dorsal/arxiv
View SchemaDecoherent Histories Approach to the Arrival Time Problem
| Authors | J. J. Halliwell, E. Zafiris |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9706045 |
| URL | https://arxiv.org/abs/quant-ph/9706045 |
| DOI | 10.1103/PhysRevD.57.3351 |
| Journal | Phys.Rev. D57 (1998) 3351-3364 |
Abstract
We use the decoherent histories approach to quantum theory to compute the probability of a non-relativistic particle crossing $x=0$ during an interval of time. For a system consisting of a single non-relativistic particle, histories coarse-grained according to whether or not they pass through spacetime regions are generally not decoherent, except for very special initial states, and thus probabilities cannot be assigned. Decoherence may, however, be achieved by coupling the particle to an environment consisting of a set of harmonic oscillators in a thermal bath. Probabilities for spacetime coarse grainings are thus calculated by considering restricted density operator propagators of the quantum Brownian motion model. We also show how to achieve decoherence by replicating the system $N$ times and then projecting onto the number density of particles that cross during a given time interval, and this gives an alternative expression for the crossing probability. The latter approach shows that the relative frequency for histories is approximately decoherent for sufficiently large $N$, a result related to the Finkelstein-Graham-Hartle theorem.
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"abstract": "We use the decoherent histories approach to quantum theory to compute the\nprobability of a non-relativistic particle crossing $x=0$ during an interval of\ntime. For a system consisting of a single non-relativistic particle, histories\ncoarse-grained according to whether or not they pass through spacetime regions\nare generally not decoherent, except for very special initial states, and thus\nprobabilities cannot be assigned. Decoherence may, however, be achieved by\ncoupling the particle to an environment consisting of a set of harmonic\noscillators in a thermal bath. Probabilities for spacetime coarse grainings are\nthus calculated by considering restricted density operator propagators of the\nquantum Brownian motion model. We also show how to achieve decoherence by\nreplicating the system $N$ times and then projecting onto the number density of\nparticles that cross during a given time interval, and this gives an\nalternative expression for the crossing probability. The latter approach shows\nthat the relative frequency for histories is approximately decoherent for\nsufficiently large $N$, a result related to the Finkelstein-Graham-Hartle\ntheorem.",
"arxiv_id": "quant-ph/9706045",
"authors": [
"J. J. Halliwell",
"E. Zafiris"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevD.57.3351",
"journal_ref": "Phys.Rev. D57 (1998) 3351-3364",
"title": "Decoherent Histories Approach to the Arrival Time Problem",
"url": "https://arxiv.org/abs/quant-ph/9706045"
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