Phase-Space Beam Summation: a Local Spectrum Analysis of Time-Dependent Radiation

1997 ◽  
Vol 11 (6) ◽  
pp. 739-773 ◽  
Author(s):  
T. Melamed
Keyword(s):  
Phase Space ◽  
Spectrum Analysis ◽  
Time Dependent ◽  
Local Spectrum

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

scholarly journals Time-dependent relaxed magnetohydrodynamics: Inclusion of cross helicity constraint using phase-space action

2020 ◽  
Vol 27 (6) ◽  
pp. 062504 ◽  
Author(s):  
R. L. Dewar ◽  
J. W. Burby ◽  
Z. S. Qu ◽  
N. Sato ◽  
M. J. Hole
Keyword(s):  
Phase Space ◽  
Time Dependent ◽  
Space Action

CHAOTIC SCATTERING IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

1991 ◽  
Vol 01 (03) ◽  
pp. 667-679 ◽  
Author(s):  
YING-CHENG LAI ◽  
CELSO GREBOGI
Keyword(s):  
Phase Space ◽  
Measure Zero ◽  
Invariant Set ◽  
Time Dependent ◽  
Invariant Sets ◽  
Physical Origin ◽  
Chaotic Scattering ◽  
Periodic Oscillations ◽  
Surface Of Section ◽  
Oscillating Potential

We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

A Novel Denoising Algorithm of RFID Label Image Based on Singular Spectrum Analysis of Phase Space Reconstruction

電腦學刊 ◽  
2021 ◽  
Vol 32 (4) ◽  
pp. 042-056
Author(s):  
Yabing Wang Yabing Wang ◽  
Guimin Huang Yabing Wang ◽  
Xiaowei Zhang Guimin Huang ◽  
Yiqun Li Xiaowei Zhang ◽  
Maolin Li Yiqun Li ◽  
...  
Keyword(s):  
Phase Space ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Phase Space Reconstruction ◽  
Singular Spectrum

THE QUADRATIC TIME-DEPENDENT HAMILTONIAN: EVOLUTION OPERATOR, SQUEEZING REGIONS IN PHASE SPACE AND TRAJECTORIES

1994 ◽  
Vol 08 (11n12) ◽  
pp. 1563-1576 ◽  
Author(s):  
S.S. MIZRAHI ◽  
M.H.Y. MOUSSA ◽  
B. BASEIA
Keyword(s):  
Phase Space ◽  
Unitary Transformation ◽  
Uniform Magnetic Field ◽  
Evolution Operator ◽  
Single Mode ◽  
Time Dependent ◽  
Special Cases ◽  
Complete Set ◽  
Hamiltonian Evolution ◽  
General Time

We consider the most general Time-Dependent (TD) quadratic Hamiltonian written in terms of the bosonic operators a and a+, which may represent either a charged particle subjected to a harmonic motion, immersed in a TD uniform magnetic field, or a single mode photon field going through a squeezing medium. We solve the TD Schrödinger equation by a method that uses, sequentially, a TD unitary transformation and the diagonalization of a TD invariant, and we verify that the exact solution is a complete set of TD states. We also obtain the evolution operator which is essential to express operators in the Heisenberg picture. The variances of the quadratures are calculated and a phase space of parameters introduced, in which we identify squeezing regions. The results for some special cases are presented and as an illustrative example the parametric oscillator is revisited and the trajectories in phase space drawn.

scholarly journals Time-dependent quantum correlations in phase space

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
F. Krumm ◽  
W. Vogel ◽  
J. Sperling
Keyword(s):  
Phase Space ◽  
Quantum Correlations ◽  
Time Dependent
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