Time dependent closed quantum systems: nonlinear Kohn-Sham potential operators and weak solutions

DOI10.1016/j.jmaa.2015.04.047zbMath1405.35174OpenAlexW1986891087MaRDI QIDQ2347426

Joseph W. Jerome

Publication date: 27 May 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.04.047

zbMATH Keywords

Hamiltoniantime dependent quantum systemstime-ordered evolution operatorsKohn-Sham potentialsunique weak solutions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Weak solutions to PDEs (35D30)

Related Items (9)

A COKOSNUT code for the control of the time-dependent Kohn-Sham model ⋮ Convergent iteration in Sobolev space for time dependent closed quantum systems ⋮ Stabilization for Schrödinger equation with internal damping and boundary disturbance ⋮ Consistency of local density approximations and quantum corrections for time-dependent quantum systems ⋮ Investigation of optimal control problems governed by a time-dependent Kohn-Sham model ⋮ A Theoretical Investigation of Time-Dependent Kohn--Sham Equations ⋮ Long-time behaviour of time-dependent density functional theory ⋮ A theoretical investigation of time-dependent Kohn–Sham equations: new proofs ⋮ A tight nonlinear approximation theory for time dependent closed quantum systems

Cites Work

• Dissipative operators in a Banach space
• A simplified proof of a theorem of Kato on linear evolution equations
• Approximation of nonlinear evolution systems
• Time-dependent density functional theory
• Linear evolution equations of hyperbolic type. II
• Discretization of time-dependent quantum systems: real-time propagation of the evolution operator
• One-Parameter Semigroups for Linear Evolution Equations
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