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Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment

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Abstract

We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.

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Authors and Affiliations

  1. Abdus Salam ICTP, Strada Costiera 11, 34151, Trieste, Italy

    Fernando Iemini

  2. Departamento de Física – ICEx – Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos 6627, Belo Horizonte, 31270-901, Minas Gerais, Brazil

    Leonardo da Silva Souza, André T. Cesário, Thiago O. Maciel & Reinaldo O. Vianna

  3. Universidade Tecnológica Federal do Paraná (UTFPR), Campus Cornélio Procópio, Avenida Alberto Carazzai 1640, Cornélio Procópio, 86300-000, Paraná, Brazil

    Tiago Debarba

Authors
  1. Fernando Iemini
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  2. Leonardo da Silva Souza
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  3. Tiago Debarba
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  4. André T. Cesário
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  5. Thiago O. Maciel
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  6. Reinaldo O. Vianna
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Correspondence to Fernando Iemini.

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Iemini, F., da Silva Souza, L., Debarba, T. et al. Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment. Eur. Phys. J. D 71, 119 (2017). https://doi.org/10.1140/epjd/e2017-70671-3

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  • DOI: https://doi.org/10.1140/epjd/e2017-70671-3

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