Single-parameter scaling and maximum entropy inside disordered one-dimensional systems: Theory and experiment

Article

关键词: WAVE-GUIDES;    LOCALIZATION;    TRANSMISSION;    TRANSPORT;    PROPAGATION;    DIFFUSION;    MEDIA;   

DOI  :  10.1103/PhysRevB.96.180203

来源: SCIE

【 摘 要 】

The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the particle, or energy density ln W(x) at a depth x into a random one-dimensional system. Single-parameter scaling would be the special case in which x = L (the system length). We find the result, confirmed in microwave measurements and computer simulations, that the average of ln W(x) is independent of L and equal to - x/l, with l the mean free path. At the beginning of the sample, var[lnW(x)] rises linearly with x and is also independent of L, with a sublinear increase and then a drop near the sample output. At x = L we find a correction to the value of var[ln T] predicted by single-parameter scaling.

【 授权许可】

Free