Non-equilibrium quantum systems: Divergence between global and local descriptions

TL;DR

This paper compares local and global descriptions of non-equilibrium quantum systems, revealing significant differences under open conditions with temperature gradients, which impacts modeling of nanoscale phenomena like photosynthesis.

Contribution

It demonstrates the failure of local and global approaches to be equivalent in open quantum systems with temperature gradients, emphasizing the need for careful method selection.

Findings

Global and local descriptions diverge under non-equilibrium conditions.

Significant differences in steady-state populations and heat flux calculations.

Highlights the importance of method applicability in nanoscale quantum modeling.

Abstract

Even photosynthesis -- the most basic natural phenomenon underlying Life on Earth -- involves the non-trivial processing of excitations at the pico- and femtosecond scales during light-harvesting. The desire to understand such natural phenomena, as well as interpret the output from ultrafast experimental probes, creates an urgent need for accurate quantitative theories of open quantum systems. However it is unclear how best to generalize the well-established assumptions of an isolated system, particularly under non-equilibrium conditions. Here we compare two popular approaches: a description in terms of a direct product of the states of each individual system (i.e. a local approach) versus the use of new states resulting from diagonalizing the whole Hamiltonian (i.e. a global approach). We show that their equivalence fails when the system is open, in particular under the experimentally ubiquitous condition of a temperature gradient. By solving for the steady-state populations and calculating the heat flux as a test observable, we uncover stark differences between the formulations. This divergence highlights the need to establish rigorous ranges of applicability for such methods in modeling nanoscale transfer phenomena -- including during the light-harvesting process in photosynthesis.