Related papers: Perspective on Moreau-Yosida Regularization in Den…
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
This note is intended for expanding the details on the derivation and properties of density functional theory, in hope to make them more systematic, better motivated, and step-by-step for readers new to the domain. The note starts with…
We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable. We obtain strong forms of necessary and sufficient…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed.…
Using a dynamical density functional theory we analyze the density profile of a colloidal liquid near a wall under shear flow. Due to the symmetries of the system considered, the naive application of dynamical density functional theory does…
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…
In this paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth and positively $\alpha$-far). Based on the Moreau-Yosida regularization, we prove the existence of solutions under…
This is a short guide to some uses of the zeta-function regularization procedure as a a basic mathematical tool for quantum field theory in curved space-time (as is the case of Nambu-Jona-Lasinio models), in quantum gravity models (in…
Approximations to the many-fermion free energy density functional that include the Thomas-Fermi (TF) form for the non-interacting part lead to singular densities for singular external potentials (e.g. attractive Coulomb). This limitation of…
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling…
A density-functional theory is established for inhomogeneous superfluids at finite temperature, subject to time-dependent external fields in isothermal conditions. After outlining parallelisms between a neutral superfluid and a charged…
We discuss several aspects of the dielectric response theory application to the density functional theory. This field has been an unceasing source of confusion during several decades. The most frequent reasons for this confusion are (a)…
Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the…
We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training…
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…
We consider a general optimization problem of minimizing a composite objective functional defined over a class of probability distributions. The objective is composed of two functionals: one is assumed to possess the variational…
Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural…