Dequantized particle algorithm for the nonlinear Vlasov-Poisson system

• URL: http://arxiv.org/abs/2507.05151v1
• Date: Mon, 07 Jul 2025 16:01:37 GMT
• Title: Dequantized particle algorithm for the nonlinear Vlasov-Poisson system
• Authors: Hong Qin, Michael Q. May, Jacob Molina,
• Abstract summary: We present a dequantization algorithm for the Vlasov--Poisson (VP) system.<n>We show that it furnishes a structure-preserving discretization of the Schr"odinger--Poisson (SP) equations.
• Score: 16.726991700162817
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We present a dequantization algorithm for the Vlasov--Poisson (VP) system, termed the dequantized particle algorithm, by systematically dequantizing the underlying many-body quantum theory. Starting from the second-quantized Hamiltonian description, we derive a finite-dimensional dequantized system and show that it furnishes a structure-preserving discretization of the Schr\"odinger--Poisson (SP) equations. Through the Wigner or Husimi transformations, this discretization provides an efficient approximation of the VP system when quantum effects are negligible. Unlike conventional structure-preserving algorithms formulated in 6D phase space, this dequantized particle algorithm operates in 3D configuration space, potentially offering more compact and efficient representations of physical information under appropriate conditions. A numerical example of the classical nonlinear two-stream instability, simulated using merely 97 dequantized particles, demonstrates the efficiency, accuracy, and conservation properties of the algorithm and confirms its potential as a foundation for developing quantum and quantum-inspired classical algorithms for kinetic plasma dynamics.

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