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Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

Gabriel G. Carlo*, Leonardo Ermann†, Alejandro M. F. Rivas‡, and María E. Spina§

  • Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina

  • *carlo@tandar.cnea.gov.ar
  • †ermann@tandar.cnea.gov.ar
  • ‡rivas@tandar.cnea.gov.ar
  • §spina@tandar.cnea.gov.ar
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Phys. Rev. E 93, 042133 – Published 25 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042133

Abstract

We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏeff values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏeff and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.

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Phys. Rev. E 93, 042133– Published 25 April, 2016
  • Received 11 February 2016

©2016 American Physical Society

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