Crossover from regular to chaotic behavior in the conductance of periodic quantum chains

Abstract

The conductance of a waveguide containing finite number of periodically placed identical point-like impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the Landauer-Büttiker formula. In the case of few impurities the conductance is proportional to the number of the open channels N of the empty waveguide and shows a regular staircase like behavior with step heights ≈ 2e 2 /h. For large number of impurities the influence of the band structure of the infinite periodic chain can be observed and the conductance is approximately the number of energy bands (smaller than N ) times the universal constant 2e 2 /h. This lower value is reached exponentially with increasing number of impurities. As the strength of the impurity is increased the system passes from integrable to quantum-chaotic. The conductance, in units of 2e 2 /h, changes from N corresponding to the empty waveguide to ∼ N/2 corresponding to chaotic or disordered system. It turnes out, that the conductance can be expressed as (1 − c/2)N where the parameter 0 < c < 1 measures the chaoticity

Determinant approach to the scattering matrix elements in quasi-one-dimensional and two-dimensional disordered systems

“…The latter coincides with the asymptotic expression of the average conductance obtained in Ref. 6 on the basis of a numerical calculation. Using Eq.…”

“…The quantum transport of electrons in quasi-onedimensional ͑Q1D͒ and two-dimensional ͑2D͒ disordered systems has been studied extensively over the past decades both theoretically and experimentally. [1][2][3][4][5][6][7] In particular, research interest was connected with the fact that electron transmission caused by elastic scattering with impurities in such size-quantized systems changes the shape of the conductance quantization due to the presence of evanescent modes. In most of the theoretical work where quantuminterference effects are important, the Anderson tight-binding model ͑see, e.g., Refs.…”

Spectral determinant method for interactingN-body systems including impurities

“…[16] to investigate the diffraction of the electron by the impurities, and in Ref. [17] to study the crossover behavior of the localization problem in a waveguide with periodically placed identical point-like impurities. In this paper an extension of Grosche's approach to treat many-body interacting systems including impurities is presented.…”

Negative Length Orbits in Normal-Superconductor Billiard Systems

“…where r nm (k F ) is the matrix of reflection amplitudes of the normal system [16] for the entrance lead, G 0 (x, z|x ′ , z ′ ) is the Green's function of the empty waveguide. D = −iλ/ 1 −λG 0 (x 0 , z 0 |x 0 , z 0 ) can be regarded as the diffraction constant of the scatterer, whereλ is the renormalized strength of the scatterer [21]. On the upper part of Fig.…”