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Solving the Lindblad equation with methods from computational fluid dynamics.

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Summary
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This study introduces a novel numerical method for solving the Lindblad equation in open quantum systems. The Kurganov-Tadmor scheme offers efficient and stable solutions for complex quantum dynamics.

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Area of Science:

  • Quantum Physics
  • Computational Physics

Background:

  • Liouvillian dynamics governs closed quantum systems.
  • The Lindblad equation extends this to open quantum systems, crucial in solid-state and nuclear physics.
  • Analytical solutions for the Lindblad equation are limited to simple systems.

Purpose of the Study:

  • To propose and evaluate a new numerical method for solving the Lindblad equation.
  • To demonstrate the efficiency and stability of the Kurganov-Tadmor scheme for quantum system dynamics.
  • To explore new insights into Lindblad dynamics via an advection-diffusion equation analogy.

Main Methods:

  • Application of the Kurganov-Tadmor central (finite-volume) scheme from computational fluid dynamics.
  • Numerical solution of the Lindblad equation in position-space representation.
  • Benchmark tests comparing numerical results with analytical solutions.

Main Results:

  • The Kurganov-Tadmor scheme shows advantages in efficiency regarding initial conditions, discretization, and stability.
  • Benchmark tests confirm the applicability and accuracy of the scheme.
  • Reformulation of the Lindblad equation as an advection-diffusion equation provides new qualitative insights.

Conclusions:

  • The Kurganov-Tadmor scheme is an efficient and stable numerical method for solving the Lindblad equation.
  • This approach expands the applicability of quantum dynamics simulations to more complex systems.
  • The advection-diffusion analogy offers a new perspective on open quantum system evolution.