TY - JOUR
T1 - Time dependent closed quantum systems
T2 - Nonlinear Kohn-Sham potential operators and weak solutions
AU - Jerome, Joseph W.
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015
Y1 - 2015
N2 - We discuss time dependent quantum systems on bounded domains from the perspective of nonlinear, time-dependent potentials. The time dependence of the Kohn-Sham potentials distinguishes this study from that of the so-called nonlinear Schrödinger equation, much studied in the mathematical community. We are interested in establishing a framework for potentials including the external potential, the Hartree potential and the exchange correlation potential that occur in time dependent density functional theory (TDDFT). As in the previous work, we make use of the time-ordered evolution operator. A departure from the previous work is the use of weak solutions for the nonlinear model; this necessitates a new framework for the evolution operator based upon dual spaces. We are able to obtain unique global solutions. The author thanks Eric Polizzi for discussions leading to the incorporation of a version of the exchange correlation potential in the model.
AB - We discuss time dependent quantum systems on bounded domains from the perspective of nonlinear, time-dependent potentials. The time dependence of the Kohn-Sham potentials distinguishes this study from that of the so-called nonlinear Schrödinger equation, much studied in the mathematical community. We are interested in establishing a framework for potentials including the external potential, the Hartree potential and the exchange correlation potential that occur in time dependent density functional theory (TDDFT). As in the previous work, we make use of the time-ordered evolution operator. A departure from the previous work is the use of weak solutions for the nonlinear model; this necessitates a new framework for the evolution operator based upon dual spaces. We are able to obtain unique global solutions. The author thanks Eric Polizzi for discussions leading to the incorporation of a version of the exchange correlation potential in the model.
KW - Hamiltonian
KW - Kohn-Sham potentials
KW - Time dependent quantum systems
KW - Time-ordered evolution operators
KW - Unique weak solutions
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U2 - 10.1016/j.jmaa.2015.04.047
DO - 10.1016/j.jmaa.2015.04.047
M3 - Article
AN - SCOPUS:84933182575
SN - 0022-247X
VL - 429
SP - 995
EP - 1006
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -