System Of Schr Research Articles

Absence of Eigenvalues of Dirac and Pauli Hamiltonians via the Method of Multipliers

By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corresponding system of Schrödinger operators has no point spectrum. In particular, this allows us to prove analogous results for Pauli operators under the same electromagnetic conditions and, in turn, as a consequence of the supersymmetric structure, also for magnetic Dirac operators.

Solvability for boundary value problem of the general Schr\xf6dinger equation with general superlinear nonlinearity

This paper is mainly concerned with the boundary value problems for the general Schrödinger equation with general superlinear nonlinearity introduced in (Sun et al. in J. Inequal. Appl. 2018:100, 2018). We firstly study a new algorithm for finding the meromorphic solution for the mentioned equation via meromorphic inequalities presented in (Xu in J. Math. Study 38(1):71–86, 2015). Then we deal with the necessary and sufficient conditions of convergence and obtain the general solutions and the conditions of solvability for the mentioned equation by means of the meromorphic inequalities for the classical boundary value problems developed in (Guillot in J. Nonlinear Math. Phys. 25(3):497–508, 2018). These results generalize some previous results concerning the asymptotic behavior of solutions of non-delay systems of Schrödinger equations by applying the maximum principle approach with respect to the Schrödinger operator in (Wan in J. Inequal. Appl. 2017:104, 2017).

The dynamical diquark model: first numerical results

We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schrödinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.

Regular and Irregular Solutions in the Problem of Dislocations in Solids

For an initial differential equation with deviations of the spatial variable, we consider asymptotic solutions with respect to the residual. All solutions are naturally divided into classes depending regularly and irregularly on the problem parameters. In different regions in a small neighborhood of the zero equilibrium state of the phase space, we construct special nonlinear distribution equations and systems of equations depending on continuous families of certain parameters. In particular, we show that solutions of the initial spatially one-dimensional equation can be described using solutions of special equations and systems of Schr¨odinger-type equations in a spatially two-dimensional argument range.

Nonlinear optical response due to resonant enhancement of the internal field with particular spatial distribution

Peculiar properties of nonlinear response, due to a resonant enhancement of internal field are predicted for the mesoscopic systems by means of a nonlocal theory of nonlinear response. In this theory, self-consistent motions of the internal field and the induced polarization, which are related nonlocally with each other, are determined by solving the equation system of Schr\"odinger and Maxwell's equations. A study with a model of ultrathin films consisting of one-dimensional Frenkel excitons has clarified the following points: As a result of a self-consistent motion with the induced polarization, the internal field with a characteristic spatial distribution associated with each quantized exciton state is enhanced at a particular resonant energy including a radiative correction that depends on system size. This resonant enhancement of the internal field greatly strengthens the nonlinear signal of a particular third-order process, leading to a remarkable size and energy dependence of the nonlinear response. This effect is explicitly demonstrated for a particular type of pump-probe spectroscopy. \textcopyright{} 1996 The American Physical Society.