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Exponential integrators for stochastic Schrödinger equations.

Jingze Li1, Xiantao Li2

  • 1Beijing Normal University, Beijing 100875, People's Republic of China.

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|February 20, 2020
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Summary
This summary is machine-generated.

We developed new exponential integrators for stochastic Schrödinger equations in open quantum systems. These methods offer efficient and accurate computation of quantum system dynamics using Krylov subspace projection.

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Area of Science:

  • Quantum Mechanics
  • Computational Physics
  • Numerical Analysis

Background:

  • Modeling open quantum systems requires solving stochastic Schrödinger equations.
  • Existing methods may lack efficiency or accuracy for complex quantum dynamics.
  • Kunita's representation offers a framework for expressing quantum system solutions.

Purpose of the Study:

  • To present a novel class of exponential integrators for stochastic Schrödinger equations.
  • To enable efficient and accurate computation of quantum dynamics in open systems.
  • To integrate stochastic methods within the same framework as deterministic counterparts.

Main Methods:

  • Utilized Kunita's representation to express the solution operator.
  • Applied truncations to represent the solution operator as matrix exponentials.
  • Employed Krylov subspace projection for efficient implementation of matrix exponentials.
  • Introduced third-order commutators to enhance local accuracy.

Main Results:

  • Demonstrated strong convergence by comparing computed trajectories.
  • Verified weak convergence by comparing density-matrix operators.
  • Showcased improved local accuracy through the inclusion of third-order commutators.
  • Validated the effectiveness of the methods using a known example from literature.

Conclusions:

  • The proposed exponential integrators provide an efficient and accurate approach for solving stochastic Schrödinger equations.
  • The Krylov subspace projection method facilitates practical implementation.
  • The developed techniques are suitable for modeling complex open quantum systems.