相关论文: A New Look at Linear (Non-?) Symplectic Ion Beam O…
We introduce a practical approach to extract the symplectic transfer maps for arbitrary magnetic beam-line elements. Beam motion in particle accelerators depends on linear and nonlinear magnetic fields of the beam-line elements. These…
Symplectic tracking of beam particles using point magnets is achieved using a reference orbit made of circular arcs and straight lines that join smoothly with each other. For this choice of the reference orbit, results are given for the…
Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
Due to the emergence of symplectic geometry, the geometric treatment of mechanics underwent a great development during the last century. In this scenario the pressence of symmetries in Hamiltonian systems leads naturally to the existence of…
Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These…
The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on conservation of the adiabatic invariant, magnetic moment.…
The concept of guiding center is potent in astrophysics, space plasmas, fusion researches, and arc plasmas to solve the multi-scale dynamics of magnetized plasmas. In this letter, we rigorously prove that the guiding center dynamics can…
Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between…
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics…
We describe a technique for constructing a symplectic transfer map for a charged particle moving through an accelerator component with arbitrary three-dimensional static magnetic field. The transfer map is constructed by symplectic…
In the usual approaches to mechanics (classical or quantum) the primary object of interest is the Hamiltonian, from which one tries to deduce the solutions of the equations of motion (Hamilton or Schr\"odinger). In the present work we…
We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non trivial way. These systems depend on a parameter t $\in$ [0, 1] and exhibit different behaviors…
We investigate the electromagnetic dynamics of spin-nondegenerate classical particle models arising from Lorentz-violating sectors of the Standard-Model Extension, focusing on the $b_\mu$ background. Starting from the type-2 relativistic…
In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\{q^i,p_k\}$ the canonical symplectic two-form is $\omega_0=dq^i\wedge dp_i$. It is well known in…
For two-electron diatomic molecules, we investigate magnetic field effects in non-sequential double ionization where recollisions prevail. We do so by formulating a three-dimensional semi-classical model that fully accounts for the Coulomb…
Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of…
An alternative model for a description of magnetization processes in coupled 2D spin-electron systems has been introduced and rigorously examined using the generalized decoration-iteration transformation and the corner transfer matrix…
The relativistic momentum equation of a collisionless plasma is reformulated to describe the time evolution of canonical vorticity. Compared to the non-relativistic counterpart, an additional source term for canonical vorticity is…
A consistent theory to describe the correlated dynamics of quantum mechanical itinerant spins and semiclassical local magnetization is given. We consider the itinerant spins as quantum mechanical operators, whereas local moments are…