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.

Convergence to equilibrium under a random Hamiltonian.

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.