Spectral Statistics: From Disordered to Chaotic Systems

The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to extend results obtained in the diffusive regime to general chaotic systems. In particular, the two--point level density correlator and the structure factor for general chaotic systems are calculated and characterized. The behavior of the structure factor around the Heisenberg time is quantitatively described in terms of short periodic orbits.Comment: uuencoded file with 1 eps figure, 4 page

Semiclassical theory of quasiparticles in the superconducting state

We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the superconducting state and includes an account of the Bohr-Sommerfeld quantisation rule, the Maslov index, torus quantisation, topological phases arising from lines of phase singularities (vortices), and semiclassical wave functions for multi-dimensional systems. The method is illustrated by studying the problem of an SNS junction and a single vortex.Comment: 74 pages, 19 figures, 3 tables. Submitted to Academic Press for possible publicatio

Paraxial propagation of a quantum charge in a random magnetic field

The paraxial (parabolic) theory of a near forward scattering of a quantum charged particle by a static magnetic field is presented. From the paraxial solution to the Aharonov-Bohm scattering problem the transverse transfered momentum (the Lorentz force) is found. Multiple magnetic scattering is considered for two models: (i) Gaussian $\delta$ -correlated random magnetic field; (ii) a random array of the Aharonov-Bohm magnetic flux line. The paraxial gauge-invariant two-particle Green function averaged with respect to the random field is found by an exact evaluation of the Feynman integral. It is shown that in spite of the anomalous character of the forward scattering, the transport properties can be described by the Boltzmann equation. The Landau quantization in the field of the Aharonov-Bohm lines is discussed.Comment: Figures and references added. Many typos corrected. RevTex, 25 pages, 9 figure

Spectral correlations : understanding oscillatory contributions

We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models

Statistics of pre-localized states in disordered conductors

The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the distribution of relatively small amplitudes can be approximated by the universal Porter-Thomas formulae known from the random matrix theory, the statistics of large amplitudes is strongly modified by localization effects. In particular, we find a multifractal behavior of eigenstates in 2D conductors which follows from the non-integer power-law scaling for the inverse participation numbers (IPN) with the size of the system. This result is valid for all fundamental symmetry classes (unitary, orthogonal and symplectic). The multifractality is due to the existence of pre-localized states which are characterized by power-law envelopes of wave functions, $|\psi_t(r)|^2\propto r^{-2\mu}$, $\mu <1$. The pre-localized states in short quasi-1D wires have the power-law tails $|\psi (x)|^2\propto x^{-2}$, too, although their IPN's indicate no fractal behavior. The distribution function of the largest-amplitude fluctuations of wave functions in 2D and 3D conductors has logarithmically-normal asymptotics.Comment: RevTex, 17 twocolumn pages; revised version (several misprint corrected

Semiclassical Field Theory Approach to Quantum Chaos

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix nonlinear $\sigma$-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.Comment: uuencoded file, 21 pages, latex, one eps figur

Floquet scattering in parametric electron pumps

A Floquet scattering approach to parametric electron pumps is presented and compared with Brouwer's adiabatic scattering approach [Phys. Rev. B 58, R10135 (1998)] for a simple scattering model with two harmonically oscillating delta-function barriers. For small strength of oscillating potentials these two approaches give exactly equivalent results while for large strength, these clearly deviate from each other. The validity of the adiabatic theory is also discussed by using the Wigner delay time obtained from the Floquet scattering matrix.Comment: 10 pages, 7 figure

Spin-polarized Tunneling in Hybrid Metal-Semiconductor Magnetic Tunnel Junctions

We demonstrate efficient spin-polarized tunneling between a ferromagnetic metal and a ferromagnetic semiconductor with highly mismatched conductivities. This is indicated by a large tunneling magnetoresistance (up to 30%) at low temperatures in epitaxial magnetic tunnel junctions composed of a ferromagnetic metal (MnAs) and a ferromagnetic semiconductor (GaMnAs) separated by a nonmagnetic semiconductor (AlAs). Analysis of the current-voltage characteristics yields detailed information about the asymmetric tunnel barrier. The low temperature conductance-voltage characteristics show a zero bias anomaly and a V^1/2 dependence of the conductance, indicating a correlation gap in the density of states of GaMnAs. These experiments suggest that MnAs/AlAs heterostructures offer well characterized tunnel junctions for high efficiency spin injection into GaAs.Comment: 14 pages, submitted to Phys. Rev.

Conductance fluctuations in diffusive rings: Berry phase effects and criteria for adiabaticity

We study Berry phase effects on conductance properties of diffusive mesoscopic conductors, which are caused by an electron spin moving through an orientationally inhomogeneous magnetic field. Extending previous work, we start with an exact, i.e. not assuming adiabaticity, calculation of the universal conductance fluctuations in a diffusive ring within the weak localization regime, based on a differential equation which we derive for the diffuson in the presence of Zeeman coupling to a magnetic field texture. We calculate the field strength required for adiabaticity and show that this strength is reduced by the diffusive motion. We demonstrate that not only the phases but also the amplitudes of the h/2e Aharonov-Bohm oscillations are strongly affected by the Berry phase. In particular, we show that these amplitudes are completely suppressed at certain magic tilt angles of the external fields, and thereby provide a useful criterion for experimental searches. We also discuss Berry phase-like effects resulting from spin-orbit interaction in diffusive conductors and derive exact formulas for both magnetoconductance and conductance fluctuations. We discuss the power spectra of the magnetoconductance and the conductance fluctuations for inhomogeneous magnetic fields and for spin-orbit interaction.Comment: 18 pages, 13 figures; minor revisions. To appear in Phys. Rev.

"Level Curvature" Distribution for Diffusive Aharonov-Bohm Systems: analytical results

We calculate analytically the distributions of "level curvatures" (LC) (the second derivatives of eigenvalues with respect to a magnetic flux) for a particle moving in a white-noise random potential. We find that the Zakrzewski-Delande conjecture is still valid even if the lowest weak localization corrections are taken into account. The ratio of mean level curvature modulus to mean dissipative conductance is proved to be universal and equal to $2\pi$ in agreement with available numerical data.Comment: 12 pages. Submitted to Phys.Rev.