Quantum arrival and dwell times via idealized clocks
- Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
A number of approaches to the problem of defining arrival- and dwell-time probabilities in quantum theory makes use of idealized 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.
- OSTI ID:
- 22068487
- Journal Information:
- Physical Review. A, Vol. 84, Issue 2; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Probabilities in quantum cosmological models: A decoherent histories analysis using a complex potential
Clock ambiguity and the emergence of physical laws