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Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the…

We report equations of motion for the occupation numbers of natural spin orbitals and show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading…

With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced-density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the…

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem…

We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation.…

The ground state of atoms from H to Ar was calculated using a self-interaction correction to local and gradient dependent density functionals. The correction can significantly improve the total energy and makes the orbital energies…

We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant…

The adiabatic approximation in time-dependent density functional theory (TDDFT) is known to give an incorrect pole structure in the quadratic response function, leading to unphysical divergences in excited state-to-state transition…

The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and…

We present a new formulation of the time-dependent self-interaction correction (TDSIC). It is derived variationally obeying explicitly the constraints on orthonormality of the occupied single-particle orbitals. The thus emerging rather…

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground…

A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…

We discuss the adiabatic basis dependence of particle number in time-dependent backgrounds. In particular, we focus on preheating after inflation, and show that, for the optimal basis, the time dependence of the produced particle number can…

The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate…

We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove…

The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that…

We show that the time dependent single electron, nuclear density matrix of an interacting electronic system coupled to nuclear degrees of freedom can be exactly reproduced by that of an electronic system with arbitrarily specified…

We show that the difference of adiabatic phases, that are basis-dependent, in noncyclic evolution of non-degenerate quantum systems have to be taken into account to give the correct interference result in the calculation of physical…

We construct a measure for the adiabatic contribution to quantum transitions in an arbitrary basis, tackling the generic complex case where dynamics is only partially adiabatic, simultaneously populates several eigenstates and transitions…

Many recent applications of time-dependent density functional theory begin in an initially excited state, and propagate it using an adiabatic approximation for the exchange-correlation potential. This however inserts the excited-state…