1106.4767 (J. M. Yearsley et al.)

Quantum Arrival and Dwell Times via Idealised Clocks    [PDF]

J. M. Yearsley, D. A. Downs, J. J. Halliwell, A. K. Hashagen

A number of approaches to the problem of defining arrival and dwell time
probabilities in quantum theory make use of idealised models of clocks. An
interesting question is the extent to which the probabilities obtained in this
way are related to standard semiclassical results. In this paper we explore
this question using a reasonably general clock model, solved using path
integral methods. We find that in the weak coupling regime where the energy of
the clock is much less than the energy of the particle it is measuring, the
probability for the clock pointer can be expressed in terms of the probability
current in the case of arrival times, and the dwell time operator in the case
of dwell times, the expected semiclassical results. In the regime of strong
system-clock coupling, we find that the arrival time probability is
proportional to the kinetic energy density, consistent with an earlier model
involving a complex potential. We argue that, properly normalized, this may be
the generically expected result in this regime. We show that these conclusions
are largely independent of the form of the clock Hamiltonian.

View original: http://arxiv.org/abs/1106.4767