Related papers: Generalised action-angle coordinates defined on is…
Quasi-poloidal (QP) magnetic fields have desirable properties for confining plasma: no radial drift of guiding centres (with positive implications for neoclassical transport), zero Pfirsch-Schl\"uter current, a lower level of damping for…
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
We present algebraic projective geometry definitions of 3D rotations so as to bridge a small gap between the applications and the definitions of 3D rotations in homogeneous matrix form. A general homogeneous matrix formulation to 3D…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
Shaking a lattice system, by modulating the location of its sites periodically in time, is a powerful method to create effective magnetic fields in engineered quantum systems, such as cold gases trapped in optical lattices. However, such…
Equations of magneto-gasdynamics in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the nonlinear vector wave equation coupled with the incompressibility…
The mapping of the Galactic Magnetic Field (GMF) in three dimensions is essential to comprehend various astrophysical processes that occur within the Milky Way. This study endeavors to map the GMF by utilizing the latest MM2 technique, the…
Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give…
When generalizing the principle of least action for fields containing higher order derivatives, in general, it is not possible not to take into account the surface integrated term since it gives direct contribution to the forms of the…
We consider a 1D mechanical system $$\bar {\mathtt H}(\mathtt P,\mathtt Q)=\mathtt P^2+\bar {\mathtt G}(\mathtt Q)$$ in action-angle variable $(\mathtt P,\mathtt Q)$ where $\bar {\mathtt G}$ is a $2\pi$-periodic analytic function with non…
With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that makes use of Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. In order to master all…
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…
Force-free electrodynamics describes the electromagnetic field of the magnetically dominated plasma found near pulsars and active black holes, but gives no information about the underlying particles that ultimately produce the observable…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Neural implicit representation of geometric shapes has witnessed considerable advancements in recent years. However, common distance field based implicit representations, specifically signed distance field (SDF) for watertight shapes or…
Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The…
For tokamaks with uniform magnetic shear, Martin and Taylor have proposed a symplectic map has been used to describe the magnetic field lines at the plasma edge perturbed by an ergodic magnetic limiter. We propose an analytical magnetic…