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Spin currents resulting in the zero-bias spin separation have been observed in unbiased diluted magnetic semiconductor structures (Cd,Mn)Te/(Cd,Mg)Te. The pure spin current generated due to the electron gas heating by terahertz radiation is converted into a net electric current by application of an external magnetic field. We demonstrate that polarization of the magnetic ion system enhances drastically the conversion due to the spin-dependent scattering by localized Mn(2+) ions and the giant Zeeman splitting., Comment: 6 pages, 4 figures

We report a fast, room temperature detection scheme for the polarization ellipticity of laser radiation, with a bandwidth that stretches from the infrared to the terahertz range. The device consists of two elements, one in front of the other, that detect the polarization ellipticity and the azimuthal angle of the ellipse. The elements respectively utilise the circular photogalvanic effect in a narrow gap semiconductor and the linear photogalvanic effect in a bulk piezoelectric semiconductor. For the former we characterized both a HgTe quantum well and bulk Te, and for the latter, bulk GaAs. In contrast with optical methods our device is an easy to handle all-electric approach, which we demonstrated by applying a large number of different lasers from low power, continuous wave systems to high power, pulsed sources., Comment: 7 pages, 5 figures

We report on the observation of the circular (helicity-dependent) and linear photogalvanic effects in Si-MOSFETs with inversion channels. The developed microscopic theory demonstrates that the circular photogalvanic effect in Si structures it is of pure orbital nature originating from the quantum interference of different pathways contributing to the light absorption., Comment: 5 pages, 4 figures

We report on the observation of terahertz radiation induced photogalvanic currents in semiconductor heterostructures with one-dimensional lateral periodic potential. The potential is produced by etching a grating into the sample surface. The electric current response is well described by phenomenological theory including both the circular and linear photogalvanic effects. Experimental data demonstrate that the inversion asymmetry of the periodic lateral pattern can be varied by means of electron beam lithography to produce classical lateral ratchets. A novel microscopical mechanism for the polarization-dependent photogalvanic effects has been proposed to interpret the experimental findings. The photocurrent generation is based on the combined action of the lateral periodic potential and the modulated in-plane pumping. The latter modulation stems from near-field effects of the radiation propagating through the grating., Comment: 8 pages, 6 figures

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes., Comment: 11 pages, figures improved, minor changes to the text

Symmetry and spin dephasing of in (110)-grown GaAs quantum wells (QWs) are investigated applying magnetic field induced photogalvanic effect (MPGE) and time-resolved Kerr rotation. We show that MPGE provides a tool to probe the symmetry of (110)-grown quantum wells. The photocurrent is only observed for asymmetric structures but vanishes for symmetric QWs. Applying Kerr rotation we prove that in the latter case the spin relaxation time is maximal, therefore these structures set upper limit of spin dephasing in GaAs QWs. We also demonstrate that structure inversion asymmetry can be controllably tuned to zero by variation of delta-doping layer position., Comment: 4 pages, 4 figures

Two types of room temperature detectors of terahertz laser radiation have been developed which allow in an all-electric manner to determine the plane of polarization of linearly polarized radiation and the Stokes parameters of elliptically polarized radiation, respectively. The operation of the detectors is based on photogalvanic effects in semiconductor quantum well structures of low symmetry. The photogalvanic effects have nanoseconds time constants at room temperature making a high time resolution of the polarization detectors possible.

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is an open problem. In the last years some progress on this problem was achieved. In this survey article we want to explain these results and some of their applications. Among other things, the material developed in our previous papers math.DG/0312243, math.DG/0408249, and math.DG/0503220 is presented in a unified way., Comment: 55 pages; To appear in: Recent developments in pseudo-Riemannian Geometry, ESI Lectures in Mathematics and Physics, EMS Publishing House

The coverage of vicinal, stepped surfaces with molecules is simulated with the help of a two-dimensional Ising model including local distortions and an Ehrlich-Schwoebel barrier term at the steps. An effective two-spin model is capable to describe the main properties of this distorted Ising model. It is employed to analyze the behavior of the system close to the critical points. Within a well-defined regime of bonding strengths and Ehrlich-Schwoebel barriers we find a reduction of coverage (magnetization) at low temperatures due to the presence of the surface step. This results in a second, low-temperature transition besides the standard Ising order-disorder transition. The additional transition is characterized by a divergence of the susceptibility as a finite-size effect. Due to the surface step the mean-field specific heat diverges with a power law., Comment: corrected version 7 pages, 4 figures

