Related papers: Comment on ``A new efficient method for calculatin…
We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and…
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
An algorithm for Electric Power System (EPS) quantum/relativistic security and efficiency computation for a day-ahead via perturbative renormalization of the EPS, finding the computation flowcharts, verification and validation is built in…
We discuss a numerical method to compute the homogeneous solutions of the Teukolsky equation which is the basic equation of the black hole perturbation method. We use the formalism developed by Mano, Suzuki and Takasugi, in which the…
Some exact and approximate methods commonly used to calculate corrections to the Bethe stopping formula are modified and adapted by the authors to the calculation of the energy loss straggling. An intercomparison is carried out for results…
Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired…
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is considered.
A non-subtractive recipe of Casimir energy renormalization efficient in the presence of logarithmically divergent terms is proposed. It is demonstrated that it can be applied even then, when energy levels can be obtained only numerically…
The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the…
The dynamics of the nuclear-spin quantum computer with large number (L=1000) of qubits is considered using a perturbation approach, based on approximate diagonalization of exponentially large sparse matrices. Small parameters are introduced…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
In this article I show why the fundamental constants obtain perturbative corrections in higher orders, why the renormalizations work and how to reformulate the theory in order to avoid these technical and conceptual complications. I…
Perturbative calculations in quantum field theory often require the regularization of infrared divergences. In quantum electrodynamics, such a regularization can for example be accomplished by a photon mass introduced via the Stueckelberg…
The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical since the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically…
Singular charge sources in terms of Dirac delta functions present a well-known numerical challenge for solving Poisson's equation. For a sharp interface between inhomogeneous media, singular charges could be analytically treated by…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding…
We describe regularizing effects in the linearization of a kinetic equation that arises in study of a system of nonlinear waves satisfying the Schr\"odinger equation in terms of weak turbulence and condensate. The problem is first…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. In Part I, we critiqued a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and…