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- Nyqvist, Robert
(författare)
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Algebraic Dynamical Systems, Analytical Results and Numerical Simulations
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study discrete dynamical system, given by a polynomial, over both finite extension of the fields of p-adic numbers and over finite fields. Especially in the p-adic case, we study fixed points of dynamical systems, and which elements that are attracted to them. We show with different examples how complex these dynamics are.For certain polynomial dynamical systems over finite fields we prove that the normalized average of the numbers of linear factors modulo prime numbers exists. We also show how to calculate the average, by using Chebotarev's Density Theorem. The non-normalized version of the average of the number of linear factors of linearized polynomials modulo prime numbers, tends to infinity, so in that case we find an asymptotic formula instead.We have also used a computer to study different behaviors, such as iterations of polynomials over the p-adic fields and the asymptotic relation mention above. In the last chapter we present the computer programs used in different part of the thesis.
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| 2. |
- Adenier, Guillaume, et al.
(författare)
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Fair sampling and rotational invariance in EPR experiments
- 2007
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Ingår i: The Nature of Light: What Are Photons?. - : SPIE. - 9780819468123
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We have previously shown that the use of the fair sampling assumption in EPR experiments could be questioned on the basis of experimental data. We continue our analysis of the data from the optical EPR experimental performed by Weihs et al. in Innsbruck 1997-1998, and we discuss whether a non-rotationally invariant source can account for the experimental results.
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| 3. |
- Adenier, Guillaume, et al.
(författare)
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Fair Sampling vs No-Signalling Principle in EPR experiments
- 2007
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Ingår i: Beyond the Quantum. - : World Scientific Publishing, Singapore. - 9789812771179 ; , s. 181-187
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Konferensbidrag (populärvet., debatt m.m.)abstract
- We present some recent results of a new statistical analysis of the optical EPR experiment performed by Weihs et al in Innsbruck 1997-1998. Under the commonly used assumption of fair sampling, we show that the coincidence counts exhibit a small and anomalous non-signalling component, which seems impossible to explain by using the conventional quantum mechanics, and we discuss some possible interpretations of this phenomenon.
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| 4. |
- Adenier, Guillaume, et al.
(författare)
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Is the fair sampling assumption supported by EPR experiments?
- 2007
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Ingår i: Journal of Physics B: At. Mol. Opt. Phys.. - : Institute of Physics ( IOP ), Bristol. - 0953-4075 .- 1361-6455. ; 40:1, s. 131-141
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Tidskriftsartikel (refereegranskat)abstract
- We analyse optical EPR experimental data performed by Weihs et al in Innsbruck 1997–1998. We show that for some linear combinations of the raw coincidence rates, the experimental results display some anomalous behaviour that a more general source state (like non-maximally entangled state) cannot straightforwardly account for. We attempt to explain these anomalies by taking account of the relative efficiencies of the four channels. For this purpose, we use the fair sampling assumption, and assume explicitly that the detection efficiencies for the pairs of entangled photons can be written as a product of the two corresponding detection efficiencies for the single photons. We show that this explicit use of fair sampling cannot be maintained to be a reasonable assumption as it leads to an apparent violation of the no-signalling principle.
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