We show that the Friedrichs–Lee model, which describes one-excitation sector of a two-level atom interacting with structured boson field, can be generalized to singular atom–field couplings. provide characterization its spectrum and resonances discuss inverse spectral problem.

For singular even order symmetric differential operators we find the matrices which determine all extensions of minimal operator. And for each these is bounded below boundary condition its Friedrichs extension. The regular problems are and thus one has a extension See also https://ejde.math.txstate.edu/special/02/b1/abstr.html

In this paper we propose to find the best constant for the Friedrichs-KnappStein inequality in F2n,2, that is the free nilpotent Lie group of step two on 2n generators, and to prove the second order differentiability of subelliptic p-harmonic functions in an interval of p.

We show that the Aharonov-Bohm Hamiltonian considered on a disc has a four-parameter family of self-adjoint extensions. Among the infinitely many self-adjoint extensions, we determine to which parameters the Friedrichs extension HF corresponds and its lowest eigenvalue is found. Moreover, we note that the diamagnetic inequality holds for HF .

Submit Manuscript | http://medcraveonline.com Abbreviations: 1D: One-Dimensional; 2D: Two-Dimensional; 3D: Three-Dimensional; DGTD: Discontinuous Galerkin TimeDomain; FEs: Finite Elements; TM: Transverse Magnetic; TE: Transverse Electric; ODE: Ordinary Differential Equations; LSERK: Low-Storage Explicit Runge-Kutta; CFL: Courant-Friedrichs-Levy; TD: Time-Domain; PEC: Perfect Electric Conductor;...

In this paper, we study the one-level Friedrichs model with using the quantum time super-operator that predicts the excited state decay inside the continuum. Its survival probability in long time limit is an algebraically decreasing function and an exponentially decreasing multiplied by the oscillating functions.

The dispersion and dissipation properties of numerical methods are very important in wave simulations. In this paper, such properties are analyzed for Runge-Kutta discontinuous Galerkin methods and Lax-Wendroff discontinuous Galerkin methods when solving the linear advection equation. With the standard analysis, the asymptotic formulations are derived analytically for the discrete dispersion re...