TY - JOUR
T1 - Local existence and uniqueness of solutions to the time-dependent Kohn–Sham equations coupled with classical nuclear dynamics
AU - Baumeier, Björn
AU - Çaylak, Onur
AU - Mercuri, Carlo
AU - Peletier, Mark
AU - Prokert, Georg
AU - Scharpach, Wouter
PY - 2025/1/15
Y1 - 2025/1/15
N2 - We prove the short-time existence and uniqueness of solutions to the initial-value problem associated with a class of time-dependent Kohn–Sham equations coupled with Newtonian nuclear dynamics, combining Yajima's theory for time-dependent Hamiltonians with Duhamel's principle, based on suitable Lipschitz estimates. We consider a pure power exchange term within a generalisation of the so-called local-density approximation, identifying a range of exponents for the existence and uniqueness of H2 solutions to the Kohn–Sham equations.
AB - We prove the short-time existence and uniqueness of solutions to the initial-value problem associated with a class of time-dependent Kohn–Sham equations coupled with Newtonian nuclear dynamics, combining Yajima's theory for time-dependent Hamiltonians with Duhamel's principle, based on suitable Lipschitz estimates. We consider a pure power exchange term within a generalisation of the so-called local-density approximation, identifying a range of exponents for the existence and uniqueness of H2 solutions to the Kohn–Sham equations.
KW - Local density approximation
KW - Mixed quantum-classical dynamics
KW - Nonlinear evolution equations
KW - Semigroup theory
KW - Time-dependent Kohn–Sham equations
KW - Time-dependent nonlinear Schrödinger equations
UR - http://www.scopus.com/inward/record.url?scp=85199268134&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2024.128688
DO - 10.1016/j.jmaa.2024.128688
M3 - Article
AN - SCOPUS:85199268134
SN - 0022-247X
VL - 541
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 128688
ER -