31 citations · 60 across the 9 of their papers we have counts for
10 papers
Continuum Limit for One-Dimensional Moiré Relaxation
Hao Lan, Michael Hott, Jeff Calder +1
We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional a…
Mathematical foundations of phonons in incommensurate materials
Michael Hott, Alexander B. Watson, Mitchell Luskin
In some models, periodic configurations can be shown to be stable under, both, global or local perturbations. This is not the case for aperiodic media. The specific class…
Derivation of renormalized Hartree-Fock-Bogoliubov and quantum Boltzmann equations in an interacting Bose gas
Thomas Chen, Michael Hott
Our previous work [37] presented a rigorous derivation of quantum Boltzmann equations near a Bose-Einstein condensate (BEC). Here, we extend it with a complete characterization of…
From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit
Michael Hott, Alexander B. Watson, Mitchell Luskin
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body…
Upper bounds on homogeneous fractional Gagliardo-Nirenberg-Sobolev constants via parabolic estimates
Michael Hott
Common proofs of the Gagliardo-Nirenberg-Sobolev (GNS) do not provide explicit bounds on the involved constants, unless a sharp constant is being determined. GNS inequalities natur…
On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
Thomas Chen, Michael Hott
In this work, we study the quantum fluctuation dynamics in a Bose gas on a torus that exhibits Bose-Einstein condensation, beyond the leading order Hartree-Fock…
Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
Michael Hott
This is a work extending the results of \cite{AH} and \cite{AHH}. We want to show convergence of the Schrödinger equation towards the Hartree equation with more natural assumptions…
Derivation of the Hartree equation for compound Bose gases in the mean field limit
Ioannis Anapolitanos, Michael Hott, Dirk Hundertmark
We consider mixtures of Bose gases of different species. We prove that in the mean field limit and under suitable conditions on the initial condition a system composed of two Bose…
A simple proof of convergence to the Hartree dynamics in Sobolev trace norms
Ioannis Anapolitanos, Michael Hott
The derivation of the Hartree equation from many-body systems of Bosons in the mean field limit has been very intensively studied in the last couple of years. However, very few res…
The Lieb--Thomas strategy for strongly coupled fermionic multipolarons with general external fields
Ioannis Anapolitanos, Michael Hott
In this article, we prove that the ground-state energy of a fermionic Fröhlich multipolaron can be approximated, in the strong electron-phonon coupling limit, by the ground-state e…