# 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} }

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…

## 4 Citations

### Conductance distribution in the magnetic field

- PhysicsPhilosophical Magazine
- 2018

ABSTRACT Using a modification of the Shapiro scaling approach, we derive the distribution of conductance in the magnetic field applicable in the vicinity of the Anderson transition. This distribution…

### Hidden symmetry in 1D localisation

- MathematicsPhilosophical Magazine Letters
- 2022

ABSTRACT Resistance ρ of an one-dimensional disordered system of length L has the log-normal distribution in the limit of large L. Parameters of this distribution depend on the Fermi level position,…

### Conductance Distribution in 1D Systems: Dependence on the Fermi Level and the Ideal Leads

- PhysicsJournal of Experimental and Theoretical Physics
- 2019

The correct definition of the conductance of finite systems implies a connection to the system of the massive ideal leads. Influence of the latter on the properties of the system appears to be rather…

### Electron transport and electron density inside quasi-one-dimensional disordered conductors

- PhysicsPhysical Review B
- 2020

We consider the problem of electron transport across a quasi-one-dimensional disordered multiply-scattering medium, and study the statistical properties of the electron density inside the system. In…

## References

SHOWING 1-10 OF 60 REFERENCES

### The generalized DMPK equation revisited: towards a systematic derivation

- Physics
- 2014

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

- Physics
- 2002

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

- Mathematics
- 2016

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

- Physics
- 2005

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

- Mathematics
- 1980

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

- Physics
- 2012

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

- Physics
- 1999

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

- Physics
- 2011

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…