Following the approach to pseudo-Riemannian symmetric spaces developed in math.DG/0408249 we exhibit examples of indefinite hyper-Kaehler symmetric spaces with non-abelian holonomy. Moreover, we classify indecomposable hyper-Kaehler symmetric spaces whose metric has signature (4,4n). Such spaces exist if and only if n=0,1,3., Comment: 20 pages

In the present paper we develop a framework in which questions of quantum ergodicity for operators acting on sections of hermitian vector bundles over Riemannian manifolds can be studied. We are particularly interested in the case of locally symmetric spaces. For locally symmetric spaces, we extend the recent construction of Silberman and Venkatesh (math.RT/0407413) of representation theoretic lifts to vector bundles., Comment: 32 pages

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric space M to a triple consisting of (i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M), (ii) a semi-simple orthogonal module of the Lie algebra with involution, and (iii) a quadratic cohomology class of this module. That leads to a classification scheme of indecomposable non-simple pseudo-Riemannian symmetric spaces. In addition, we obtain a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results due to Cahen/Parker and Neukirchner math.DG/0301326)., Comment: 37 pages

The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module A in a canonical way. Identifying equivalence classes of quadratic extensions of l by A with a certain cohomology set H^2_Q(l,A) we obtain a classification scheme for general metric Lie algebras and a complete classification of metric Lie algebras of index 3., Comment: 53 pages

We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2., Comment: 30 pages; minor corrections

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of math.DG/9810146. Based on this investigation we provide proofs of the Hodge theoretic results for the cohomology of real hyperbolic manifolds announced in math.DG/0009038, improve the bounds for the critical exponents obtained by Corlette for the quaternionic and the Cayley case, compute the L^2-cohomology for the corresponding locally symmetric spaces, prove a version of the Harder-Borel conjecture for real hyperbolic manifolds, and compute higher cohomology groups with coefficients in hyperfunctions supported on the limit set., Comment: 121 pages

We obtain sufficient conditions exlcuding the existence of non-trivial distribution sections of bundles over the boundary of symmetric spaces of negative curvature which are invariant with respect to a geometrically finite group of isometries and are supported on the limit set in a strong sense., Comment: 14 pages

We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in terms of the conformal weight, the Hausdorff dimension of the limit set, and the maximal rank of the cusps of the group., Comment: 58 pages; corrected version - The main theorem of the previous version was incorrect in the case that the invariant distribution is not a cusp form. We thank W. Schmid for showing us a counterexample to this wrong claim

We explain how the Harish-Chandra Plancherel Theorem and results in relative Lie algebra cohomology can be used in order to compute in a uniform way the $L^2$-Betti numbers, the Novikov-Shubin invariants, and the $L^2$-torsion of compact locally symmetric spaces thus completing results previously obtained by Borel, Lott, Mathai, Hess and Schick. It turns out that the behaviour of these invariants is essentially determined by the fundamental rank of the group of isometries of the corresponding globally symmetric space. In particular, we show the nonvanishing of the $L^2$-torsion whenever the fundamental rank is equal to 1., Comment: 18 pages; The introduction now contains more precise references to the work of other people on Novikov-Shubin invariants, in particular to a recent paper of Lohoue and Mehdi

Let $Y=\Gamma\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $\Gamma$-invariant currents on the sphere at infinity of $H^n$ with support on the limit set of $\Gamma$. These spaces are finite-dimensional. The main result identifies the cohomology of $Y$ with a quotient of such spaces. We explain in which sense this result generalizes the classical Hodge theorem for compact quotients. We obtain analogous results for the cohomology groups $H^p(\Gamma,F)$, where $F$ is a finite-dimensional representation of the full group of orientation preserving isometries of $H^n$., Comment: 9 pages, to appear in the Proceedings of "Lie Theory and Its Applications in Physics - Lie III" (World Scientific, 2000)

