# Remark on the Adiabatic Limit of Quantum Zakharov System

## TL;DR

This paper investigates the low regularity well-posedness of the quantum Zakharov system's adiabatic limit, proving rigorously that the modified nonlinear Schrödinger equation converges to the standard NLSE as the quantum parameter approaches zero.

## Contribution

It provides a rigorous proof of the convergence of the quantum Zakharov system to the standard NLSE in the adiabatic limit, addressing low regularity solutions.

## Key findings

- Rigorous proof of convergence as quantum parameter tends to zero
- Establishment of well-posedness at low regularity
- Connection between quantum and classical nonlinear Schrödinger equations

## Abstract

This paper is concerned with the low regularity well-posedness of the adiabatic limit of the quantum Zakharov system, which is a modified nonlinear Schr\"odinger equation (NLSE). As the quantum parameter tends to zero, the modified NLSE formally converges to the standard NLSE, and we show this rigorously.