scholarly journals Quantized invariant tori in Andreev billiards of mixed phase space

2006 ◽  
Vol 73 (21) ◽  
Author(s):  
Z. Kaufmann ◽  
A. Kormányos ◽  
J. Cserti ◽  
C. J. Lambert
Keyword(s):  
Phase Space ◽  
Invariant Tori ◽  
Mixed Phase ◽  
Andreev Billiards

scholarly journals Excitation Spectrum of Andreev Billiards with a Mixed Phase Space

1999 ◽  
Vol 82 (14) ◽  
pp. 2951-2954 ◽  
Author(s):  
H. Schomerus ◽  
C. W. J. Beenakker
Keyword(s):  
Phase Space ◽  
Excitation Spectrum ◽  
Mixed Phase ◽  
Andreev Billiards

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 Illustration of microphysical processes in Amazonian deep convective clouds in the Gamma phase space: Introduction and potential applications

2017 ◽  
Author(s):  
Micael A. Cecchini ◽  
Luiz A. T. Machado ◽  
Manfred Wendisch ◽  
Anja Costa ◽  
Martina Krämer ◽  
...  
Keyword(s):  
Phase Space ◽  
Cloud Droplet ◽  
Mixed Phase ◽  
Relative Dispersion ◽  
Gamma Phase ◽  
Liquid Droplets ◽  
Phase Layer ◽  
Cloud Properties ◽  
Common Framework ◽  
Space Approach

Abstract. The behavior of tropical clouds remains a major open scientific question, given that the associated phys-ics is not well represented by models. One challenge is to realistically reproduce cloud droplet size dis-tributions (DSD) and their evolution over time and space. Many applications, not limited to models, use the Gamma function to represent DSDs. However, there is almost no study dedicated to understanding the phase space of this function, which is given by the three parameters that define the DSD intercept, shape, and curvature. Gamma phase space may provide a common framework for parameterizations and inter-comparisons. Here, we introduce the phase-space approach and its characteristics, focusing on warm-phase microphysical cloud properties and the transition to the mixed-phase layer. We show that trajectories in this phase space can represent DSD evolution and can be related to growth processes. Condensational and collisional growth may be interpreted as pseudo-forces that induce displacements in opposite directions within the phase space. The actually observed movements in the phase space are a result of the combination of such pseudo-forces. Additionally, aerosol effects can be evaluated given their significant impact on DSDs. The DSDs associated with liquid droplets that favor cloud glaciation can be delimited in the phase space, which can help models to adequately predict the transition to the mixed phase. We also consider possible ways to constrain the DSD in two-moment bulk microphysics schemes, where the relative dispersion parameter of the DSD can play a significant role. Overall, the Gamma phase-space approach can be an invaluable tool for studying cloud microphysical evolution and can be readily applied in many scenarios that rely on Gamma DSDs.

Quantum chaotic scattering with a mixed phase space: The three-disk billiard in a magnetic field

2000 ◽  
Vol 61 (1) ◽  
pp. 382-389 ◽  
Author(s):  
Markus Eichengrün ◽  
Walter Schirmacher ◽  
Wolfgang Bregmann
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Mixed Phase ◽  
Chaotic Scattering

scholarly journals Semiclassical Spectra from Periodic-Orbit Clusters in a Mixed Phase Space

1997 ◽  
Vol 79 (6) ◽  
pp. 1022-1025 ◽  
Author(s):  
Henning Schomerus ◽  
Fritz Haake
Keyword(s):  
Phase Space ◽  
Periodic Orbit ◽  
Mixed Phase

scholarly journals Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

2017 ◽  
Vol 34 ◽  
Author(s):  
Ali Taani ◽  
Juan C. Vallejo
Keyword(s):  
Phase Space ◽  
Invariant Tori ◽  
Dynamical Behavior ◽  
Dark Halo ◽  
Short Axis ◽  
Poincaré Section ◽  
Invariant Curves ◽  
Poincare Section ◽  
Dynamical Behaviors ◽  
Stable Periodic

AbstractWe describe the dynamical behavior of isolated old ( ⩾ 1Gyr) objects-like Neutron Stars (NSs). These objects are evolved under smooth, time-independent, gravitational potentials, axisymmetric and with a triaxial dark halo. We analysed the geometry of the dynamics and applied the Poincaré section for comparing the influence of different birth velocities. The inspection of the maximal asymptotic Lyapunov (λ) exponent shows that dynamical behaviors of the selected orbits are nearly the same as the regular orbits with 2-DOF, both in axisymmetric and triaxial when (ϕ, qz)= (0,0). Conversely, a few chaotic trajectories are found with a rotated triaxial halo when (ϕ, qz)= (90, 1.5). The tube orbits preserve direction of their circulation around either the long or short axis as appeared in the triaxial potential, even when every initial condition leads to different orientations. The Poincaré section shows that there are 2-D invariant tori and invariant curves (islands) around stable periodic orbits that bound to the surface of 3-D tori. The regularity of several prototypical orbits offer the means to identify the phase-space regions with localized motions and to determine their environment in different models, because they can occupy significant parts of phase-space depending on the potential. This is of particular importance in Galactic Dynamics.

scholarly journals Effective dynamics in Hamiltonian systems with mixed phase space

2005 ◽  
Vol 71 (3) ◽  
Author(s):  
Adilson E. Motter ◽  
Alessandro P. S. de Moura ◽  
Celso Grebogi ◽  
Holger Kantz
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Mixed Phase ◽  
Effective Dynamics

Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space

2020 ◽  
Vol 91 ◽  
pp. 105440
Author(s):  
Diogo Ricardo da Costa ◽  
Matheus S. Palmero ◽  
J.A. Méndez-Bermúdez ◽  
Kelly C. Iarosz ◽  
José D. Szezech Jr ◽  
...  
Keyword(s):  
Phase Space ◽  
Mixed Phase

scholarly journals Diffusion phenomena in a mixed phase space

2020 ◽  
Vol 30 (1) ◽  
pp. 013108 ◽  
Author(s):  
Matheus S. Palmero ◽  
Gabriel I. Díaz ◽  
Peter V. E. McClintock ◽  
Edson D. Leonel
Keyword(s):  
Phase Space ◽  
Mixed Phase ◽  
Diffusion Phenomena
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