smaller than a critical value, the heat conductivity increases with the system size in power law with an exponent considerably smaller than 1. However, as the temperature difference exceeds the critical value, the system' s behavior undergoes a transition and the heat conductivity tends to diverge linearly with the system size. Correspondingly, an ordered structure emerges. These findings suggest a new direction for exploring the transport problems in one dimension.support by NSFC (Grants No. 11535011, No. 11335006, and No. 11275159), by MIUR-PRIN, and by the CINECA project Nanostructures for Heat Management and Thermoelectric Energy Conversion

Anomalous heat conduction and anomalous diffusion in one-dimensional systems

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is =2Dt(alpha)(01) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results

Long-lasting Exponential Spreading in Periodically Driven Quantum Systems

Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudo-classical map, both qualitatively and quantitatively. Possible applications of our findings are also briefly discussed.Comment: 4 figures, 6 pages (including supplementary material), published in the 2nd of December, 2011 issue of PR

Anderson transition in a three-dimensional kicked rotor

We investigate Anderson localization in a three-dimensional (3D) kicked rotor. By a finite-size scaling analysis we identify a mobility edge for a certain value of the kicking strength k=k(c). For k>k(c) dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3D Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region k approximate to k(c) we carry out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations, the number variance is linear, level repulsion is still observed, and quantum diffusion is anomalous with proportional to t(2/3). We note that in the 3D kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3D kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion. However we have found that certain choices of irrational periods enhance Anderson localization effects

Energy transfer process in gas models of Lennard-Jones interactions

We perform simulations to investigate how the energy carried by a molecule transfers to others in an equilibrium gas model. For this purpose we consider a microcanonical ensemble of equilibrium gas systems, each of them contains a tagged molecule located at the same position initially. The ensuing transfer process of the energy initially carried by the tagged molecule is then exposed in terms of the ensemble-averaged energy density distribution. In both a 2D and a 3D gas model with Lennard-Jones interactions at room temperature, it is found that the energy carried by a molecule propagates in the gas ballistically, in clear contrast with the Gaussian diffusion widely assumed in previous studies. A possible scheme of experimental study of this issue is also proposedComment: 5 pages,3 figur

Semi-Poisson statistics in quantum chaos

We investigate the quantum properties of a nonrandom Hamiltonian with a steplike singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by semi-Poisson statistics (SP) typical of pseudointegrable systems. It is also shown that our results are universal, namely, they depend exclusively on the presence of the steplike singularity and are not modified by smooth perturbations of the potential or the addition of a magnetic flux. Although the quantum properties of our system are similar to those of a disordered conductor at the Anderson transition, we report important quantitative differences in both the level statistics and the multifractal dimensions controlling the transition. Finally, the study of quantum transport properties suggests that the classical singularity induces quantum anomalous diffusion. We discuss how these findings may be experimentally corroborated by using ultracold atoms techniques

Fractional ℏ\hbar-scaling for quantum kicked rotors without cantori

Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length $L$) characterized by fractional $\hbar$-scaling, ie $L \sim \hbar^{2/3}$ in regimes and phase-space regions close to `golden-ratio' cantori. In contrast, in typical chaotic regimes, the scaling is integer, $L \sim \hbar^{-1}$. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle (RP-KP), obtained by randomizing the phases every second kick; it has no KAM mixed phase-space structures, like golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but $L \sim \hbar^{-2/3}$. A semiclassical analysis indicates that the $\hbar^{2/3}$ scaling here is of quantum origin and is not a signature of classical cantori.Comment: 5 pages, 4 figures, Revtex, typos removed, further analysis added, authors adjuste