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Reduced density matrix for nonequilibrium steady states: a modified Redfield solution approach.

Juzar Thingna1, Jian-Sheng Wang2, Peter Hänggi1

  • 1Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117551, Republic of Singapore and Institut für Physik Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Researchers developed a new method for calculating the reduced density matrix (RDM) in nonequilibrium steady states. This approach accurately describes quantum systems interacting with their environment, crucial for understanding complex quantum phenomena.

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Area of Science:

  • Quantum Chemistry and Physics
  • Theoretical Chemistry
  • Condensed Matter Physics

Background:

  • Accurate description of quantum systems interacting with an environment is essential.
  • Nonequilibrium steady states present unique challenges for theoretical modeling.
  • Reduced density matrix (RDM) is a key quantity for characterizing system properties.

Purpose of the Study:

  • To develop a method for calculating the RDM up to second order in system-bath coupling.
  • To apply this method to nonequilibrium steady-state situations.
  • To validate the method against exact solutions and compare it with other quantum master equations.

Main Methods:

  • Utilized an analytic continuation scheme with a time-local Redfield-like quantum master equation.
  • Employed the nonequilibrium Green's function technique for exact RDM calculation of a quantum harmonic oscillator.
  • Compared the developed method with time-local Redfield-like and Lindblad-like quantum master equations.

Main Results:

  • Successfully obtained the reduced density matrix (RDM) accurate to second order in system-bath coupling for nonequilibrium steady states.
  • Validated the modified Redfield solution against exact RDM for a quantum harmonic oscillator.
  • Highlighted differences between the proposed scheme and other quantum master equations (QMEs).

Conclusions:

  • The analytic continuation scheme provides an accurate method for calculating RDMs in nonequilibrium steady states.
  • This approach offers a reliable tool for studying open quantum systems under non-equilibrium conditions.
  • The study elucidates the distinctions between various quantum master equation formalisms.