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PreprintarXiv licencearXiv

Dynamical Tensor Train Approximation for Wigner--Fokker--Planck Equation with Applications to Open Quantum Systems

  • Geshuo Wang
  • Jingwei Hu
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Abstract

We develop a dynamical tensor-train method for the Wigner--Fokker--Planck equation arising in continuous-variable open quantum systems. The Wigner function is evolved directly in tensor-train form using a projector-splitting integrator, while the nonlocal Wigner pseudo-differential operator is treated through low-rank representations of the potential difference and matrix-free exponential actions. The resulting method avoids full tensor-product computations in high-dimensional phase space. Numerical experiments in one, two, and three spatial dimensions demonstrate the accuracy and scalability of the method, including simulations in a six-dimensional phase space.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026dynamical,
  title = {{Dynamical Tensor Train Approximation for Wigner--Fokker--Planck Equation with Applications to Open Quantum Systems}},
  author = {Geshuo Wang and Jingwei Hu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36257},
  eprint = {2610.36257},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36257},
}
RIS
TY  - UNPB
TI  - Dynamical Tensor Train Approximation for Wigner--Fokker--Planck Equation with Applications to Open Quantum Systems
AU  - Geshuo Wang
AU  - Jingwei Hu
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36257
UR  - https://arxiv.org/abs/2610.36257
AB  - We develop a dynamical tensor-train method for the Wigner--Fokker--Planck equation arising in continuous-variable open quantum systems. The Wigner function is evolved directly in tensor-train form using a projector-splitting integrator, while the nonlocal Wigner pseudo-differential operator is treated through low-rank representations of the potential difference and matrix-free exponential actions. The resulting method avoids full tensor-product computations in high-dimensional phase space. Numerical experiments in one, two, and three spatial dimensions demonstrate the accuracy and scalability of the method, including simulations in a six-dimensional phase space.
ER  -