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We present a general analytic method for evaluating the generallytime-dependent pointer states of a subsystem, which are defined by theircapability not to entangle with the states of another subsystem. In this way,we show how in practice the global state of the system and the environment mayevolve into a diagonal state as a result of the natural evolution of the totalcomposite system. We explore the conditions under which the pointer states ofthe system become independent of time; so that a preferred basis of measurementcan be realized. As we show, these conditions include the so-called quantumlimit of decoherence and the so-called quantum measurement limit; as well assome other specific conditions which are discussed in the paper. We relate themathematical conditions for having time-independent pointer states to someclasses of possible symmetries in the Hamiltonian of the total compositesystem. Indeed, our theory would serve as a generalization of the existingtheory for determination of the preferred basis of measurement. By exploitingthis new theory we can obtain those regimes of the parameter space for a giventotal Hamiltonian defining our system-environment model for which a preferredbasis of measurement can be realized. Moreover, we can predict thecorresponding preferred basis of measurement for each regime. We can alsoobtain the time-dependent pointer states of the system and the environment inmost of the other regimes where the pointer states of the system aretime-dependent and a preferred basis of measurement cannot be realized at all.This ability to obtain time-dependent pointer states is specifically importantin decoherence studies; as pointer states correspond to those initialconditions for the state of the system and the environment for which we canhave longer decoherence times.

Time-dependent pointer states and determination of the preferred basis of measurement