General form of DMPK Equation

@article{Suslov2018GeneralFO,
  title={General form of DMPK Equation},
  author={I M Suslov},
  journal={Journal of Experimental and Theoretical Physics},
  year={2018},
  volume={127},
  pages={131-142}
}
  • I. Suslov
  • Published 6 March 2017
  • Mathematics
  • Journal of Experimental and Theoretical Physics
The Dorokhov–Mello–Pereyra–Kumar (DMPK) equation, using in the analysis of quasi-onedimensional systems and describing evolution of diagonal elements of the many-channel transfer-matrix, is derived under minimal assumptions on the properties of channels. The general equation is of the diffusion type with a tensor character of the diffusion coefficient and finite values of non-diagonal components. We suggest three different forms of the diagonal approximation, one of which reproduces the usual… 

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References

SHOWING 1-10 OF 60 REFERENCES

The generalized DMPK equation revisited: towards a systematic derivation

The generalized Dorokov–Mello–Pereyra–Kumar (DMPK) equation has recently been used to obtain a family of very broad and highly asymmetric conductance distributions for three-dimensional disordered

Generalization of the DMPK equation beyond quasi one dimension

Electronic transport properties in a disordered quantum wire are very well described by the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation, which describes the evolution of the transmission eigenvalues

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one

Conductance distribution in strongly disordered mesoscopic systems in three dimensions

Recent numerical simulations have shown that the distribution of conductance P(g) in 3D strongly localized regiem differs significally from the expected log normal distribution. To understand the

Disordered system withn orbitals per site: Lagrange formulation, hyperbolic symmetry, and goldstone modes

We give a Lagrange formulation of the gauge invariantn-orbital model for disordered electronic systems recently introduced by Wegner. The derivation proceeds analytically without use of diagrams, and

Conductance of finite systems and scaling in localization theory

The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas,

Generalized Fokker-Planck Equation For Multichannel Disordered Quantum Conductors

The Dorokhov-Mello-Pereyra-Kumar (DMPK) equation, which describes the distribution of transmission eigenvalues of multichannel disordered conductors, has been enormously successful in describing a

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case
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