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Formal Features of a General Theoretical Framework for Decoherence in Open and Closed Systems

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Abstract

Two complementary decoherence formalisms, Environment Induced Decoherence (EID) for open systems and Self Induced Decoherence (SID) for close systems are compared under a common General Theoretical Formalism for Decoherence (GTFD). The differences and similarities of EID and SID are studied, e.g. that the main difference is that EID only considers the relevant information of the proper system S and neglects the rest, while SID considers all possible information available from a certain class of measurement instruments and neglects the non-available information.

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Notes

  1. See the mathematical definition in Eq. (35).

  2. If we were working in a finite dimensional space \(\mathcal{O}\), we could choose α=(i,j), β=(k,l), \(\vert O_{R}^{\alpha} ) =\vert i \rangle \langle j\vert \), (ρ β|=|k〉〈l| so \(( \rho^{\beta}|O_{R}^{\alpha} ) =\mathrm{Tr} ( \vert i \rangle \langle j|k \rangle \langle l\vert ) =\delta_{jk}\delta_{il}\).

  3. In fact, decoherence is one of the steps of the classical limit for macroscopic systems.

  4. Following the laws of the thermodynamic, the total energy is conserved, but the mechanical energy is “degraded” in heat.

  5. The non-rigorous δ(ω−ω′) will soon disappear from this text. In fact the formalism below is precisely a way to eliminate this δ(ω−ω′). We will use this heuristic object “δ(ω−ω′)” just to give some examples below.

  6. See [43] Sect. 8.2 (p. 210) for the definition of these observables.

  7. More precisely \(\varPhi\subset\mathcal{H}\subset \varPhi^{\times}\), and F:Φ→ℂ in the complex case, where Φ × is the anti-dual space (see [48]).

  8. In each example of EID this preferred basis is defined unambiguously, a general definition can be found in [2].

  9. See the discussion about t DS in paper [2].

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Authors and Affiliations

  1. CONICET, IAFE (CONICET-UBA), IFIR and FCEN (University of Buenos Aires), Buenos Aires, Argentina

    Mario Castagnino

  2. CONICET, IAFE (CONICET-UBA) and FCEN (University of Buenos Aires), Buenos Aires, Argentina

    Sebastian Fortin

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  1. Mario Castagnino
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  2. Sebastian Fortin
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Correspondence to Sebastian Fortin.

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Castagnino, M., Fortin, S. Formal Features of a General Theoretical Framework for Decoherence in Open and Closed Systems. Int J Theor Phys 52, 1379–1398 (2013). https://doi.org/10.1007/s10773-012-1456-4

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