Coherent states via decoherence

Abstract

The rate at which pure initial states deteriorate into mixtures is computed for a harmonic oscillator interacting with an environment in thermal equilibrium. The decoherence process resulting from this interaction selects a set of states characterized by maximal stability (or minimal loss of predictive power) which can be quantified by the rate of increase in either linear or statistical entropy. In the weak cou- It was shown for various idealized models (invented primarily to study the "reduction of the state vector" in the context of idealized measurements) that, when the environment -that is, degrees of freedom which interact with the record-keeping "pointer" of a quantum apparatus -is taken into account, the vast majority of pure states become in effect inaccessible [7][8][9]. This is because a continuous interaction with the environment destroys, on a very short decoherence trme scale, the purity of nearly all of the initial superpositions. Thus, only the observations which refer to a preferred set of stable states or the associated set of observables will exhibit one of the key attributes of "classical reality, " -the predictive power of the associated records.Such an interaction can be thought of as a continuous monitoring of the macroscopic quantum system by the environment.Neglecting the self-Hamiltonian of the sys-

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