A discussion of chaos degree for quantum dynamics in spin 1/2 system

Kei Inoue

Roderick V. Jensen, R. Shankar

Numerical studies of the dynamics of finite quantum spin chains are presented which show that quantum systems with few degrees of freedom ($N=7$) can be described by equilibrium statistical mechanics. The success of the statistical description is seen to depend on the interplay between the initial state, the observable, and the Hamiltonian. This work clarifies the impact of integrability and conservation laws on statistical behavior. The relation to quantum chaos is also discussed.

Declan Mulhall

A. G. Lazerson, Alexey Alexeevich Boikov

Nicolás Mirkin, Diego A. Wisniacki

The environment of an open quantum system is usually modelled as a large and complex many-body quantum system. However, the question of how large and complex this many-body quantum system must be in order to play the role of a genuine environment and thus generate decoherence is an often elusive key-point in the literature. In this work, by studying the reduced dynamics of a spin connected to a generic spin chain, we show that the physical mechanism responsible for generating stronger decoherence on the reduced spin relies mostly on the chaotic behaviour of the chain. More interestingly, even in the case of an extremely short spin chain composed of two spins, by analyzing the decoherence dynamics of the reduced system we are able to reproduce the whole integrable to chaos transition. Finally, we discuss implications on quantum control experiments and show that quantum chaos reigns over the best degree of control achieved, even in small chains.

稔彦 大野, Toshihko Ohno