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- W2028602934 abstract "We present a new specific interpretation of a previously derived general method [D. Sanjin'es and J.-P. Gallinar, J. Phys.: Condens. Matter 11, 3729 (1999)] for studying electronic wave-packet evolution within the one-band approximation. As a result of analytical properties of Bessel functions, it is shown that in a homogeneous time-dependent electric field an electron's motion in a tight-binding band can be interpreted in terms of a phasor (polygonal) construction in the complex plane. The length of the phasors is proportional to the electronic-hopping matrix element and to the time increment of the dynamical evolution. When this time increment is infinitesimal, the directions of the phasors are expressed in terms of a time integral of the external field. Wave-packet mean position and velocity are also geometrically interpreted. Based upon our polygonal-curve construction, an interesting mathematical analogy is established between wave-packet evolution in a constant or in a linearly time-dependent electric field, and the optical phenomena of Fraunhofer or Fresnel diffraction, respectively. The first type of diffraction is related to the usual Bloch oscillation effect, while---associated with the mathematical properties of the Cornu spiral---the second one leads to ``asymptotic localization'' of the electron. Finally, for harmonically driven fields dynamical localization can also be elucidated within our complex-plane representation." @default.
- W2028602934 created "2016-06-24" @default.
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- W2028602934 date "2001-07-13" @default.
- W2028602934 modified "2023-09-25" @default.
- W2028602934 title "Phasorlike interpretation of tight-binding electronic motion in homogeneous electric fields" @default.
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- W2028602934 doi "https://doi.org/10.1103/physrevb.64.054301" @default.
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