相关论文: Mass splitting in the Thomas-Fermi-Dirac-von Weizs…

We prove a sharp higher differentiability result for local minimizers of functionals of the form $$\mathcal{F}\left(w,\Omega\right)=\int_{\Omega}\left[ F\left(x,Dw(x)\right)-f(x)\cdot w(x)\right]dx$$ with non-autonomous integrand $F(x,\xi)$…

We provide a set of theoretical constraints on models in which the Standard Model field content is extended by vector-like fermions and in some cases also by a real scalar singlet. Our approach is based on the study of electroweak vacuum…

We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation…

We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen…

In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed…

We describe an advanced version of the AFW-technique proposed in [Lett. Math. Phys., 113, 121 (2023)],[Lobachevskii J. Math., 44(6), 2169 (2023)] which allows us to obtain lower semicontinuity bounds, continuity bounds and local lower…

We consider the nonlinear Schr\''odinger equation on a strip with Neumann boundary conditions and a delta condition on the $x$-axis. First, we show the existence of ground states as minimizers of the action or of the energy under suitable…

The paper studies violation of conventional rules of SUSY quantum mechanics for the centrifugal potential V(r) within the limit-circle (LC) range. A special attention is given to transformation properties of the Titchmarsh-Weyl m-function…

We review recent results on three families of minimization problems, defined on subsets of nonnegative functions with fixed integral. The competition between attractive and repulsive forces leads to transitions between parameter regimes,…

The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the…

We study the minimizers of the sum of the principal Dirichlet eigenvalue of the negative Laplacian and the perimeter with respect to a general norm in the class of Jordan domains in the plane. This is equivalent (modulo scaling) to…

In this paper, we perform a detailed study of the scaling properties of a ferromagnetic thin film model. Recently, interest has increased in the scaling properties of the magnetic domain wall (MDW) motion in disordered media when an…

We report on the theoretical investigation of Wigner distribution function (WDF) reconstruction of the motional quantum state of large molecules in de Broglie interference. De Broglie interference of fullerenes and as the like already…

Partially-projected Gutzwiller variational wavefunctions are used to describe the ground state of disordered interacting systems of fermions. We compare several different variational ground states with the exact ground state for disordered…

The terahertz (THz) band is a key enabler for future wireless systems, promising ultra-high data rates and dense spatial reuse. However, the reliability of THz links remains a major challenge due to severe path loss and small-scale fading…

In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the $T\bar{T}$ family. Our construction generalizes…

We discuss two problems which are particularly challenging for approximations in time-dependent density functional theory (TDDFT) to capture: momentum-distributions in ionization processes, and memory-dependence in real-time dynamics. We…

We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…

We calculate the perturbative corrections in the strong coupling to the unpolarized quark transverse-momentum dependent parton distribution function (TMDPDF) operator within a background-field framework, extending the approach of Ref. [1].…

We study the short-time dynamics of a mean-field model with non-conserved order parameter (Curie-Weiss with Glauber dynamics) by solving the associated Fokker-Planck equation. We obtain closed-form expressions for the first moments of the…