Timeline for Continuous Measurement in Quantum Mechanics
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 5, 2013 at 16:16 | comment | added | Ron Maimon | @SebastianMeznaric: This is usually deterministic--- the "mixed state" stops being mixed as the time-steps become small, as the probability of deviating from the eigenvector path goes as "epsilon squared", while the number of timesteps only goes as 1/epsilon, so that in the continuous measurement limit, you have deterministic evolution. This only fails when the eigenvalues collide, which is measure zero, but at this point, you get a definite stochastic splitting depending only on the eigenvectors of the Hamiltonian just after and just before the collision. | |
| May 4, 2012 at 16:18 | comment | added | Sebastian Meznaric | I didn't see your comment earlier Ron. This is not usually deterministic. If $H_t$ is not constant then the spectrum may well change. Most importantly, if the eigenvectors change then even at a later step a pure state which was before an eigenvector of the Hamiltonian will be mapped to a mixed state due to it now not being an eigenvector anymore. That is if I am understanding the question correctly, and the distribution gets mapped to the mixed state corresponding to the distribution of outcomes rather than a particular outcome. | |
| Aug 3, 2011 at 19:10 | comment | added | Ron Maimon | This answer is not accurate--- the stochastic process, (on every step after the first (ignoring collisions) is entirely deterministic, and takes pure states to pure states. | |
| Aug 2, 2011 at 5:08 | comment | added | Alexander Moll | Thanks, Sebastian - this certainly settles my first question, and you're right to point out the obvious difficulties with this construction in the Heisenberg (or interaction) picture. I do think that the "Quantum Zeno effect" (see Ron's answer below) is what I was after, and I'd need to read a lot of what's out there before trying to get back on the horse. Thanks again! | |
| Aug 1, 2011 at 17:49 | history | answered | Sebastian Meznaric | CC BY-SA 3.0 |