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

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.

7 pages, 3 figures

References in corpus (4)

• Efficiency of energy transfer in a light-harvesting system under quantum coherence
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Markovian Master Equations: A Critical Study
• Non-Markovian generalization of the Lindblad theory of open quantum systems

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• Quantum Optical Two-Atom Thermal Diode
• Two coupled qubits interacting with a thermal bath: A comparative study of different models
• Local master equations bypass the secular approximation
• Nonequilibrium quantum absorption refrigerator
• The smallest absorption refrigerator: the thermodynamics of a system with quantum local detailed balance
• Local master equations may fail to describe dissipative critical behavior
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions