The Construction of a Quantum Markov Partition

Abstract

We present a method for constructing a quantum Markov partition. Its elements are obtained by quantizing the characteristic function of the classical rectangles. The result is a set of quantum operators which behave asymptotically as projectors over the classical rectangles except from edge and corner effects. We investigate their spectral properties and different methods of construction. The quantum partition is shown to induce a symbolic decomposition of the quantum evolution operator. In particular, an exact expression for the traces of the propagator is obtained having the same structure as Gutzwiller periodic orbit sum.

9 latex pages including 7 ps figures

References in corpus (1)

• Boundary contributions to the semiclassical traces of the baker's map

Cited by in corpus (8)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Resonances in open quantum maps
• Quantum Iterated Function Systems
• Quantum dynamical entropy and decoherence rate
• Decoherence and linear entropy increase in the quantum baker's map
• Quantum symmetries and the Weyl-Wigner product of group representations
• Transient features of quantum open maps