[BOOK][B] Schrödinger operators: eigenvalues and Lieb–Thirring inequalities
RL Frank, A Laptev, T Weidl - 2022 - books.google.com
The analysis of eigenvalues of Laplace and Schrödinger operators is an important and
classical topic in mathematical physics with many applications. This book presents a …
classical topic in mathematical physics with many applications. This book presents a …
Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
RL Frank, J Sabin - American Journal of Mathematics, 2017 - muse.jhu.edu
We generalize the theorems of Stein-Tomas and Strichartz about surface restrictions of
Fourier transforms to systems of orthonormal functions with an optimal dependence on the …
Fourier transforms to systems of orthonormal functions with an optimal dependence on the …
[PDF][PDF] The Lieb-Thirring inequalities: recent results and open problems
RL Frank - arxiv preprint arxiv:2007.09326, 2020 - arxiv.org
arxiv:2007.09326v1 [math-ph] 18 Jul 2020 Page 1 arxiv:2007.09326v1 [math-ph] 18 Jul 2020
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …
The Hartree equation for infinitely many particles I. Well-posedness theory
M Lewin, J Sabin - Communications in Mathematical Physics, 2015 - Springer
We show local and global well-posedness results for the Hartree equation i\partial_t γ=-Δ+
w*\rho_ γ, γ, i∂ t γ=-Δ+ w∗ ρ γ, γ, where γ is a bounded self-adjoint operator on L^ 2 (R^ d) …
w*\rho_ γ, γ, i∂ t γ=-Δ+ w∗ ρ γ, γ, where γ is a bounded self-adjoint operator on L^ 2 (R^ d) …
Universal functionals in density functional theory
In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and
interaction energy that can be reached with all possible quantum states having a given …
interaction energy that can be reached with all possible quantum states having a given …
The Hartree equation for infinitely many particles, II: Dispersion and scattering in 2D
M Lewin, J Sabin - Analysis & PDE, 2014 - msp.org
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 (− Δ) …
particles and we investigate the large-time stability of the stationary states of the form f (− Δ) …
[HTML][HTML] On the Strichartz estimates for orthonormal systems of initial data with regularity
The classical Strichartz estimates for the free Schrödinger propagator have recently been
substantially generalised to estimates of the form‖∑ j λ j| eit Δ fj| 2‖ L pt L xq≲‖ λ‖ ℓ α for …
substantially generalised to estimates of the form‖∑ j λ j| eit Δ fj| 2‖ L pt L xq≲‖ λ‖ ℓ α for …
Asymptotic stability of a wide class of stationary solutions for the Hartree and Schr\"{o} dinger equations for infinitely many particles
S Hadama - arxiv preprint arxiv:2308.15929, 2023 - arxiv.org
We consider the Hartree and Schr\"{o} dinger equations describing the time evolution of
wave functions of infinitely many interacting fermions in three-dimensional space. These …
wave functions of infinitely many interacting fermions in three-dimensional space. These …
Global well-posedness of the NLS system for infinitely many fermions
T Chen, Y Hong, N Pavlović - Archive for rational mechanics and analysis, 2017 - Springer
In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely
many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi …
many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi …
Plasmons for the Hartree equations with Coulomb interaction
TT Nguyen, C You - arxiv preprint arxiv:2306.03800, 2023 - arxiv.org
In this work, we establish the existence and decay of {\em plasmons}, the quantum of
Langmuir's oscillatory waves found in plasma physics, for the linearized Hartree equations …
Langmuir's oscillatory waves found in plasma physics, for the linearized Hartree equations …