低维系统反常热输运和能量超扩散的局限性和非普适性
Confinement and non-universality of anomalous heat transport and superdiffusion of energy in low-dimensional systems
摘要：
利用分子动力学模拟研究了零温和非零温下一维分子链中不同粒子间相互作用势下的热输运和热能扩散。我们模拟的热导率（TC）和能量扩散的耦合转子链和Lennard-Jones链中没有或限制抛物原子间的潜力。所考虑的链没有限制势有正常的TC和能量扩散，而相应的链与限制势的特点是异常（发散与系统长度）TC和超扩散的能量。我们确认在这样一种方式，令人惊讶的是，限制使热输运和能量扩散异常低维声子系统。我们表明，链，它有一个有限的TC，也具有正常的能量扩散的热化链（在非零温度），而超扩散的热能发生在热化链与只有异常TC。我们提出的论点，支持我们的模拟，指数之间的标度关系的时间依赖性的均方位移的热能分布和长度依赖性的异常TC是不普遍的，可以是不同的，这取决于能量传输的主要机制：由弱散射波或由非相互作用碰撞粒子执行Levy飞行。
英文摘要：
We provide molecular dynamics simulation of heat transport and thermal 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 in the coupled rotator chain and in the Lennard-Jones chain either without or with the confining parabolic interatomic potential. The considered chains without the confining potential have normal TC and energy diffusion, while the corresponding chains with the confining potential are characterized by anomalous (diverging with the system length) TC and superdiffusion of energy. We confirm in such a way that, surprisingly, the confinement makes both heat transport and energy diffusion anomalous in low-dimensional phononic systems. We show that the chain, which has a finite TC, is also characterized by the normal energy diffusion in the thermalized chain (at non-zero temperature), while the superdiffusion of thermal energy occurs in the thermalized chains with only anomalous TC. We present the arguments, supported by our simulations, that the scaling relation between the exponents in time dependence of the mean square displacement of thermal energy distribution and in length dependence of the anomalous TC is not universal and can be different, depending on the main mechanism of energy transport: by weakly-scattered waves or by noninteracting colliding particles performing Levy flights.
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