Abstract There are two standard ways of classifying transport behavior of systems. The first is via time scaling of spread of correlations in the isolated system in thermodynamic limit. The second is via system size scaling of conductance in the steady state of the open system. We show here that these correspond to taking the thermodynamic limit and the long time limit of the integrated equilibrium current–current correlations of the open system in different order. In general, the limits may not commute leading to a conflict between the two standard ways of transport classification. Nevertheless, the full information is contained in the equilibrium current–current correlations of the open system. We show this analytically by rigorously deriving the open-system current fluctuation dissipation relations starting from an extremely general open quantum set-up and then carefully taking the proper limits. We test our theory numerically on the non-trivial example of the critical Aubry–André–Harper model, where, it has been recently shown that, the two standard classifications indeed give different results. We find that both the total current autocorrelation and the long-range local current correlations of the open system in equilibrium show signatures of diffusive transport up to a time scale. This time scale grows as square of system size. Beyond this time scale a steady state value is reached. The steady state value is conductance, which shows sub-diffusive scaling with system size.
Developing mechanisms to control transport in correlated quantum systems is essential for advancing quantum circuit technologies. In this work, we establish a rectification mechanism for both particle and energy flow in a fermionic system coupled to external baths, in the presence of a tilted potential modulated locally by a time-periodic drive. The drive generates particle and energy currents even in the absence of chemical or thermal bias between the baths. These drive-induced currents are enhanced at resonant frequencies at which avoided crossings occur in the Floquet quasienergy spectrum, reflecting the role of the Floquet states as intermediate channels for transport. Once a bias between the baths is introduced, the drive-induced current contribution can reinforce, compete with, or even cancel the bias-induced contribution. These effects enable rectification in the non-interacting regime, which we quantify via the rectification coefficient
R. This coefficient measures the asymmetry between transport up the tilt (forward bias) and down the tilt (reverse bias). In addition to standard rectification, where transport is reduced under reverse bias, we identify a regime of bipolar rectification, in which the current flows only up the tilt regardless of the bias polarity. At the boundary between standard and bipolar regimes, the system achieves perfect rectification, corresponding to complete suppression of the reverse-bias current. In the presence of interactions between particles, the parameter region that supports bipolar rectification is enlarged and
R can be enhanced by many orders of magnitude. Our results establish a rectification mechanism for particle and energy transport that can be experimentally realized in condensed matter and cold atom systems.