One-dimensional disordered systems with a random potential of a small amplitude and short-range correlations are considered near the initial band edge. The evolution equation is obtained for the ...mutual distribution
P
(ρ, ψ) of the Landauer resistance ρ and the phase variable ψ = θ – φ (θ and φ are phases entering the transfer matrix) when the system length
L
is increased. In the limit of large
L
, the equation allows separation of variables, which provides the existence of the stationary distribution
P
(ψ), determining the coefficients in the evolution equation for
P
(ρ). The limiting distribution
P
(ρ) for
L
→ ∞ is log-normal and does not depend on boundary conditions. It is determined by the “internal” phase distribution, whose form is established in the whole energy range including the forbidden band of the initial crystal. The random phase approximation is valid in the depth of the allowed band, but strongly violated for other energies. The phase ψ appears to be the “bad” variable, while the “correct” variable is ω = –cotψ/2. The form of the stationary distribution
P
(ω) is determined by the internal properties of the system and is independent of boundary conditions. Variation of the boundary conditions leads to the scale transformation ω →
s
ω and translations ω → ω + ω
0
and ψ → ψ + ψ
0
, which determinates the “external” phase distribution entering the evolution equations. Independence of the limiting distribution
P
(ρ) on the external distribution
P
(ψ) makes it possible to speak about the hidden symmetry, whose character is revealed below.
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, but are ...independent on the boundary conditions. However, the boundary conditions essentially affect the distribution of phases entering the transfer matrix and generally change the parameters of the evolution equation for the distribution
. This visible contradiction is resolved by the existence of the hidden symmetry, whose nature is revealed by the derivation of the equation for the stationary phase distribution and by analysis of its transformation properties.
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 ...essential and is studied below on the simplest example of the 1D case. In the log-normal regime, this influence is reduced to the change of the absolute scale of conductance, but generally changes the whole distribution function. Under the change of the system length
L
, its resistance may undergo the periodic or aperiodic oscillations. Variation of the Fermi level induces qualitative changes in the conductance distribution, resembling the smoothed Anderson transition.
Universal conductance fluctuations are usually observed in the form of aperiodic oscillations in the magnetoresistance of thin wires under variation of the magnetic field
B
. A Fourier analysis of ...aperiodic oscillations observed in the classical experiments by Webb and Washburn reveals a practically discrete spectrum in agreement with the scenario based on the analogy with one-dimensional systems, according to which conductance fluctuations are due to the superposition of incommensurate harmonics. A more detailed analysis reveals the existence of a continuous component, whose smallness is explained theoretically. A lot of qualitative results are obtained that confirm the presented picture: the distribution of phases, frequency differences, and the growth exponents is consistent with theoretical predictions; discrete frequencies weakly depend on the processing procedure; and the discovered shift oscillations confirm the analogy with one-dimensional systems. Microscopic estimates show that the results obtained are consistent with the geometrical dimensions of the sample.
General form of DMPK Equation Suslov, I. M.
Journal of experimental and theoretical physics,
07/2018, Letnik:
127, Številka:
1
Journal Article
Recenzirano
Odprti dostop
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 DMPK equation and its generalization suggested by Muttalib and co-workers. Two other variants lead to equations of the same structure, but with different definitions of their parameters. They contain additional terms, which are absent in the first variant. The coefficients of additional terms are shown to be finite beyond the metallic phase by calculation of the Lyapunov exponents and their comparison with numerical experiments. Consequences of the obtained equations for the problem of the conductance distribution and the status of the nonlinear sigma-models are discussed.
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 ...correspondence with conductance distributions for quasi-one-dimensional systems of size
L
d
–1
×
L
z
, characterizing by parameters
L
/ξ and
L
z
/
L
(ξ is the correlation length,
d
is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension
d
= 2 + ϵ obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small
g
and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at
g
= 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for
d
= 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio
L
/ξ.
This paper describes a usage of a low-current coaxial plasmatron for generation of nitrogen oxide molecules. Glow-type discharge in vortex air flow is sustained at an average current from 0.05 to 0.2 ...A that corresponds to an average discharge power from 65 to 160 W. The diameter of an exit nozzle of the plasmatron is of 0.5 cm, and the air flow is varied from 0.2 to 1.5 g/s. In such conditions, the discharge burns in nonsteady-state regime, when a sustainment of a plasma jet/plume and a plasma column in the plasmatron nozzle is accompanied by the spontaneous glow-to-spark transitions. Due to the special design of the anode nozzle, an efficient interaction of the air flow with the plasma plume and plasma column is provided. Typical contents of nitric monoxide in the output gas are of about several grams per cubic meter, and the cost for formation of one molecule is from 50 to 35 eV.
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