| 1. |
- Khrennikov, Andrei, 1958-, et al.
(author)
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Classical signal model reproducing quantum probabilities for single and coincidence detections
- 2012
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In: Journal of Physics, Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 361
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Journal article (peer-reviewed)abstract
- We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wavemodel. QM predicts that the relative probability of coincidence detection, the coefficient g((2)) (0); is zero (for one photon states), but in (semi-) classicalmodels g((2)) (0) >= 1 : In TSD the coefficient g((2)) (0) decreases as 1/epsilon(2)(d); where epsilon(d) > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g((2)) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g((2)) (0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.
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| 2. |
- Khrennikov, Andrei, 1958-, et al.
(author)
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Distance Dependence of Entangled Photons in Waveguides
- 2012
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In: AIP Conference Proceedings. - : AIP. - 0094-243X .- 1551-7616. - 9780735410046 ; 1424, s. 262-269
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Journal article (peer-reviewed)abstract
- The distance dependence of the probability of observing two photons in a waveguide is investigated and the Glauber correlation functions of the entangled photons are considered. First the case of a hollow waveguide with modal dispersion is treated in detail: the spatial and temporal dependence of the correlation functions is evaluated and the distance dependence of the probability of observing two photons upper bounds and asymptotic expressions valid for large distances are derived. Second the generalization to a real fibre with both material and modal dispersion, allowing dispersion shift, is discussed.
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| 3. |
- Khrennikov, Andrei, 1958-, et al.
(author)
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Quantization of propagating modes in optical fibres
- 2012
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In: Physica Scripta. - : IOP Publishing. - 0031-8949 .- 1402-4896. ; 85
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Journal article (peer-reviewed)abstract
- The electromagnetic fields of a single optic fibre mode are quantized based on the observationthat these fields can be derived from a scalar harmonic oscillator function depending on onlytime and the axial wavenumber. Asymptotic results for both the one-photon probabilitydensity and two-photon correlation density functions within the forward light cone arepresented, showing an algebraic decay for large times or distances. This algebraic decay,increasing the uncertainty in the arrival time of the photons, also remains in the presence ofdispersion shift, in qualitative agreement with experimental results. Also presented are explicitformulae to be used in parameter studies to optimize quantum optic fibre communications.
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| 4. |
- Toft, Joachim, 1964-, et al.
(author)
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Decompositions of Gelfand-Shilov kernels into kernels of similar class
- 2012
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In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 396:1, s. 315-322
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Journal article (peer-reviewed)abstract
- We prove that any linear operator with kernel in a Gelfand-Shilov space is a composition of two operators with kernels in the same Gelfand-Shilov space. We also give links on numerical approximations for such compositions. We apply these composition rules to establish Schatten-von Neumann properties for such operators.
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