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Advances in Condensed Matter Physics
Volume 2015 (2015), Article ID 615727, 7 pages
Research Article

Nonequilibrium Quantum Systems: Divergence between Global and Local Descriptions

1Physics Department, University of Miami, Coral Gables, FL 33126, USA
2Departamento de Física, Universidad de Los Andes, A.A. 4976, Bogotá, Colombia

Received 29 October 2014; Revised 26 January 2015; Accepted 27 January 2015

Academic Editor: Yuri Galperin

Copyright © 2015 Pedro D. Manrique et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Even photosynthesis—the most basic natural phenomenon underlying life on Earth—involves the nontrivial 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 nonequilibrium 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). The main difference lies in finding suitable operators to derive the Lindbladian and hence the master equation. 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.