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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 generally be described as a constrained canonical Hamiltonian system with two constraints in six dimensional phase space, and that the solution flow of the guiding center lies on a canonical symplectic sub-manifold. The guiding center can thus be modeled as a pseudo-particle with an intrinsic magnetic moment, which properly replaces the charged particle dynamics on time scales larger than the gyro-period. The complete dynamical behaviors, such as the velocity and force, of the guiding center pseudo-particle can be clearly deduced from the model. Furthermore, a series of related theories, such as symplectic numerical methods, the canonical gyro-kinetic theory, and canonical particle-in-cell algorithms can be systematically developed based on the canonical guiding center system. The canonical guiding center theory also provides an enlightenment for the origin of the intrinsic magnetic moment., Comment: 14pages, 4 figures

Gyrocenter dynamics of charged particles plays a fundamental role in plasma physics. In particular, accuracy and conservation of energy are important features for correctly performing long-time simulations. For this purpose, we here propose arbitrarily high-order energy conserving methods for its simulation. The analysis and the efficient implementation of the methods are fully described, and some numerical tests are reported., Comment: 23 pages, 4 figures

We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it is diagonalizable or not. This result is different from Mostafazadeh's, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between eigenmodes with different Krein signatures., Comment: 11pages, 1 figure. arXiv admin note: text overlap with arXiv:1801.01676

Parity-Time (PT)-symmetry is being actively investigated as a fundamental property of observables in quantum physics. We show that the governing equations of the classical two-fluid interaction and the incompressible fluid system are PT-symmetric, and the well-known Kelvin-Helmholtz instability is the result of spontaneous PT-symmetry breaking. It is expected that all classical conservative systems governed by Newton's law admit PT-symmetry, and the spontaneous breaking thereof is a generic mechanism for classical instabilities. Discovering the PT-symmetry of systems in fluid dynamics and plasma physics and identifying the PT-symmetry breaking responsible for instabilities enable new techniques to classical physics and enrich the physics of PT-symmetry., Comment: 11 pages, 1 figure

It is generally believed that Parity-Time (PT)-symmetry breaking occurs when eigenvalues or both eigenvalues and eigenvectors coincide. However, we show that this well-accepted picture of PT-symmetry breaking is incorrect. Instead, we demonstrate that the physical mechanism of PT-symmetry breaking is the resonance between positive- and negative-action modes. It is proved that PT-symmetry breaking occurs when and only when this resonance condition is satisfied, and this mechanism applies to all known PT-symmetry breakings observed in different branches of physics. The result is achieved by proving a remarkable fact that in finite dimensions, a PT-symmetric Hamiltonian is necessarily pseudo-Hermitian, regardless whether it is diagonalizable or not., Comment: 15 pages, 3 figures

Three-wave instability is a fundamental process that has important applications in many branches of physics. It is widely accepted that the resonant condition $\omega_{z}\approx\omega_{x}+\omega_{y}$ for participating waves is the criteria for the onset of the instability. We show that this condition is neither sufficient nor necessary, instead, the exact criteria for the onset of the instability is that a positive-action mode resonates with a negative-action mode. This mechanism is imposed by the topology and geometry of the spectral space. Guided by this new theory, additional instability bands previously unknown are discovered., Comment: 14 pages, 4 figures

A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy-momentum conservation law corresponding to the discrete space-time symmetry. These conservative properties make the discrete system an effective algorithm for numerically solving the governing differential equations on continuous space-time. Moreover, the lattice model, respecting all conservation laws and geometric structures, is as good as and probably more preferable than the continuous Maxwell model. Under the simulation hypothesis by Bostrom and in consistent with the discussion on lattice QCD by Beane et al., the two interpretations of physics laws on space-time lattice could be essentially the same., Comment: 12 pages