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

Area of Science:

• Quantum Mechanics
• Computational Chemistry
• Condensed Matter Physics

Background:

• Time-dependent density functional theory (TDDFT) is a powerful tool for studying quantum systems.
• Existing TDDFT functionals often struggle to capture complex electronic processes.
• The density matrix contains more information than the particle density alone.

Purpose of the Study:

• To develop a method for evaluating the density matrix of quantum systems.
• To extend the capabilities of TDDFT by incorporating off-diagonal density matrix elements.
• To investigate processes inaccessible by density alone, such as momentum-resolved photoemission.

Main Methods:

• Utilizing the adiabatic connection perturbation method.
• Expanding the many-body density matrix in powers of the coupling constant (λ).
• Calculating the reduced density matrix ρ_{λ}(r,r',t) with λ-independent diagonal elements.

Main Results:

• The off-diagonal elements of the density matrix are crucial for describing processes beyond simple density.
• Momentum-resolved photoemission was calculated to the first order in λ (exact exchange level).
• Significant quantitative and conceptual differences were observed compared to the Fermi's golden rule formula.

Conclusions:

• The developed method provides a more complete description of quantum systems than standard TDDFT.
• Off-diagonal density matrix elements are essential for understanding phenomena like photoemission.
• This approach offers a pathway to more accurate theoretical predictions in quantum mechanics.