相关论文: Higher order energy functionals

Let $\psi$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $\varphi$ be a holomorphic self-map of $\BB$, associated with normal weights $\nu$ and $\mu$. We consider the weighted composition operator $…

The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface $S$ is a function $E_\rho$ on Teichm\"uller space $\Teich$ which is a qualitative invariant of the holonomy representation…

This paper is motivated by a gauged Schr\"odinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem: $$ - \Delta u(x) + \left(\omega +…

We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular case. We build…

In this work, two multi-harmonic Hamiltonian models for mean motion resonances are formulated and their applications to first-order resonances are discussed. For the $k_p$:$k$ resonance, the usual critical argument $\varphi = k \lambda -…

An exchange-correlation energy functional $ E_{\mathrm xc} $ and the resultant exchange-correlation potential $ v_{\mathrm xc}({\bf r}) $ in density-functional theory are proposed using orbital-dependent coupling-constant-averaged pair…

The relation between the derivative of the energy with respect to occupation number and the orbital energy, $\partial E/\partial n_i = \epsilon_i$, was first introduced by Slater for approximate total energy expressions such as Hartree-Fock…

We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times. Ultimately, we…

We study the Hartree-Fock equation and the Hartree-Fock energy functional universally used in many-electron problems. We prove that the set of all critical values of the Hartree-Fock energy functional less than a constant smaller than the…

Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…

We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…

Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…

New sets of functions with arbitrary large finite cardinality are constructed for two-electron atoms. Functions from these sets exactly satisfy the Kato's cusp conditions. The new functions are special linear combinations of Hylleraas-…

In the celebrated work of Friesecke, James and M\"uller '06 the authors derive a hierarchy of models for plates by carefully analyzing the $\Gamma$-convergence of the rescaled nonlinear elastic energy. The key ingredient of their proofs is…

Harmonic wave functions for integer and half-integer angular momentum are given in terms of the Euler angles $(\theta,\phi,\psi)$ that define a rotation in $SO(3)$, and the Euclidean norm in ${\mathbb R}^3$. Following a classical work by…

A set of density functionals coming from different rungs on Jacob's ladder are employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical…

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\,\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that…

The Hartree-Fock equation which is the Euler-Lagrange equation corresponding to the Hartree-Fock energy functional is used in many-electron problems. Since the Hartree-Fock equation is a system of nonlinear eigenvalue problems, the study of…

In recent works, arbitrary structural sets in the non-commutative Clifford analysis context have been used to introduce non-trivial generalizations of harmonic Clifford algebra valued functions in $\mathbb{R}^m$. Being defined as the…

In this work, we study the two following minimization problems for $r \in \mathbb{N}^{*}$, \begin{equation*} \begin{array}{ccc} S_{0,r}(\varphi)=\displaystyle\inf_{u\in H_{0}^{r}(\Omega)\,|u+\varphi\|_{L^{2^{*r}}}=1}\|u\|_{r}^{2}&…