arXiv subjects
Publications and source records attributed to Alexander Altland.
We derive an effective low-energy theory of disordered interacting quantum wires. Our theory describes Anderson localization in the limit of vanishing dephasing and reduces to standard abelian bosonization in the limit of vanishing disorder. In a system with many transport channels, it exhibits the diffusive physics characteristic for multi-channel quantum wires.
We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively describe this mechanism in two different ways: the explicit description of transition probabilities in terms of interfering trajectories, and an hierarchical integration over fluctuations in the classical phase space of the array cavities.
We formulate and approximately solve a specific many-body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of quantum interference in chaotic systems and show how semiclassical 'diagrams' involving near action degenerate sets of periodic orbits emerge in the field theoretical description. We further discuss how the universality phenomenon (i.e. the fact that individual chaotic systems behave according to the prescriptions of random matrix theory) can be understood from the perspective of the field theory.
Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.
A crossover theory connecting Altshuler-Aronov electron-electron interaction corrections and Luttinger liquid behavior in quasi-1D disordered conductors has been formulated. Based on an interacting non-linear sigma model, we compute the tunneling density of states and the interaction correction to the conductivity, covering the full crossover.
We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the non-oscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.
At low values of external doping graphene displays a wealth of unconventional transport properties. Perhaps most strikingly, it supports a robust 'metallic' regime, with universal conductance of the order of the conductance quantum. We here apply a combination of mean field and bosonization methods to explore the large scale transport properties of the system. We find that, irrespective of the doping level, disordered graphene is subject to common mechanisms of Anderson localization. However, at low doping a number of renormalization mechanisms conspire to protect the conductivity of the system, to an extend that strong localization may not be seen even at temperatures much smaller than those underlying present experimental work.
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 non--linear $σ$--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.
Transport properties of granular systems are governed by Coulomb blockade effects caused by the discreteness of the electron charge. We show that, in the limit of vanishing mean level spacing on the grains, the low-temperature behavior of 1d and 2d arrays is insulating at any inter-grain coupling (characterized by a dimensionless conductance g.) In 2d and g>>1, there is a sharp Berezinskii-Kosterlitz-Thouless crossover to the conducting phase at a certain temperature, T_{BKT}. These results are obtained by applying an instanton analysis to map the conventional `phase' description of granular arrays onto the dual `charge' representation.
We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $σ$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons and Zirnbauer \cite{LSZ}, we compute the {\em exact} density of transmission matrix eigenvalues of superconducting wires (of symmetry class $C$I.) For the unitary class of metallic systems (class $A$) we are able to obtain the density function, save for its large transmission tail.
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 $K(τ)$ as power series in the time $τ$. Each term $τ^n$ 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 non-trivial properties of permutations. We show our series to be equivalent to perturbative implementations of the non-linear sigma models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs are one-to-one with Feynman diagrams known from the sigma model.
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the non-linear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor. Far-reaching structural parallels, as well as a number of differences, to recent semiclassical approaches to the problem are discussed.
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 non--universal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.
We consider thermodynamic and transport properties of a long granular array with strongly connected grains (inter-grain conductance g>>1.) We find that the system exhibits activated behavior of conductance and thermodynamic density of states ~exp(-T*/T) where the gap, T*, is parametrically larger than the energy at which conventional perturbation theory breaks down. The scale T* represents energy needed to create a long single-electron charge soliton propagating through the array.
Quasiparticles in the cuprates appear to be subject to anomalously strong inelastic damping mechanisms. To explain the phenomenon, Sachdev and collaborators recently proposed to couple the system to a critically fluctuating order parameter mode of either id_{xy}- or is-symmetry. Motivated by the observation that the energies relevant for the dynamics of this mode are comparable to the scattering rate induced by even moderate impurity concentrations, we here generalize the approach to the presence of static disorder. In the id-case, we find that the coupling to disorder renders the order parameter dynamics diffusive but otherwise leaves much of the phenomenology observed in the clean case intact. In contrast, the interplay of impurity scattering and order parameter fluctuations of is-symmetry entails the formation of a secondary superconductor transition, with a critical temperature exponentially sensitive to the disorder concentration.
We present a numerical study of the quasi-particle density of states (DoS) of two-dimensional d-wave superconductors in the presence of disorder, focusing on the influence of the range of the disorder. We find qualitatively different behavior for smooth and short-ranged disorder. In the former case, we find power law scaling of the DoS with an exponent depending on the strength of the disorder and the superconducting order parameter in quantitative agreement with the theory of Nersesyan {\em et al.}. For strong disorder, a qualitative change to an energy independent DoS occurs. In contrast, for short-ranged disorder of sufficient strength, we find localization by analyzing the system size dependence of the Thouless numbers. Near zero energy we find a micro gap in the DoS. The width of this micro gap is given by the mean level spacing of a localization volume. From the system size and disorder dependence of the width of the micro gap we derive the dependence of the localization length on the disorder strength.