Kumar Manoj, Kundu Anupam, Kulkarni Manas, Huse David A, Dhar Abhishek
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.
Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom.
Phys Rev E. 2020 Aug;102(2-1):022130. doi: 10.1103/PhysRevE.102.022130.
We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Δ, and temperature T. The conductivity κ_{N}, obtained for finite length (N), saturates to a value κ_{∞}>0 in the large N limit, for all values of disorder strength Δ and temperature T>0. We show evidence that for any Δ>0 the conductivity goes to zero faster than any power of T in the (T/Δ)→0 limit, and find that the form κ_{∞}∼e^{-B|ln(CΔ/T)|^{3}} fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be κ_{N}<κ_{∞} due to boundary resistance when the bulk conductivity is high (the weak disorder case), or κ_{N}>κ_{∞} due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.
我们研究了经典简谐振子无序非线性链中的输运性质，从而确定了一个表现出与量子多体局域化系统类似行为的区域。通过对该系统两端连接到不同温度热浴的广泛数值模拟，我们计算了非平衡稳态下的热流和温度分布，作为系统大小(N)、无序强度(\Delta)和温度(T)的函数。对于有限长度（(N)）得到的电导率(\kappa_N)，在大(N)极限下对于所有无序强度(\Delta)和温度(T>0)都饱和到一个值(\kappa_{\infty}>0)。我们证明，对于任何(\Delta>0)，在((T/\Delta)\to0)极限下，电导率比(T)的任何幂次都更快地趋于零，并发现形式(\kappa_{\infty}\sim e^{-B|\ln(C\Delta/T)|^{3}})符合我们的数据。这种形式此前已由基于多振子混沌岛动力学的理论提出。当体电导率高时（弱无序情况），由于边界电阻，有限尺寸效应可能导致(\kappa_N<\kappa_{\infty})；而当体导电弱时（强无序情况），由于通过体局域模的直接浴间耦合，可能导致(\kappa_N>\kappa_{\infty})。我们还给出了关于平衡动态关联函数以及混沌对输运性质作用的结果。最后，我们通过研究经典版本的时间无序对易子，探索了弱混沌和强混沌区域中混沌增长和传播的差异。
