Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.08763 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914463073959936 |
|---|---|
| author | He, Andrew Qing Cai, Wei Shao, Sihong |
| author_facet | He, Andrew Qing Cai, Wei Shao, Sihong |
| contents | We extend the Weak Adversarial Neural Pushforward Method to the Wigner transport equation governing the phase-space dynamics of quantum systems. The central contribution is a structural observation: integrating the nonlocal pseudo-differential potential operator against plane-wave test functions produces a Dirac delta that exactly inverts the Fourier transform defining the Wigner potential kernel, reducing the operator to a pointwise finite difference of the potential at two shifted arguments. This holds in arbitrary dimension, requires no truncation of the Moyal series, and treats the potential as a black-box function oracle with no derivative information. To handle the negativity of the Wigner quasi-probability distribution, we introduce a signed pushforward architecture that decomposes the solution into two non-negative phase-space distributions mixed with a learnable weight. The resulting method inherits the mesh-free, Jacobian-free, and scalable properties of the original framework while extending it to the quantum setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08763 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation He, Andrew Qing Cai, Wei Shao, Sihong Quantum Physics Machine Learning Numerical Analysis 65N75, 68T07, 81Q05, 81S30 We extend the Weak Adversarial Neural Pushforward Method to the Wigner transport equation governing the phase-space dynamics of quantum systems. The central contribution is a structural observation: integrating the nonlocal pseudo-differential potential operator against plane-wave test functions produces a Dirac delta that exactly inverts the Fourier transform defining the Wigner potential kernel, reducing the operator to a pointwise finite difference of the potential at two shifted arguments. This holds in arbitrary dimension, requires no truncation of the Moyal series, and treats the potential as a black-box function oracle with no derivative information. To handle the negativity of the Wigner quasi-probability distribution, we introduce a signed pushforward architecture that decomposes the solution into two non-negative phase-space distributions mixed with a learnable weight. The resulting method inherits the mesh-free, Jacobian-free, and scalable properties of the original framework while extending it to the quantum setting. |
| title | Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation |
| topic | Quantum Physics Machine Learning Numerical Analysis 65N75, 68T07, 81Q05, 81S30 |
| url | https://arxiv.org/abs/2604.08763 |