# The Hartree equation for infinitely many particles, II: Dispersion and scattering in 2D

@article{Lewin2014TheHE, title={The Hartree equation for infinitely many particles, II: Dispersion and scattering in 2D}, author={M. Lewin and J. Sabin}, journal={Analysis & PDE}, year={2014}, volume={7}, pages={1339-1363} }

We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form $f(-\Delta)$, describing an homogeneous Fermi gas. Under suitable assumptions on the interaction potential and on the momentum distribution $f$, we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of $f(-\Delta)$ in a… CONTINUE READING

30 Citations

Stability of Steady States for Hartree and Schrodinger Equations for Infinitely Many Particles

- Mathematics, Physics
- 2020

On the scattering problem for infinitely many fermions in dimensions $d\geq3$ at positive temperature

- Mathematics, Physics
- 2016

10

On Orbital Stability of Ground States for Finite Crystals in Fermionic Schrödinger-Poisson Model

- Computer Science, Mathematics
- 2018

1

Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit

- Physics, Mathematics
- 2017

4

On orbital stability of ground states for finite crystals in fermionic Schr\"odinger--Poisson model

- Mathematics, Physics
- 2017

The nonlinear Schr\"odinger equation for orthonormal functions: I. Existence of ground states

- Mathematics, Physics
- 2020

3

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 24 REFERENCES

The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

- Mathematics, Physics
- 2015

39

Existence of a Stable Polarized Vacuum in the Bogoliubov-Dirac-Fock Approximation

- Physics, Mathematics
- 2005

77