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The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave…
The optimal exponentials of the thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells. We obtain that the lower bounds of the optimal exponentials are $4/3,$ $3/2,$ and $1,$ for the hyperbolic…
We apply near-field matter-wave interferometry to determine the absolute scalar polarizability of the fullerenes C$_{60}$ and C$_{70}$. A key feature of our experiment is the combination of good transmission and high spatial resolution,…
By means of a suitable rational approximation to the logarithmic derivative of the wavefunction we obtain tight upper and lower bounds to the eigenvalues and critical parameters of the quartic double-well potential.
A method for the generation of ultrarelativistic electron beams with high spin polarization is put forward, where a tightly-focused linearly-polarized ultraintense laser pulse interacts with a nonprepolarized transverse-size-tailored solid…
Material resonances are fundamentally important in the field of nano-photonics and optics. So it is of great interest to know what are the limits to which they can be tuned. The bandwidth of the resonances in materials is an important…
We consider the multiphase shape optimization problem $$\min\Big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ \hbox{open},\ \Omega_i\subset D,\ \Omega_i\cap\Omega_j=\emptyset\Big\},$$ where $\alpha>0$ is a given constant…
Using some special properties of a permeability-near-zero material, the radiation of a line current is greatly enhanced by choosing appropriately the dimension of a dielectric domain in which the source lies and that of a…
Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale…
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…
We study maximal estimates for the wave equation with orthonormal initial data. In dimension $d=3$, we establish optimal results with the sharp regularity exponent up to the endpoint. In higher dimensions $d \ge 4$ and also in $d=2$, we…
Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete…
We prove two bounds for the first Robin eigenvalue of the Finsler Laplacian with negative boundary parameter in the planar case. In the constant area problem, we show that the Wulff shape is the maximizer only for values which are close to…
Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning-Rosen (MR) potential. Bound states accurate up to ten significant figure are obtained by employing a…
We discuss multiple classes of piece-wise Pareto-like power law probability density functions $p(x)$ with two regimes, a non-pathological core with non-zero, finite values for support $0\leq x\leq x_{\mathrm{min}}$ and a power-law tail with…
Annual Review of Astronomy and Astrophysics, Volume 51, page 511e studied for coherently driven single photon sources, such as atoms and quantum dots. Maximal squeezing is realized, if the electronic subsystem of the emitter is in a pure…
In this article we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The…
We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…
We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)= - {\alpha}/cosh({\beta}x), which provides a good fit for potential…
Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks.…