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Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS).

Richard Hartmann1, Walter T Strunz1

  • 1Institut für Theoretische Physik, Technische Universität Dresden , D-01062 Dresden, Germany.

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The Hierarchy of Pure States (HOPS) method accurately calculates open quantum system dynamics, even in strong coupling regimes with sub-Ohmic environments. This method offers a unified approach across various conditions.

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Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Open quantum systems require accurate methods to describe their dynamics.
  • Sub-Ohmic spectral densities present unique challenges due to algebraic decay in bath correlation functions.

Purpose of the Study:

  • To demonstrate the applicability of the Hierarchy of Pure States (HOPS) method for open quantum systems.
  • To investigate the performance of HOPS for environments with sub-Ohmic spectral densities.

Main Methods:

  • Utilized the general and numerically exact Hierarchy of Pure States (HOPS) method.
  • Applied HOPS to the spin-boson model across weak to strong coupling regimes.
  • Incorporated importance sampling via nonlinear HOPS for strong coupling challenges.
  • Developed a strategy for nonzero-temperature effects using zero-temperature bath correlation functions and stochastic Hamiltonians.

Main Results:

  • HOPS accurately calculates reduced dynamics for open quantum systems.
  • Perfect agreement was found between HOPS and other established methods for the spin-boson model.
  • The nonlinear HOPS variant effectively addresses strong coupling challenges.
  • A favorable approach for including nonzero-temperature effects in strong coupling was identified.

Conclusions:

  • The Hierarchy of Pure States (HOPS) method is a versatile and accurate tool for studying open quantum system dynamics.
  • HOPS provides a unified framework applicable from weak to strong coupling and across temperatures.
  • The developed methods offer robust solutions for complex quantum system simulations.