Whether spin-independent Coulomb interaction can be the origin of a realistic ferromag-netism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrr odinger equation has N d-fold degenerate ground states. The degeneracy N d is proportional ...

In the one-dimensional Klein-Fock-Gordon theory, probability density is a discontinuous function at point where step potential discontinuous. Thus, mean value of external classical force operator cannot be calculated from corresponding formula value. To resolve this issue, we obtain quantity directly equation in Hamiltonian form, or Feshbach-Villars wave equation. Not without surprise, result o...

We discuss the exceptional Laguerre and Jacobi orthogonal polynomials in framework of supersymmetric quantum mechanics (SUSYQM). express differential equations for (EOP) as eigenvalue make an analogy with time independent Schr\"odinger equation to define "Hamiltonians" enables us study EOPs SUSYQM realize underlying shape invariance associated such systems. show that symmetry is responsible sol...

Through solution of the multielectron, semirelativistic, time-dependent Schr\"odinger equation, we show that angular streaking produces strongly spin-polarized electrons in a noble gas. The degree spin polarization increases with Keldysh parameter, so streaking---ordinarily applied to investigate tunneling---may be repurposed generate electron bunches. Additionally, explore modifications scheme...

We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schr\"odinger equation in $d=1$ at $L^2$ regularity. Our construction starts with truncated subcritical problem. With presence truncation, we construct critical as limit solutions. then obtain uniform bounds on solutions problems that allow us remove truncation limit.

We study the existence and symmetry property of multi-bump solutions of Especially when the potential V is radially symmetric, multi-bump solutions are constructed with bumps concentrating on a single connected component of the set of global minimum points of V. Furthermore, conditions are given to assure that the multi-bump solutions obtained have prescribed subgroups of O(N) as their exact sy...

It is proved that modulation in time and space of periodic wave trains, the defocussing nonlinear Schr\"odinger equation, can be approximated by solutions Whitham equations, hyperbolic case, on a natural scale. The error estimates are based existence, uniqueness, energy arguments, Sobolev spaces real line. An essential part proof inclusion higher-order corrections to theory, concomitant estimat...

A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on coupled nonlinear Schr\"odinger equation in birefringent fibers. At same time, elastic collision process mixed bright-dark soliton predicted. Compared predicted results with exact solution, method proven be effective solve equation. Moreover, d...

The sharp range of Sobolev spaces is determined in which the Cauchy problem for classical Zakharov system well-posed, includes existence solutions, uniqueness, persistence initial regularity, and real-analytic dependence on data. In addition, under a condition data Schr\"odinger equation at lowest admissible global well-posedness scattering proved. results cover energy-critical energy-supercrit...

We study the multiplicity and concentration of complex valued solutions for a fractional magnetic Schr\"odinger equation involving scalar continuous electric potential satisfying local condition nonlinearity with subcritical growth. The main results are obtained by applying penalization technique, generalized Nehari manifold method Ljusternik-Schnirelman theory. also prove Kato's inequality Lap...