Physics – Quantum Physics
Scientific paper
2001-02-03
Int.J.Mod.Phys. A17 (2002) 4007-4024
Physics
Quantum Physics
16 pages, latex; new material and references added
Scientific paper
10.1142/S0217751X0201056X
We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $\rho(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from $t = 0$ to $T$, where $E$ is a projector obeying $E\rho(0) E = \rho(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness conditions in $t$. Then the probability of always finding $E(t) = 1$ from $t = 0$ to $T$ is unity. Generically $E(T) \neq E$ and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.
Balachandran Aiyalam P.
Roy Shasanka Mohan
No associations
LandOfFree
Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-517584