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Quantum transport beyond DC

Abstract

This introductory paper for the special issue on Quantum transport beyond DC has two main goals. First, we discuss the reasons why such a special issue is timely and relevant. Second, we present a brief summary of the subsequent papers included in it. Along the paper, we emphasize didactic explanations in front of formal mathematical developments.

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Fig. 1
Fig. 2
Fig. 3

Notes

  1. 1.

    The divergence of the Maxwell generalization of the Ampere law, ×H=J p +∂D/∂t, is equal to zero because the divergence of a rotational is null. Therefore, ⋅(J p +∂D/∂t)=0 (see Ref. [5]).

  2. 2.

    P.A.M. Dirac, wrote in 1929: “The general theory of quantum mechanics is now almost complete. The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.

  3. 3.

    The problem of interpreting |ψ(r,t)|2 as a charge density is clearly seen when dealing with 3 electrons whose (many-particle) wave function “lives” in a configuration space of 9 variables, while the charge density is still defined in the real 3 dimensions.

  4. 4.

    In scenarios with a very large number of particles, which “occupy” almost all the real space, then n(r,t)=Nd r 2,d r 3,…,d r N |ψ(r,r 2,…,r N ,t)|2 can be quite similar to the charge density.

  5. 5.

    The ontological meaning of the dotted empty waves drawn in Fig. 2 depends on which interpretation of quantum mechanics is selected (we mentioned some of them in Refs. [1115]). In any case, such selection is not at all relevant in our argument. We only want to emphasize the experimental fact that, in the ammeter, we only detect a transmitted or reflected electron, but not both.

  6. 6.

    Forced by the necessity in quantum field theory, where the number of particles is a dynamical variable, second quantization is widely used in non-relativistic many-body theory (where the particle number is conserved) as a powerful tool to tackle the indistinguishability of particles.

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Acknowledgements

The authors acknowledge discussion with G. Albareda, F.L. Traversa, T. Novotný, J. Mateos and T. González. This work has been partially supported by the “Ministerio de Ciencia e Innovación” through the Spanish Project TEC2012-31330.

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Correspondence to X. Oriols.

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The authors wish to dedicate this paper to the memory of Dr. Daniel Pardo, Professor of Electronics at Universidad de Salamanca (Spain), who had more influence than he could possible imagine on some parts of this paper.

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Oriols, X., Ferry, D.K. Quantum transport beyond DC. J Comput Electron 12, 317–330 (2013). https://doi.org/10.1007/s10825-013-0461-z

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Keywords

  • Quantum transport
  • Displacement current
  • Quantum noise
  • Multi-time measurement
  • Decoherence
  • Scattering matrix
  • Green’s functions
  • Quantum master equation
  • Bohmian trajectories
  • Time-dependent density functional theory
  • Full counting statistics