Density-matrix Approach to Coherent Transport and the Measurement Problem

Bloch-type equations for description of coherent transport in mesoscopic systems are applied for a study of the continuous measurement process. Both the detector and the measured system are described quantum mechanically. It is shown that the Schrödinger evolution of the entire system cannot be accommodated with the measurement collapse. The latter leads to quantum jumps which can be experimentally detected. In a recent elegant experiment Buks et al. [1] realized a nondistructive continuous monitoring of a quantum system in the linear superposition by using the ballistic point-contact as a detector [1]. Experiments of this type are very important for understanding of the measurement process, in particular since the quantum-mechanical behavior of the detector can be traced out. The latter allows us to investigate of whether the measurement collapse generates experimentally observed effects, which are not described by the Schrödinger equation applied to the entire system. As an example we consider continuous monitoring of 1