Statistical Properties Of Wave Functions Research Articles

Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

We investigate the statistical properties of wave functions in chaotic nanostructures with spin-orbit coupling (SOC), focussing in particular on spatial correlations of eigenfunctions. Numerical results from a microscopic model are compared with results from random matrix theory in the crossover from the gaussian orthogonal to the gaussian symplectic ensembles (with increasing SOC); one- and two-point distribution functions were computed to understand the properties of eigenfunctions in this crossover. It is found that correlations of wave function amplitudes are suppressed with SOC; nevertheless, eigenfunction correlations play a more important role in the two-point distribution function(s), compared to the case with vanishing SOC. Experimental consequences of our results are discussed.

Wave function statistics in open chaotic billiards.

We study the statistical properties of wave functions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wave functions cross over from real to complex. Each wave function is characterized by a phase rigidity, which is itself a fluctuating quantity. We calculate the probability distribution of the phase rigidity and discuss how phase rigidity fluctuations cause long-range correlations of intensity and current density. We also find that phase rigidities for wave functions with different incoming wave boundary conditions are statistically correlated.

Wavefunction statistics and multifractality at the spin quantum Hall transition

The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $\Delta_q$ governing the scaling of moments $<|\psi|^{2q}>\sim L^{-qd-\Delta_q}$ with the system size $L$ and the spatial decay of wave function correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values $\Delta_2=-1/4$ and $\Delta_3=-3/4$. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation $\Delta_q\simeq q(1-q)/8$ but shows detectable deviations. We also study statistics of the two-point conductance $g$, in particular, the spectrum of exponents $X_q$ characterizing the scaling of the moments $<g^q >$. Relations between the spectra of critical exponents of wave functions ($\Delta_q$), conductances ($X_q$), and Green functions at the localization transition with a critical density of states are discussed.

Signature of ballistic effects in disordered conductors

Statistical properties of energy levels, wave functions and quantum-mechanical matrix elements in disordered conductors are usually calculated assuming diffusive electron dynamics. Mirlin has pointed out [Phys. Rep. 326, 259 (2000)] that ballistic effects may, under certain circumstances, dominate diffusive contributions. We study the influence of such ballistic effects on the statistical properties of wave functions in quasi-one dimensional disordered conductors. Our results support the view that ballistic effects can be significant in these systems.

Exact diagonalization study of rare events in disordered conductors

We determine the statistical properties of wave functions in disordered quantum systems by exact diagonalization of one-, two- and quasi-one dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we find that the tails of the distribution of wave-function amplitudes are described by the non-linear �-model. In two dimensions, the tails of the distribution function are consistent with a recent prediction based on a direct optimal fluctuation method. 72.15.Rn,71.23.An,05.40.-a

Statistics of conductance fluctuations in quantum dots.

We present a complete analytical theory of conductance fluctuations in quantum dots in the regime of chaotic dynamics. Using the supersymmetry method we calculate for the first time exactly the conductance distribution function for a system of noninteracting electrons. Knowledge of this quantity enables us to obtain information about statistical properties of wave functions of a closed dot. The far tail of the distribution function describes fluctuations of resonance conductance in the Coulomb blockade regime