The Role of Heat Bath and Pointer Modes in Quantum Measurement

We present an exact derivation of a process in which a microscopic measured system interacts with "heat bath" and pointer modes of a measuring device, via a linear coupling involving Hermitian operator $\Lambda$ of the system. In the limit of strong interaction with these modes, over a small time interval, we show that the measured system and the "pointer" part of the measuring device evolve into a statistical mixture of direct-product states such that the system is in each eigenstate of $\Lambda$ with the correct quantum-mechanical probability, whereas the expectation values of pointer-space operators retain amplified information of the system's eigenstate.