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Thermalization of Fermionic Quantum Walkers

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Abstract

We consider the discrete time dynamics of an ensemble of fermionic quantum walkers moving on a finite discrete sample, interacting with a reservoir of infinitely many quantum particles on the one dimensional lattice. The reservoir is given by a fermionic quasifree state, with free discrete dynamics given by the shift, whereas the free dynamics of the non-interacting quantum walkers in the sample is defined by means of a unitary matrix. The reservoir and the sample exchange particles at specific sites by a unitary coupling and we study the discrete dynamics of the coupled system defined by the iteration of the free discrete dynamics acting on the unitary coupling, in a variety of situations. In particular, in absence of correlation within the particles of the reservoir and under natural assumptions on the sample’s dynamics, we prove that the one- and two-body reduced density matrices of the sample admit large times limits characterized by the state of the reservoir which are independent of the free dynamics of the quantum walkers and of the coupling strength. Moreover, the corresponding asymptotic density profile in the sample is flat and the correlations of number operators have no structure, a manifestation of thermalization.

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Acknowledgements

This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX- 0025-01) funded by the French program Investissement d’avenir, and a joint Science and Technology Development Fund & Institut Français d’Egypte Grant (STDF-IFE 2015).

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Authors and Affiliations

  1. Faculty of Science, Cairo University, Cairo, 12613, Egypt

    Eman Hamza

  2. Université Grenoble Alpes, CNRS, Institut Fourier, 38000, Grenoble, France

    Alain Joye

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  1. Eman Hamza
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  2. Alain Joye
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Correspondence to Eman Hamza.

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Hamza, E., Joye, A. Thermalization of Fermionic Quantum Walkers. J Stat Phys 166, 1365–1392 (2017). https://doi.org/10.1007/s10955-017-1727-9

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  • DOI: https://doi.org/10.1007/s10955-017-1727-9

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