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  • Open Access

User-Friendly Truncated Wigner Approximation for Dissipative Spin Dynamics

Hossein Hosseinabadi1,*, Oksana Chelpanova1,*, and Jamir Marino1,2,†

  • *These authors contributed equally to this work.
  • †Contact author: jamirmar@buffalo.edu
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PRX Quantum 6, 030344 – Published 8 September, 2025

DOI: https://doi.org/10.1103/1wwv-k7hg

Abstract

We put forward a user-friendly framework of the truncated Wigner approximation (TWA) for dissipative quantum many-body systems. Our approach is computationally affordable and it features a straightforward implementation. The leverage of the method can be ultimately traced to an intimate connection between the TWA and the semiclassical limit of the quantum Langevin equation, which we unveil by resorting to a path-integral representation of the Lindbladian. Our approach allows us to explore dynamics from early to late times in a variety of models at the core of modern atomic, molecular, and optical research, including lasing, central-spin models, driven arrays of Rydbergs, and correlated emission in free space. Notably, our TWA approach outperforms the cumulant-expansion method in certain models and performs comparably well in others, all while offering significantly lower computational costs and a much simpler formulation of the dynamical equations. We therefore argue that TWA could, in the near future, become a primary tool for a fast and efficient first exploration of driven-dissipative many-body dynamics on consumer-grade computers.

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Popular Summary

Understanding the behavior of quantum systems coupled to their environments, a regime known as open quantum systems, is one of the central challenges in modern physics. These systems are relevant to a wide range of experimental platforms in atomic, molecular, and optical physics, including quantum simulators, optical lattices, and trapped-ion arrays. However, the complexity of their dynamics grows rapidly with system size, making exact simulations intractable even for modestly sized systems. Approximation methods are therefore essential. The truncated Wigner approximation (TWA) is a powerful semiclassical method that has been widely applied to isolated systems. Extending it to dissipative spin systems, however, has remained difficult because of conceptual and technical obstacles. In this work, we present a general, robust, and user-friendly formulation of dissipative TWA that overcomes these challenges.

Our approach provides a practical tool for simulating the nonequilibrium dynamics of driven-dissipative quantum systems, with advantages in both speed and accuracy over standard methods such as mean-field or cumulant expansions. It requires minimal prior knowledge to implement, runs efficiently on standard hardware, and scales to system sizes well beyond the reach of exact methods. Importantly, it retains enough quantum character to faithfully describe key features of the dynamics, while remaining computationally tractable.

This framework lowers the barrier to exploration of complex quantum many-body phenomena and enables rapid development of physical intuition. As such, we expect it to become a go-to theoretical tool for both theorists and experimentalists working in the growing field of open quantum systems.

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PRX Quantum 6, 030344– Published 8 September, 2025
  • Received 8 April 2025
  • Revised 7 June 2025
  • Accepted 1 August 2025
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