We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of normalized orbital integrals associated to the hyperbolic conjugacy classes of this subgroup is an invariant distribution on the group, and we state precise conjecture about its Fouriertransform. We apply our trace formula to resolvent kernels. This yields functional equations of Selberg zeta functions and information about their singularities. The paper leaves open several interesting questions concerning the proof of the conjecture mentioned above on the one hand (this has to do with estimating the growth of the Eisenstein series as the spectral parameter turns to infinity), and the integrality of the multiplicities and of certain residues on the other hand., Comment: 46 pages

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution $\epsilon$, according to the dependence of the $(\epsilon,\tau)$-entropy, $h(\epsilon, \tau)$, and of the finite size Lyapunov exponent, $\lambda(\epsilon)$, on $\epsilon$., Comment: 24 pages RevTeX, 9 eps figures included, two references added, minor corrections, one section has been split in two (submitted to PRE)

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding. This embedding allows us to identify the local character of the equations of motion. Based on this method we present an approximate estimate of the entropy density by the correlation integral., Comment: 4 pages, 5 figures included

We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering matrices and their functional equations., Comment: 105 pages, revised version (considerable revision of the arguments in Subsection 3.9)

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian manifolds. We develop a geometric version of scattering theory. The paper is an update of dg-ga/9609011, which is completely rewritten from the point of view of representation theory. In particular, we are now able to show the meromorphy of Eisenstein series for all parameters., Comment: 79 pages

We analyze the classical and quantum properties of the integrable dimer problem. The classical version exhibits exactly one bifurcation in phase space, which gives birth to permutational symmetry broken trajectories and a separatrix. The quantum analysis yields all tunneling rates (splittings) in leading order of perturbation. In the semiclassical regime the eigenvalue spectrum obtained by numerically exact diagonalization allows to conclude about the presence of a separatrix and a bifurcation in the corresponding classical model., Comment: 4 pages, 3 figures, REVTEX

A Kleinian manifold Y is a quotient of a rank-one symmetric space of non-compact type by a convex-cocompact discrete group of isometries. We describe the spectral decomposition of the space of square integrable sections of locally homogeneous bundles on Y with respect to locally invariant differential operators. In the course of the proof we obtain meromorphic continuations of Eisenstein series and scattering matrices., Comment: 64 pages, LATEX

We prove Patterson's conjecture about the singularities of the Selberg zeta function associated to a convex-cocompact, torsion free group acting on a hyperbolic space., Comment: 63 pages, published version

We prove the finiteness of the cohomology of torsion-free lattices in a semisimple Lie group of real rank one with coefficients in the distribution vector globalization of Harish-Chandra modules. The cohomology is expressed in terms of automorphic and cusp forms. We also consider the Lie-algebra cohomology of these globalizations for the nilpotent part of the Iwasawa decomposition of the group., Comment: 32 pages, Latex

We compute the cohomology of a Fuchsian group of the second kind with coefficients in the hyperfunction vectors of the principal series representations of $SL(2,R)$ supported on the limit set., Comment: 22 pages, LATEX

We provide a simple way to obtain the meromorphic extension of Eisenstein series and Scattering matrices under conditions which generalize the case of discrete groups acting convex cocompactly on hyperbolic spaces., Comment: 9 pages, LATEX

We propose a new method for studying $n$- and $\Gamma$-cohomology of globalizations of Harish-Chandra modules, where $G=KAN$ is a rank one semisimple Lie group, $\Gamma$ is a discrete subgroup of $G$ and $n=Lie(N)$. We prove a conjecture of Patterson relating the singularities of Selberg zeta functions with the $\Gamma$-cohomology of principal series representations if $\Gamma$ is cocompact and torsion free., Comment: 21 pages, LATEX

For a Riemann surface with cusps we define a theta function using the eigenvalues of the Laplacian and the singularities of the scattering determinant. We provide its meromorphic continuation and discuss its singularities., Comment: 16 pages, Latex, reportSFB288-112

We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one., Comment: 71 pages, Latex, reportSFB288-118

This paper is a continuation of our work on theta and zeta functions In the previous papers we considered the case of even dimensional rank one symmetric spaces of non-compact type. The present is concerned with the odd-dimensional case, i.e. with odd-dimensional real hyperbolic manifolds. It is the natural appearence of eta invariants in connection with super theta and zeta functions what makes this case particularly interesting. (authors name corrected), Comment: 27 pages, Latex, reportSFB288-1994