Transport in nano-scale systems often display intriguing quantum mechanical effects, which will be illustrated using two examples in this talk:
Coherent quantum transport in disordered systems displays an optimal diffusion constant at an intermediate level of noise/temperature.  Detailed calculations indicate the crucial role of Anderson localization and predict scaling laws that can be verified experimentally. Further, we demonstrate 1D-2D transition in the diffusion along nanotubes and ballistic dynamics in dipolar lattices.  In addition, a new technique based on dynamical maps will be introduced to predict the dynamics of these large-scale open systems. 
Symmetry in molecular systems such as benzene rings, LH2 complexes or generic three-level systems can result in multiple steady state solutions in non-equilibrium measurements. However, disorder in open systems will break the symmetry and thus the degeneracy of multiple solutions, leading to a unique current. To reveal the symmetry hidden under disorder, we have analyzed the slow relaxation of dynamical currents and uncovered unique signatures of multiple steady states.  Understanding the role of symmetry sheds light on coherent effects in light-harvesting devices and in quantum heat engines.
(1) Moix, Khasin, Cao, “Coherent quantum transport in disordered systems I. The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems” NJP15, 085010 (2013)
(2) Quantum diffusion on molecular tubes: Universal scaling of the 1D to 2D transition. C. Chuang, C. K. Lee, J. M. Moix, J. Knoester, and J. Cao, arXiv:1511.0119
(3) Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories. J. Cerrillo and J. Cao, Phys. Rev. Lett., 112, 110401 (2014)
(4) Thinga, Manzano, and Cao http://arxiv.org/abs/1507.05705