Due to its excellent long term accuracy, the Boris algorithm is de facto standard for advancing a charged particle. Despite popularity, up now there has been no convincing explanation why this advantageous feature. In paper, we provide an answer question. We show that conserves phase space volume, even though it not symplectic. The global bound on energy error typically associated with symplectic algorithms still holds algorithm, making effective multi-scale dynamics of plasmas.

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using formalism discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], field solver, interpolation scheme, and particle advance algorithm are derived through minimization a single theory action. As consequence ensuring that action invariant under gauge transformations, exactly conserves Gauss’s law.

We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional linearly-ramped flip operation and thereby two periodic revivals of the walker distribution. In our beam-displacer interferometer, corresponds to movement between discretely separated transverse modes field serving as lattice sites, is effected by implementing different angle optical axis half-wave plate light propagation at each step. Each quantum-walk...

A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed long-time simulation studies magnetized plasmas. Instead discretizing differential equations motion, action discretized and minimized to obtain iteration rules advancing dynamics. The conserves exactly a discrete Lagrangian structure, has better numerical properties over long integration time, compared with standard integrators, such as variable time-step fourth...

Particle-in-Cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for Vlasov-Maxwell system by discretizing Poisson bracket. A fast local algorithm to solve implicit time advance discovered without root searching or global matrix inversion, enabling applications of proposed very large-scale simulations with many, e.g., $10^{9}$, degrees...

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The conserve a discrete structure derived from Lagrangian of system, which is naturally in particles. electromagnetic field spatially discretized using method exterior calculus with interpolating differential forms cubic grid. resulting time-domain assumes structure. It also gauge invariant and conserves charge. system then...

Plasmas have been recently studied as topological materials. However, a comprehensive picture of phases and phase transitions in cold magnetized plasmas is still missing. Here we systematically map out all the establish bulk-edge correspondence plasmas. We find that for linear eigenmodes, there are 10 parameter space density $n$, magnetic field $B$, parallel wavenumber $k_{z}$, separated by surfaces Langmuir wave-L wave resonance, wave-cyclotron zero field. For fixed $B$ only transition at...

A theoretical framework is developed to describe the Topological Langmuir-Cyclotron Wave (TLCW), a recently identified topological surface excitation in magnetized plasmas. As wave, TLCW propagates unidirectionally without scattering complex boundaries. The studied theoretically as spectral flow of Hamiltonian Pseudo-Differential-Operator (PDO) $\hat{H}$ for waves an inhomogeneous plasma. semi-classical parameter Weyl quantization plasma be ratio between electron gyro-radius and...

A variational symplectic integrator for the guiding center motion of charged particles in general magnetic fields is developed to enable accurate long-time simulation studies magnetized plasmas. Instead discretizing differential equations motion, action discretized and minimized obtain iteration rules advancing dynamics. The conserves exactly a discrete Lagrangian structure globally bounds numerical error energy by small number all time steps. Compared with standard integrators, such as...

Smoothing functions are commonly used to reduce numerical noise arising from coarse sampling of particles in particle-in-cell (PIC) plasma simulations. When applying smoothing symplectic algorithms, the conservation structure should be guaranteed preserve good properties. In this paper, we show how construct a variational multi-symplectic PIC algorithm with for Vlasov-Maxwell system. The and reduction make specifically suitable simulating long-term dynamics plasmas, such as those...

Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a splitting technique. The functional is split into five parts, which produces exactly solvable subsystems. Each subsystem system equipped with Morrison-Marsden-Weinstein Poisson bracket. Compositions of exact solutions provide structure preserving/Hamiltonian methods arbitrary high order equations. They then accurate and conservative over long because Poisson-preserving nature.

Secular dynamics of relativistic charged particles has theoretical significance and a wide range applications. However, conventional algorithms are not applicable to this problem due the coherent accumulation numerical errors. To overcome difficulty, we develop volume-preserving algorithm (VPA) with long-term accuracy conservativeness via systematic splitting method. Applied simulation runaway electrons time-span over 10 magnitudes, VPA generates accurate results enables discovery new...

Dynamics of a charged particle in the canonical coordinates is Hamiltonian system, and well-known symplectic algorithm has been regarded as de facto method for numerical integration systems due to its long-term accuracy fidelity. For simulations with high efficiency, explicit algorithms are desirable. However, it generally believed that only available sum-separable Hamiltonians, this restriction limits application dynamics. To overcome difficulty, we combine familiar sum-split generating...

Abstract Estimating the number of communities is one fundamental problems in community detection. We re-examine Bayesian paradigm for stochastic block models (SBMs) and propose a "corrected information criterion" (CBIC), to determine show that proposed criterion consistent under mild conditions as size network go infinity. The CBIC outperforms those used Wang Bickel Saldana, Yu, Feng which tend underestimate overestimate communities, respectively. results are further extended degree...

In this paper, we study the Vlasov-Maxwell equations based on Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for system by employing finite element in space and splitting time. order to derive semi-discrete that possesses a discrete non-canonical Poisson structure, present criterion choosing appropriate spaces. It is confirmed some conforming elements, e.g., Nédélec's mixed satisfy requirement. When method used discretize time, resulting algorithm...

The topology of photons in vacuum is interesting because there are no with $\mathbit{k}=0$, creating a hole momentum space. We show that while the set all forms trivial vector bundle $\ensuremath{\gamma}$ over this space, $R$ and $L$ form topologically nontrivial subbundles ${\ensuremath{\gamma}}_{\ifmmode\pm\else\textpm\fi{}}$ first Chern numbers $\ensuremath{\mp}2$. In contrast, has linearly polarized subbundles, number associated linear polarizations. It known difficulty standard version...

The gyrocenter dynamics of charged particles in time-independent magnetic fields is a non-canonical Hamiltonian system. canonical description the has both theoretical and practical importance. We provide general procedure canonicalization, which expressed by series small variable ϵ depending only on parallel velocity u can be recursive manner. prove that truncation to any given order generates set exact coordinates for system, whose Lagrangian approximates original system same order. If flux...

The output incoherent spectrum and the photon blockade for two-photon near-resonant excitation are numerically investigated by using modified theories which valid an arbitrary degree of qubit-cavity interaction. Owing to effects strong coupling system, relaxation coefficients system very sensitive strength between qubit cavity mode, results in redistribution populations appearance population inversion ground state first excited state, it is demonstrated intensity spectrum. leads one cascaded...

We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it diagonalizable or not. This result different from Mostafazadeh’s [J. Math. Phys. 43, 205−214 (2002)], which requires the to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where not Our implies equivalent onset instabilities systems, was systematically studied by Krein et al. [Dokl. Akad. Nauk SSSR N.S. 73, 445 (1950)]. In...

Explicit structure-preserving geometric Particle-in-Cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the PIC [1-12], achieving goal practical applications magnetic fusion research. constructed by discretizing field theory for system charged particles and electromagnetic using Whitney forms, discrete exterior calculus, explicit non-canonical symplectic integration. In addition to truncated infinitely...