Pointer States in the Born-Markov Approximation

Quantum states least affected by interactions with environment play a pivotal role in both foundations and applications of quantum mechanics. Known as pointer states, they surprisingly lacked a systematic description. Working within the Born-Markov approximation, we combine methods of group theory and open quantum systems and derive general conditions describing pointer states. Contrary to common expectations, they are in general different from coherent states. Thus the two notions of being "closest to the classical"—one defined by the uncertainty relations and the other by the interaction with the environment—are in general different. As an example, we study spin-spin and spin-boson models with an arbitrary central spin $J$.