Related papers: Notes on orbit and spin tracking in an electrostat…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Sere and to Coti-Zelati, Ekeland and Sere,…
We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have…
Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…
The general theoretical description of the influence of oscillating horizontal magnetic and quasimagnetic fields on the spin evolution in storage rings is presented. Previous results are generalized to the case when both of the horizontal…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
We investigate a stationary process's crypticity---a measure of the difference between its hidden state information and its observed information---using the causal states of computational mechanics. Here, we motivate crypticity and cryptic…
Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously…
In this article we briefly review the current state of the experimental research on spin polarized transport in organic semiconductors. These systems, which include small molecular weight compounds and polymers, are central in the rapidly…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (\rho,z,p_\rho,p_z) and have p_\phi = m\hbar where m is the azimuthal…
Precision measurements in storage rings are increasingly limited by the ability to monitor collective spin dynamics coherently over long time scales. Existing polarimetry techniques rely on destructive scattering processes that preclude…
There is a quantitative error in the derivation for the spin decoherence rate by Talman in IPAC2012. The crucial point is a subtle confusion between the concept of `longitudinal' as in `along the reference orbit' and `parallel to the…
A spin nematic is a state which breaks spin SU(2) symmetry while preserving translational and time reversal symmetries. Spin nematic order can arise naturally from charge fluctuations of a spin stripe state. Focusing on the possible…
Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…
We prove a Nekhoroshev-type theorem for nearly integrable symplectic map. As an application of the theorem, we obtain the exponential stability symplectic algorithms. Meanwhile, we can get the bounds for the perturbation, the variation of…
The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, $\E$, such that the question of membership in this orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice corollaries: the…
Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of…
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…