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The paper provides a thorough comparison between R-continuity and other fundamental tools in optimization such as metric regularity, metric subregularity and calmness. We show that R-continuity has some advantages in the convergence rate…
A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each…
The adsorption energy of benzene on various metal substrates is predicted using the random phase approximation (RPA) for the correlation energy. Agreement with available experimental data is systematically better than 10% for both coinage…
We explore different variants of the random phase approximation (RPA) to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated…
This Ph.D. thesis derives the equations of the Faddeev Random Phase Approximation (FRPA) and applies the method to a set of small atoms and molecules. The occurence of RPA instabilities in the dissociation limit is addressed in molecules…
As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In…
Linearizing the appropriate kinetic equation we derive general response functions including selfconsistent mean fields or density functionals and collisional dissipative contributions. The latter ones are considered in relaxation time…
Background: Average energies of nuclear collective modes may be efficiently and accurately computed using a non-relativistic constrained approach without reliance on a random phase approximation (RPA). Purpose: To extend the constrained…
The accurate computation of non-linear optical properties (NLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic…
It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…
A finite rank separable approximation for the quasiparticle RPA calculations with Skyrme interactions that was proposed in our previous work is extended to take into account the coupling between one- and two-phonon terms in the wave…
Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate…
The partition function by means of the static path approximation (SPA) plus the random-phase approximation (RPA) treatment can be written as a contour integral form without solving the RPA equations for a separable interaction. This method…
The finite amplitude method (FAM), which we have recently proposed (T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)), simplifies significantly the fully self-consistent RPA calculation. Employing the FAM, we are…
Although there exists a clear and, in principle, exact theoretical formulation for the equation of motion for the response of a correlated fermionic system, its numerical implementations for atomic nuclei require feasible approximations.…
The direct random-phase approximation (dRPA) is used to calculate and compare atomization energies for the HEAT set and 10 selected molecules of the G2-1 set using both plane waves and Gaussian-type orbitals. We describe detailed procedures…
Quasiparticle random-phase approximation (QRPA) is applied to two nuclei, and overlap of the QRPA excited states based on the different nuclei is calculated. The aim is to calculate the overlap of intermediate nuclear states of the…
An expression for the dynamic density response function has been obtained for an interacting quantum gas in Random Phase Approximation (RPA) including first order self and exchange contribution. It involves the single particle wave…
We investigate the effects of plasma interactions on resonance-enhanced fusion rates in stars. Starting from basic principles we derive an expression for the fusion rate that can serve as a basis for discussion of approximation schemes. The…
The enhancement factor of the resonant thermonuclear reaction rates is calculated for the extremely dense stellar plasmas in the liquid phase. In order to calculate the enhancement factor we use the screening potential which is deduced from…