Classical and quantum discrete dynamical systems

Quantum Dynamical Entropies for Classical Stochastic Systems

We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit expression for the stochastic dynamical entropy with a clear informationtheoretical interpretation. Finally, we compare our construction with other recent proposals.

Quantum-classical transition in nonlinear dynamical systems.

Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical tran...

Quantum Dynamical Systems with Quasi–Discrete Spectrum

We study totally ergodic quantum dynamical systems with quasi–discrete spectrum. We investigate the classification problem for such systems in terms of algebraic invariants. The results are noncommutative analogs of (a part of) the theory of Abramov. Supported in part by the National Science Foundation under grant DMS–9801612

Ju n 20 04 Noise Induced Dissipation in Discrete - Time Classical and Quantum Dynamical Systems

Classical versus quantum errors in quantum computation of dynamical systems.

We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum motion when the system's parameters are perturbed or when there are unitary errors in the quantum gates implementing the quantum algorithm. While the first k...