Weak localization

The weak localization ( weak localization ) describes a quantum effect in the conductivity of the electric current and in general in the scattering of waves in disordered media, which leads to the fact that the propagation of the waves is reduced and these are "localized" .

The conductivity in an electrical conductor with impurities as scattering centers, which are responsible for the electrical resistance , can in principle be treated classically as long as the free path of the impurities in a crystal is greater than the wavelength of the electron (for the definition of see Fermi pulse ). The electrons move in a straight line and are deflected at the faults, whereby the phases of the different paths lift away on average and thus justify the classic treatment. ${\ displaystyle l}$ ${\ displaystyle 2 \ pi / k_ {F}}$ ${\ displaystyle k_ {F}}$

In the quantum mechanical treatment interference observed that in the case of coherent backscattering ( coherent backscattering occur). If an electron is scattered on a path that brings it back to its starting point, an electron can follow the same path with the same probability amplitude in the opposite direction, with the contributions of the two paths, which are of the same length, add up in phase (see also Cooperon Diagram ). The probability of backscattering is two times higher than in the classic treatment. This manifests itself in measurements as an abnormally increased resistance and was observed on thin films in the 1970s .

In the 1980s, this phenomenon was also observed directly with the scattering of coherent light ( laser ) on colloidal suspensions (e.g. very small plastic spheres in a liquid) and then with other wave phenomena (even with earthquake waves ).

The phenomenon of weak localization is considered to be the forerunner of strong or Anderson localization in disordered media, in which the concentration of the impurities is so high that the diffusive propagation of the waves does not occur at all.

Web links

Homepage of the Photonic Crystal Group ( Memento of December 14, 2009 in the Internet Archive ) on the phenomenon of weak localization in the scattering of coherent light ( Interference in random media: Coherent backscattering and Anderson localization ).

Individual evidence

↑ In quantum mechanics, electrons are described as waves
↑ It is assumed that the system is time-reversal invariant. This is e.g. B. is not the case with an external magnetic field.
^ Van Albada, Ad Lagendijk : Observation of weak localization of light in a random medium . In: Phys. Rev. Letters , Vol. 55, 1985, pp. 2692-2695, and Journal Optical Society of America , 3, 1986, P226.
↑ Weak Localization of Seismic Waves ( Memento from October 26, 2004 in the Internet Archive )
↑ Anderson localization of light was described by Wiersma et al. a. Observed 1997, Physics News Update Number 356 ( June 6, 2004 memento on the Internet Archive )

[1] In quantum mechanics, electrons are described as waves

[2] It is assumed that the system is time-reversal invariant. This is e.g. B. is not the case with an external magnetic field.

[3] Van Albada, Ad Lagendijk : Observation of weak localization of light in a random medium . In: Phys. Rev. Letters , Vol. 55, 1985, pp. 2692-2695, and Journal Optical Society of America , 3, 1986, P226.

[4] Weak Localization of Seismic Waves ( Memento from October 26, 2004 in the Internet Archive )

[5] Anderson localization of light was described by Wiersma et al. a. Observed 1997, Physics News Update Number 356 ( June 6, 2004 memento on the Internet Archive )