Conductance length autocorrelation in quasi one-dimensional disordered wires

In this letter we study the conductance G through one-dimensional quantum wires with disorder configurations characterized by long-tailed distributions (Levy-type disorder). We calculate analytically the conductance distribution which reveals a universal statistics: the distribution of conductances is fully determined by the exponent \alpha of the power-law decay of the disorder distribution and the average < ln G >, i.e., all other details of the disorder configurations are ...

We determine analytically the distribution of conductances of quasi one-dimensional disordered electron systems, neglecting electron-electron interaction, for all strengths of disorder. We find that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by ``one-sided'' log-normal distribution. For larger disorder, the tail of the log-normal distribution is cut-off for g > 1 by a Gaussian.

We calculate the distribution of the conductance G in a one-dimensional disordered wire at finite temperature T and bias voltage V in a independent-electron picture and assuming full coherent transport. At high enough temperature and bias voltage, where several resonances of the system contribute to the conductance, the distribution P(G(T,V)) can be represented with good accuracy by autoconvolutions of the distribution of the conductance at zero temperature and zero bias volt...

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of conductances P(g) for a quasi one dimensional wire within the model of non-interacting fermions. The method has been used in [1-3] to predict sharp features in P(g) near g=1 and the existence of non-analyticity in the conductance distribution in the insulating and crossover regimes, as well as to show how P(g) changes from Gaussian to log-normal behavior...

We perform a detailed numerical study of the conductance $G$ through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies $\epsilon$ of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large $\epsilon$, $P(\epsilon)\sim 1/\epsilon^{1+\alpha}$ with $\alpha\in(0,2)$. Our model serves as a generalization of 1D Lloyd's model, which corresponds to $\alpha=1$. First, we verify that the ens...

We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric sigma-model, we obtain the full dependence of the two-point correlation function on the distance between the points. In the limit of zero energy difference, our calculation reproduces the statistics of a single localized wave function. At logarithmic...

We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however, has the same binary correlator, the ...

The autocorrelation function of spectral determinants (ASD) is used to characterize the discrete spectrum of a phase coherent quasi- 1- dimensional, disordered wire as a function of its length L in a finite, weak magnetic field. An analytical function is obtained depending only on the dimensionless conductance g= xi/L where xi is the localization length, the scaled frequency x= omega/Delta, where Delta is the average level spacing of the wire, and the global symmetry of the s...

Calculating the density-density correlation function for disordered wires, we study localization properties of wave functions in a magnetic field. The supersymmetry technique combined with the transfer matrix method is used. It is demonstrated that at arbitrarily weak magnetic field the far tail of the wave functions decays with the length $L_{{\rm cu}}=2L_{{\rm co}}$, where $L_{{\rm co}}$ and $L_{{\rm cu}}$ are the localization lengths in the absence of a magnetic field and ...

The exact solution of the Dorokhov-Mello-Pereyra-Kumar-equation for quasi one-dimensional disordered conductors in the unitary symmetry class is employed to calculate all $m$-point correlation functions by a generalization of the method of orthogonal polynomials. We obtain closed expressions for the first two conductance moments which are valid for the whole range of length scales from the metallic regime ($L\ll Nl$) to the insulating regime ($L\gg Nl$) and for arbitrary chan...