MACROSCOPIC LIMIT OF A SOLVABLE DYNAMICAL MODEL

The interaction between an ultrarelativistic particle and a linear arr ay made up of N two-level systems (AgBr molecules) is studied by makin g use of a modified version of the Coleman-Hepp Hamiltonian. Energy-ex change processes between the particle and the molecules axe properly t aken into account, and the evolution of the total system is calculated exactly both when the array is initially in the ground state and in a thermal state. In the weak-coupling, macroscopic (N --> infinity) lim it, the system remains solvable and leads to interesting connections w ith the Jaynes-Cummings model, which describes the interaction of a pa rticle with a maser. The visibility of the interference pattern produc ed by the two branch waves of the particle is computed, and the condit ions under which the spin array behaves as a ''detector'' are investig ated. The behavior of the visibility yields good insights into the iss ue of quantum measurements: It is found that, in the N --> infinity li mit, a superselection-rule space appears in the description of the (ma croscopic) apparatus. In general, an initial thermal state of the ''de tector'' provokes a more substantial loss of quantum coherence than an initial ground state. It is argued that a system increasingly loses c oherence as the temperature of the detector increases. The problem of ''imperfect measurements'' is also briefly discussed.