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Intrinsic irreversibility of quantum systems with diagonal singularity

Author

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  • Antoniou, I.
  • Suchanecki, Z.
  • Laura, R.
  • Tasaki, S.

Abstract

The work of the Brussels-Austin group on irreversibility over the last years has shown that quantum large Poincaré systems with diagonal singularity lead to an extension of quantum theory beyond the conventional Hilbert space framework and logic. We characterize the algebra of observables, the states and the logic of the extended quantum theory of intrinsically irreversible systems with diagonal singularity. We illustrate the general ideas for the Friedrichs model.

Suggested Citation

  • Antoniou, I. & Suchanecki, Z. & Laura, R. & Tasaki, S., 1997. "Intrinsic irreversibility of quantum systems with diagonal singularity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 737-772.
    • Handle: RePEc:eee:phsmap:v:241:y:1997:i:3:p:737-772
    DOI: 10.1016/S0378-4371(97)00167-2
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    Cited by:

    1. Ordóñez, Adolfo R, 1998. "Rigged Hilbert spaces associated with Misra–Prigogine–Courbage theory of irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(3), pages 362-376.
    2. Gomez, Ignacio & Castagnino, Mario, 2015. "A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 99-116.
    3. Castagnino, Mario & Lombardi, Olimpia, 2009. "Towards a definition of the quantum ergodic hierarchy: Ergodicity and mixing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 247-267.
    4. Gialampoukidis, Ilias & Antoniou, Ioannis, 2015. "Age, Innovations and Time Operator of Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 140-155.
    5. Sebastian Fortin & Manuel Gadella & Federico Holik & Juan Pablo Jorge & Marcelo Losada, 2022. "An Algebraic Model for Quantum Unstable States," Mathematics, MDPI, vol. 10(23), pages 1-21, December.

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