Semi-classical Limit for the Quantum Zakharov System

Time splitting combined with exponential wave integrator Fourier pseudospectral method for quantum Zakharov system

“….4 converges to the classical ZS quadratically with respect to ε, and it is consistent with the convergence rates of the exact result in[18].…”

“…where u = N t . In recent years, the QZS (1) have been investigated extensively, for the wellposedness of QZS, we refer to [12,15,16,17,18,24,25,32,48] and references therein. The low-regularity global well-posedness of the adiabatic limit of the QZS and its semi-classical limit were studied in [12].…”

Global Well-posedness of the Adiabatic Limit of Quantum Zakharov System in 1D

“…Fang-Shih-Wang further contributed in obtaining low-regularity well-posedness results, which again formally recovered another classical result by Gibibre-Tsutsumi-Velo [16]. Finally Fang-Kuo-Shih-Wang generalised the result of [17] by obtaining a refined version of the semi-classical limit, with a convergence rate [14].…”

“…Proposition 5.1. For 1 ≤ d ≤ 9. there exists a pair (u, v) of smooth, strictly positive solution to (14) that minimises the action. There exists no non-trivial smooth solution when d ≥ 12.…”

“…Moreover the estimate blows up as ǫ → 0, and therefore this is an insufficient tool to study the semi-classical limit. For references on B-admissible Strichartz estimate, see [14,4].…”