Arrival Times in Quantum Theory from an Irreversible Detector Model

Abstract

We investigate a detector scheme designed to measure the arrival of a particle at $x=0$ during a finite time interval. The detector consists of a two state system which undergoes a transition from one state to the other when the particle crosses $x=0$, and possesses the realistic feature that it is effectively irreversible as a result of being coupled to a large environment. The probabilities for crossing or not crossing $x=0$ thereby derived coincide with earlier phenomenologically proposed expressions involving a complex potential. The probabilities are compared with similar previously proposed expressions involving sums over paths, and a connection with time operator approaches is also indicated.

19 pages, plain Tex (Fourth revision). To appear in Prog.Th.Phys. Vol. 102, No. 4

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