Semiclassical accuracy in phase space for regular and chaotic dynamics
نویسندگان
چکیده
منابع مشابه
Eigenstates ignoring regular and chaotic phase-space structures.
We report the failure of the semiclassical eigenfunction hypothesis if regular classical transport coexists with chaotic dynamics. All eigenstates, instead of being restricted to either a regular island or the chaotic sea, ignore these classical phase-space structures. We argue that this is true even in the semiclassical limit for extended systems with transporting regular islands such as the s...
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We introduce a criterion for the existence of regular states in systems with a mixed phase space. If this condition is not fulfilled chaotic eigenstates substantially extend into a regular island. Wave packets started in the chaotic sea progressively flood the island. The extent of flooding by eigenstates and wave packets increases logarithmically with the size of the chaotic sea and the time, ...
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Following recent interest in a kinetic description of the semiclassical Bloch electron dynamics, we propose a new formulation based on the previously developed Lie-Poisson formulation of dynamics. It includes modifications required to account for the Berry curvature contribution to the electron's equation of motion as well as essential ingredients of a quantum treatment of spin- 1/2 degrees of ...
متن کاملPhase Synchronization in Regular and Chaotic Systems
In this contribution we present a brief introduction to the theory of synchronization of self-sustained oscillators. Classical results for synchronization of periodic motions and eeects of noise on this process are reviewed and compared with recently found phase synchronization phenomena in chaotic oscillators. The basic notions of phase and frequency locking are reconsidered within a common fr...
متن کاملStrong Phase-Space Semiclassical Asymptotics
Wigner and Husimi transforms have long been used for the phasespace reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the strong topology, i.e. approximation of Wigner functions by solutions of the Liou...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2004
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.70.026223