# Quantum mean field asymptotics and multiscale analysis

## TL;DR

This paper investigates defect of compactness phenomena in quantum mean-field problems using multiscale analysis, combining mean-field asymptotics with second microlocalized semiclassical measures, and illustrates the phase space geometry with examples.

## Contribution

It introduces a novel multiscale analysis approach combining mean-field asymptotics and second microlocalized measures for quantum problems.

## Key findings

- Identifies defect of compactness phenomena in quantum mean-field models
- Develops a phase space geometric description of these phenomena
- Provides illustrative examples demonstrating the approach

## Abstract

We study, via multiscale analysis, some defect of compactness phenomena which occur in bosonic and fermionic quantum mean-field problems. The approach relies on a combination of mean-field asymptotics and second microlocalized semiclassical measures. The phase space geometric description is illustrated by various examples.