Explicit symplectic-like integration with corrected map for inseparable Hamiltonian

2020 ◽  
Vol 501 (1) ◽  
pp. 1511-1519
Author(s):  
Junjie Luo ◽  
Weipeng Lin ◽  
Lili Yang
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Eighth Order ◽  
Time Step ◽  
Extended Phase ◽  
Energy Error ◽  
Phase Space Structure ◽  
Compact Binary ◽  
Three Body

ABSTRACT Symplectic algorithms are widely used for long-term integration of astrophysical problems. However, this technique can only be easily constructed for separable Hamiltonian, as preserving the phase-space structure. Recently, for inseparable Hamiltonian, the fourth-order extended phase-space explicit symplectic-like methods have been developed by using the Yoshida’s triple product with a mid-point map, where the algorithm is more effective, stable and also more accurate, compared with the sequent permutations of momenta and position coordinates, especially for some chaotic case. However, it has been found that, for the cases such as with chaotic orbits of spinning compact binary or circular restricted three-body system, it may cause secular drift in energy error and even more the computation break down. To solve this problem, we have made further improvement on the mid-point map with a momentum-scaling correction, which turns out to behave more stably in long-term evolution and have smaller energy error than previous methods. In particular, it could obtain a comparable phase-space distance as computing from the eighth-order Runge–Kutta method with the same time-step.

scholarly journals Discrete phase-space structure of n-qubit mutually unbiased bases

2009 ◽  
Vol 324 (1) ◽  
pp. 53-72 ◽  
Author(s):  
A.B. Klimov ◽  
J.L. Romero ◽  
G. Björk ◽  
L.L. Sánchez-Soto
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Mutually Unbiased Bases ◽  
Phase Space Structure ◽  
Discrete Phase

scholarly journals Phase space structure of generalized Gaussian cat states

2010 ◽  
Vol 374 (43) ◽  
pp. 4385-4392 ◽  
Author(s):  
Fernando Nicacio ◽  
Raphael N.P. Maia ◽  
Fabricio Toscano ◽  
Raúl O. Vallejos
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Phase Space Structure ◽  
Cat States

scholarly journals Characterisation of negative ion beam focusing based on phase space structure

2020 ◽  
Vol 22 (2) ◽  
pp. 023017 ◽  
Author(s):  
Yasuaki Haba ◽  
Kenichi Nagaoka ◽  
Katsuyoshi Tsumori ◽  
Masashi Kisaki ◽  
Haruhisa Nakano ◽  
...  
Keyword(s):  
Phase Space ◽  
Ion Beam ◽  
Space Structure ◽  
Negative Ion ◽  
Phase Space Structure ◽  
Beam Focusing

scholarly journals Phase space structure and fractal trajectories in 1½ degree of freedom Hamiltonian systems whose time dependence is quasiperiodic

1998 ◽  
Vol 5 (2) ◽  
pp. 69-74 ◽  
Author(s):  
M. G. Brown
Keyword(s):  
Phase Space ◽  
Time Dependence ◽  
Hamiltonian Systems ◽  
Fluid Flows ◽  
Space Structure ◽  
Degree Of Freedom ◽  
Periodic Functions ◽  
Phase Space Structure ◽  
Fractal Properties ◽  
Incompressible Fluid Flows

Abstract. We consider particle motion in nonautonomous 1 degree of freedom Hamiltonian systems for which H(p,q,t) depends on N periodic functions of t with incommensurable frequencies. It is shown that in near-integrable systems of this type, phase space is partitioned into nonintersecting regular and chaotic regions. In this respect there is no different between the N = 1 (periodic time dependence) and the N = 2, 3, ... (quasi-periodic time dependence) problems. An important consequence of this phase space structure is that the mechanism that leads to fractal properties of chaotic trajectories in systems with N = 1 also applies to the larger class of problems treated here. Implications of the results presented to studies of ray dynamics in two-dimensional incompressible fluid flows are discussed.

Phase Space Structure Around Oblate Planetary Satellites

2006 ◽  
Vol 29 (1) ◽  
pp. 113-120 ◽  
Author(s):  
Juan F. San-Juan ◽  
Martin Lara ◽  
Sebastian Ferrer
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Phase Space Structure ◽  
Planetary Satellites
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