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One-directional quantum mechanical dynamics and an application to decision making

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  • Bagarello, F.

Abstract

In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian H of the system S. This Hamiltonian quite often, and in particular for systems with a finite number of degrees of freedom, gives rise to reversible and oscillatory dynamics. Sometimes this is not what physical reasons suggest. We discuss here how to use non self-adjoint Hamiltonians to overcome this difficulty: the time evolution we obtain out of them show a preferable arrow of time, and it is not reversible. Several applications are constructed, in particular in connection to information dynamics.

Suggested Citation

  • Bagarello, F., 2020. "One-directional quantum mechanical dynamics and an application to decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315584
    DOI: 10.1016/j.physa.2019.122739
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    References listed on IDEAS

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    1. Bagarello, F., 2011. "Damping in quantum love affairs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2803-2811.
    2. Bagarello, F. & Gargano, F., 2017. "Modeling interactions between political parties and electors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 243-264.
    3. Bagarello, F. & Di Salvo, R. & Gargano, F. & Oliveri, F., 2018. "(H,ρ)-induced dynamics and large time behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 355-373.
    4. Bagarello, Fabio & Oliveri, Francesco, 2014. "Dynamics of closed ecosystems described by operators," Ecological Modelling, Elsevier, vol. 275(C), pages 89-99.
    5. Asano, Masanari & Basieva, Irina & Khrennikov, Andrei & Ohya, Masanori & Tanaka, Yoshiharu, 2012. "Quantum-like dynamics of decision-making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2083-2099.
    6. Emmanuel Haven & Andrei Khrennikov & Terry Robinson, 2017. "Quantum Methods in Social Science:A First Course," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0080, February.
    7. Bagarello,Fabio, 2019. "Quantum Concepts in the Social, Ecological and Biological Sciences," Cambridge Books, Cambridge University Press, number 9781108492126, October.
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    Cited by:

    1. Bagarello, F. & Gargano, F. & Roccati, F., 2020. "Modeling epidemics through ladder operators," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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