Related papers: Angular Functions with Complex Angular Momenta
In this letter, we review the well known ambiguity in defining angular momentum (and mass dipole) fluxes in general relativity and we reinterpret recent works that resolve the ambiguity by defining invariant charges. We resolve the…
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
A new generalized St\"ormer problem is proposed. The charged particles motion around a rotating axisymmetric magnetic planet is studied using various conditions mainly in planetary magnetospheres. It is shown that the existence of specific…
We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical…
We introduce the notion of a random matrix-valued multiplicative function, generalizing Rademacher random multiplicative functions to matrices. We provide an asymptotic for the second moment based on a linear recurrence property for…
A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We develop the theory of momentum map for the Maxwell-Lorentz equations with spinning extended charged particle. This theory is indispensable for the study of long-time behaviour and radiation of the solitons of this system. The development…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…
Fundamental and applied concepts concerning the ability of light beams to carry a certain mechanical angular momentum with respect to the propagation axis are reviewed and discussed. Following issues are included: Historical reference;…
Surprisingly, apart from some special cases, simple asymptotic expansions for the associated Legendre functions $P_\nu ^\mu (z)$ and $Q_\nu ^\mu (z)$ for large degree $\nu$ or large order $\mu$ are not available in the literature. The main…
Recently, in analogy with multiphoton ionization, it has been suggested that multiparticle ionization can also be induced by massive systems. We explore in this paper the possibility that multiparticle absorption processes can also take…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the…
Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $\Delta(X) = X\otimes X$, then their generating functions obey…
Quantum theory of spin relaxation in the elastic environment is revised with account of the concept of a phonon spin recently introduced by Zhang and Niu (PRL 2014). Similar to the case of the electromagnetic field, the division of the…