Quantum Inspiration, Classical Advantage: Dequantized particle algorithm for the nonlinear Vlasov-Poisson system

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.