Related papers: Multiple parameter structure of Mielnik's isospect…
This paper gives a new perspective on how to solve the second-order linear differential equation written in normal form. Extending the argument of the potential to a complex number leads to solving exactly the Schr\"odinger equation when…
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider…
A set of factorization energies is introduced, giving rise to a generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such…
In this study, we focus on investigating the exact relativistic bound state spectra for supersymmetric, PT-supersymmetric and non-Hermitian versions of q-deformed parameter Hulthen potential. The Hamiltonian hierarchy mechanism, namely the…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either…
In this paper we derive a Toeplitz-structured closed form of the unique positive semi-definite stabilizing solution for the discrete-time algebraic Riccati equations, especially for the case that the state matrix is not stable. Based on the…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. While the WKB method generates an expansion in powers of h, the quasilinearization method (QLM) approaches the solution of the nonlinear equation…
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for…
We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the…
Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method…
In this paper we propose a method to study the Functional Renormalization Group at finite chemical potential. The method consists of mapping the FRG equations within the Fermi surface into a differential equation defined on a rectangle with…
We investigate a radiative electroweak gauge symmetry breaking scenario via the Coleman-Weinberg mechanism starting from a completely flat Higgs potential at the Planck scale ("flatland scenario"). In our previous paper, we showed that the…
A supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrodinger equations in particle physics is described at the general level. By this means we are able to introduce a nonhermitic…
Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin-Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati…