Effect of spatial reflection symmetry on the distribution of the parametric conductance derivative in ballistic chaotic cavities

Abstract

We study the effect of left-right symmetry on the distribution of the parametric derivative of the dimensionless conductance T with respect to an external parameter X , partial differentialT/ partial differentialX , of ballistic chaotic cavities with two leads, each supporting N propagating modes. We show that T and partial differentialT/ partial differentialX are linearly uncorrelated for any N . For N=1 we calculate the distribution of partial differentialT/ partial differentialX in the presence and absence of time-reversal invariance. In both cases, it has a logarithmic singularity at zero derivative and algebraic tails with an exponent different from the one of the asymmetric case. We also obtain explicit analytical results for the mean and variance of the distribution of partial differentialT/ partial differentialX for arbitrary N . Numerical simulations are performed for N=5 and 10 to show that the distribution P ( partial differentialT/ partial differentialX) tends towards a Gaussian one when N increases.

Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities

“…as expected because the distributions of ∂T /∂q and ∂R/∂q are symmetric with respect to the zero derivative [24,25].…”

“…The results presented here are valid for strong absorption. However, they reproduce those existing in the literature for the distribution of ∂T /∂X at zero absorption intensity [24,25]. In the absence of absorption the distribution of the parametric conductance derivative was calculated analytically by Brouwer et al [24] for an asymmetric quantum dot with two single-mode point contacts.…”

“…The derivative of those coefficients with respect to the external parameter has not been considered in the presence of absorption. A parametric derivative is very important in the characterization of mesoscopic systems with a chaotic classical limit [24,25], since it is analogous to the level velocity [26,27,28,29].…”

“…The reflection symmetric case was considered in Ref. 25. There, the distribution of ∂T /∂X diverges logarithmically at zero derivative, it has algebraic tails with an exponent which is different to that of the asymmetric case.…”

Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice

“…For the µ-point, it shows strong 'level repulsion' characteristic for the unitary symmetry class of random matrix theory [30]. For the γ-point, levels can appear close to each other, as happens in other periodic systems [31][32][33][34] where high lattice symmetry splits the spectrum into subsets of states corresponding to different irreducible representations of the lattice symmetry group which can appear arbitrarily close to each other [35][36][37][38][39].…”