Details
| Original language | English |
|---|---|
| Article number | 185301 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 45 |
| Issue number | 18 |
| Publication status | Published - 19 Apr 2012 |
Abstract
We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particles arrival at the counter is identified with the loss of normalization for an initial wave packet. Under the sole assumption that the absorbing term vanishes on the initial wavefunction, we show that ΔTΔE ≥ √ ph and , where 〈T〉 denotes the mean arrival time and p is the probability for the particle to be eventually absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and we propose a trapped ion experiment to realize this situation.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Journal of Physics A: Mathematical and Theoretical, Vol. 45, No. 18, 185301, 19.04.2012.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Exact energy-time uncertainty relation for arrival time by absorption
AU - Kiukas, Jukka
AU - Ruschhaupt, Andreas
AU - Schmidt, Piet Oliver
AU - Werner, Reinhard F.
PY - 2012/4/19
Y1 - 2012/4/19
N2 - We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particles arrival at the counter is identified with the loss of normalization for an initial wave packet. Under the sole assumption that the absorbing term vanishes on the initial wavefunction, we show that ΔTΔE ≥ √ ph and , where 〈T〉 denotes the mean arrival time and p is the probability for the particle to be eventually absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and we propose a trapped ion experiment to realize this situation.
AB - We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particles arrival at the counter is identified with the loss of normalization for an initial wave packet. Under the sole assumption that the absorbing term vanishes on the initial wavefunction, we show that ΔTΔE ≥ √ ph and , where 〈T〉 denotes the mean arrival time and p is the probability for the particle to be eventually absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and we propose a trapped ion experiment to realize this situation.
UR - http://www.scopus.com/inward/record.url?scp=84860324846&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/45/18/185301
DO - 10.1088/1751-8113/45/18/185301
M3 - Article
AN - SCOPUS:84860324846
VL - 45
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 18
M1 - 185301
ER -