Biomedical subjects

Alexander Altland

Publications and source records attributed to Alexander Altland.

7 recordsLinked to original sources

PubMed2005

Spectral correlations of individual quantum graphs.

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear -model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

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PubMed2005

Anderson localization from the replica formalism.

We study Anderson localization in quasi-one-dimensional disordered wires within the framework of the replica sigma model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons, and Zirnbauer, we compute the exact density of transmission matrix eigenvalues of superconducting wires (of symmetry class CI.) For the unitary class of metallic systems (class A) we are able to obtain the density function, save for its large transmission tail.

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PubMed2005

Periodic-orbit theory of universality in quantum chaos.

We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-Dyson symmetry classes, we calculate the small-time spectral form factor K(tau) as power series in the time tau. Each term tau(n) of that series is provided by specific families of pairs of periodic orbits. The contributing pairs are classified in terms of close self-encounters in phase space. The frequency of occurrence of self-encounters is calculated by invoking ergodicity. Combinatorial rules for building pairs involve nontrivial properties of permutations. We show our series to be equivalent to perturbative implementations of the nonlinear sigma models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs have a one-to-one relationship with Feynman diagrams known from the sigma model.

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PubMed2004

Universal spectral statistics in quantum graphs.

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.

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PubMed2004

Electron transport in granular metals.

We consider thermodynamic and transport properties of a long granular array with strongly connected grains (intergrain conductance g>>1). We find that the system's conductance and differential capacitance exhibits activated behavior, approximately exp([-T(*)/T]. The gap T(*) represents the energy needed to create a long single-electron charge soliton propagating through the array. This scale is parametrically larger than the energy at which conventional perturbation theory breaks down.

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PubMed2003

Quantum critical fluctuations in disordered d-wave superconductors.

To explain the strong quasiparticle damping in the cuprates, Sachdev and collaborators proposed to couple the system to a critically fluctuating id(xy)- or is-order parameter mode. Here we generalize the approach to the presence of static disorder. In the id case, the order parameter dynamics becomes diffusive, but otherwise much of the phenomenology of the clean case remains intact. In contrast, the interplay of disorder and is-order parameter fluctuations leads to a secondary superconductor transition, with a critical temperature exponentially sensitive to the impurity concentration.

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PubMed2002

Quantum transport in parallel magnetic fields: a realization of the Berry-Robnik symmetry phenomenon.

We analyze the magnetoconductance of two-dimensional electron and hole gases subject to a parallel magnetic field. It is shown that, for confining potential wells which are symmetric with respect to spatial inversion, a temperature-dependent weak localization signal exists even in the presence of a magnetic field. Deviations from this symmetry lead to magnetoconductance profiles that contain information on both the geometry of the confining potential and characteristics of the disorder.

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