TY - JOUR

T1 - Many-Body Quantum Dynamics by the Reduced Density Matrix Based on Time-Dependent Density-Functional Theory

AU - Nazarov, Vladimir U.

N1 - Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/8/29

Y1 - 2019/8/29

N2 - We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant λ naturally arises. We then find the reduced density matrix ρλ(r,r′,t), which, by construction, has the λ independent diagonal elements ρλ(r,r,t)=n(r,t), n(r,t) being the particle density. The off-diagonal elements of ρλ(r,r′,t) contribute importantly to the processes unaccessible via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in λ, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.

AB - We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant λ naturally arises. We then find the reduced density matrix ρλ(r,r′,t), which, by construction, has the λ independent diagonal elements ρλ(r,r,t)=n(r,t), n(r,t) being the particle density. The off-diagonal elements of ρλ(r,r′,t) contribute importantly to the processes unaccessible via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in λ, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.

UR - http://www.scopus.com/inward/record.url?scp=85072019609&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.123.095302

DO - 10.1103/PhysRevLett.123.095302

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C2 - 31524458

AN - SCOPUS:85072019609

SN - 0031-9007

VL - 123

JO - Physical Review Letters

JF - Physical Review Letters

IS - 9

M1 - 095302

ER -