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  • Open Access

Effective Dynamics of Disordered Quantum Systems

Chahan M. Kropf*, Clemens Gneiting, and Andreas Buchleitner†

  • Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany

  • *Chahan.Kropf@physik.uni-freiburg.de
  • †a.buchleitner@physik.uni-freiburg.de
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Phys. Rev. X 6, 031023 – Published 19 August, 2016

DOI: https://doi.org/10.1103/PhysRevX.6.031023

Abstract

We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates that encode the specific statistical properties of the Hamiltonian’s eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.

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Engineering a device or designing a physical experiment of sufficient complexity generally means that it is impossible to control all of the relevant parameters of the system. This situation is already evident even for a simple copper wire in which the presence of randomly distributed impurities can—but does not necessarily—have a significant effect on the resistance of the lead. While different wires will therefore exhibit different resistances, scientists are not so much interested in the properties of single wires but rather in the generic effect of the impurities after averaging. In the case of quantum systems, averaging over such uncontrolled parameters reveals dynamics characterized by complex, often counterintuitive, traits that, in general, deviate nontrivially from the behavior of single realizations. A comprehensive understanding of these dynamics requires an adequate mathematical method, and our work focuses on elucidating such a method.

We use a statistical approach—quantum master equations—to describe the ensemble-average dynamics of quantum systems with static, Hamiltonian disorder. These equations provide a means to distinguish the coherent and incoherent contributions to the time evolution of the averaged state. Using paradigmatic examples of a single qubit characterized by spectral disorder, we connect the characteristic properties of the disorder with their dynamical impact (i.e., average-induced decoherence) both on transient and on asymptotic time scales. We also consider more general cases of d dimensions to show that our method is scalable.

We expect that our findings will further our understanding of how to handle disordered systems and reveal new ways in which disorder can be actively employed in order to tailor desired quantum features.

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Phys. Rev. X 6, 031023– Published 19 August, 2016
  • Received 27 November 2015
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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