Constructing solvable models of the quantum measurement process

Hiromichi Nakazato, Saverio Pascazio

Hiromichi Nakazato, Saverio Pascazio

By making use of Schwinger’s oscillator model of angular momentum, we put forward an interesting connection among three solvable Hamiltonians, widely used for discussions on the quantum measurement problem. This connection implies that a particular macroscopic limit has to be taken for these models to be physically sensible. PACS: 03.65.Fd; 03.80.+r; 42.52.+x; 03,65.BzThe quantum measurement problem [1] [2] has been a central issue in the foundations and interpretation of quantum mechanics, and is profoundly related to the investigation of the internal consistency of quantum theory. In order to find a resolution within the quantum mechanical framework, one usually describes a quantum measurement process in the following way: An elementary particle Q, on which the measurement is performed, interacts with a detection system D, which is considered to be made up of N elementary constituents. Generally, it is not easy to handle such a complicated system like Q + D, however, it is also true that several solvable models of measurement processes are now at hand. Among these are the Cini [3] and Coleman-Hepp [4] Hamiltonians and its modified version [5], which were all proposed

Chang-Pu Sun

In this paper, a quantum dynamical model describing the quantum-measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and the macroscopic limit with very large particle number in the measuring instrument, this model generally realizes the wave-packet collapse in quantum measurement as a consequence of the Schr\"odinger time evolution in either the exactly solvable case or the non-exactly-solvable case. For the latter, the quasiadiabatic case is explicitly analyzed by making use of the high-order adiabatic-approximation method, which manifests the wave-packet collapse as well as in the exactly solvable case. By highlighting these analyses, it is finally found that an essence of the dynamical model of wave-packet collapse is the factorization of the Schr\"odinger evolution rather than the exact solvability. Therefore many dynamical models including the previous well-known ones, whether they are exactly solvable or not, can be shown to be only the concrete realizations of this factorizability.

ARMEN E. ALLAHVERDYAN, Roger Balian

Hiromichi Nakazato, Saverio Pascazio

A model Hamiltonian describing an energy-exhange process between an ultrarelativistic particle and a one-dimensional spin array is proposed and solved exactly. Interesting relations with the quantum measurement problem are discussed.

Gérard G. Emch