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This paper describes the Polarimetric and Helioseismic Imager on the Solar Orbiter mission (SO/PHI), the first magnetograph and helioseismology instrument to observe the Sun from outside the Sun-Earth line. It is the key instrument meant to address the top-level science question: How does the solar dynamo work and drive connections between the Sun and the heliosphere? SO/PHI will also play an important role in answering the other top-level science questions of Solar Orbiter, as well as hosting the potential of a rich return in further science. SO/PHI measures the Zeeman effect and the Doppler shift in the FeI 617.3nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO_3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders (LCVRs). The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2kx2k CMOS detector. To save valuable telemetry, the raw data are reduced on board, including being inverted under the assumption of a Milne-Eddington atmosphere, although simpler reduction methods are also available on board. SO/PHI is composed of two telescopes; one, the Full Disc Telescope (FDT), covers the full solar disc at all phases of the orbit, while the other, the High Resolution Telescope (HRT), can resolve structures as small as 200km on the Sun at closest perihelion. The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line., Comment: 36 pages, 41 figures

We describe the design of the Sunrise Filter Imager (SuFI) and the Image Stabilization and Light Distribution (ISLiD) unit onboard the Sunrise balloon borne solar observatory. This contribution provides the necessary information which is relevant to understand the instruments working principles, the relevant technical data, and the necessary information about calibration issues directly related to the science data., Comment: accepted for publication in Solar Physics on 4 September 2010

Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier perturbation treatment of disorder in a superconducting ring subjected to an imaginary vector potential proportional to a depinning field for flux lines bound to random columnar defects parallel to the axis of the ring. The absence of localization in the ring threaded by an A-B flux for sufficiently weak disorder is compatible with large free electron type persistent current obtained in recent studies of the above model.

We reconsider the problem of the enhancement of tunnelling of a quantum particle induced by disorder of a one-dimensional tunnel barrier of length $L$, using two different approximate analytic solutions of the invariant imbedding equations of wave propagation for weak disorder. The two solutions are complementary for the detailed understanding of important aspects of numerical results on disorder-enhanced tunnelling obtained recently by Kim et al. (Phys. rev. B{\bf 77}, 024203 (2008)). In particular, we derive analytically the scaled wavenumber $(kL)$-threshold where disorder-enhanced tunnelling of an incident electron first occurs, as well as the rate of variation of the transmittance in the limit of vanishing disorder. Both quantities are in good agreement with the numerical results of Kim et al. Our non-perturbative solution of the invariant imbedding equations allows us to show that the disorder enhances both the mean conductance and the mean resistance of the barrier., Comment: 10 pages

The mean and the variance of the logarithm of the conductance ($ln g$) in the localized regime in the one-dimensional Anderson model are calculated analytically for weak disorder, starting from the recursion relations for the complex reflection- and transmission amplitudes. The exact recursion relation for the reflection amplitudes is approximated by improved Born approximation forms which ensure that averaged reflection coefficients tend asymptotically to unity in the localized regime, for chain lengths $L=Na\to\infty$. In contrast the familiar Born approximation of perturbation theory would not be adapted for the localized regime since it constrains the reflection coefficient to be less than one. The proper behaviour of the reflection coefficient (and of other related reflection parameters) is responsible for various anomalies in the cumulants of $\ln g$, in particular for the well-known band center anomaly of the localization length. While a simple improved Born approximation is sufficient for studying cumulants at a generic band energy, we find that a generalized improved Born approximation is necessary to account satisfactorily for numerical results for the band center anomaly in the mean of $\ln g$. For the variance of $\ln g$ at the band center, we reveal the existence of a weak anomalous quadratic term proportional to $L^2$, besides the previously found anomaly in the linear term. At a generic band energy the variance of $\ln g$ is found to be linear in $L$ and is given by twice the mean, up to higher order corrections which are calculated. We also exhibit the $L=$independent offset terms in the variance, which strongly depend on reflection anomalies.

We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $\phi$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites of the ring is assumed to be partitioned into $M$ pairs of identical nearest-neighbour sites (dimers). The site energies for different dimers are taken to be uncorrelated gaussian variables. For this system we obtain the exact flux-dependent energy levels to second order in the random site energies, using an earlier exact transfer matrix perturbation theory. These results are used to study the mean persistent current generated by $N_e\leq N$ spinless electrons occupying the $N_e$ lowest levels of the flux-dependent energy band at zero temperature. Detailed analyses are carried out in the limit $1\ll N_e\ll N$ and for a half-filled band ($N_e=N/2$), for magnetic fluxes $-1/2 <\phi/\phi_0<1/2$. While the uncorrelated disorder leads to a reduction of the persistent current, the disorder correlation acts to enhance it. In particular, in the half-filled band case the correlated disorder leads to a global flux-dependent enhancement of persistent current which has the same form for even and odd $N_e$. At low filling of the energy band the effect of the disorder on the persistent current is found to depend on the parity of $N_e$: the correlated disorder yields a reduction of the current for odd $N_e$ and an enhancement of the current for even $N_e$., Comment: 18

Transport in a disordered tight-binding wire involves a collection of different mean free paths resulting from the distinct fermi points, which correspond to the various scattering channels of the wire. The generalization of Thouless' relation between the mean free path and the localization length $\xi$ permits to define an average channel mean free path,$\bar\ell$, such that $\xi\sim N\bar\ell$ in an $N$-channel system. The averaged mean free path $\bar\ell$ is expressed exactly in terms of the total reflection coefficient of the wire and compared with the mean free path defined in the maximum entropy approach.

We study reflection and transmission of waves in a random tight-binding system with absorption or gain for weak disorder, using a scattering matrix formalism. Our aim is to discuss analytically the effects of absorption or gain on the statistics of wave transport. Treating the effects of absorption or gain exactly in the limit of no disorder, allows us to identify short- and long lengths regimes relative to absorption- or gain lengths, where the effects of absorption/gain on statistical properties are essentially different. In the long-lengths regime we find that a weak absorption or a weak gain induce identical statistical corrections in the inverse localization length, but lead to different corrections in the mean reflection coefficient. In contrast, a strong absorption or a strong gain strongly suppress the effect of disorder in identical ways (to leading order), both in the localization length and in the mean reflection coefficient., Comment: Important revisions and expansion caused by a crucial property of $\hat Q$

We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection coefficients to fourth order in the weakly disordered site energies. These results confirm the validity of single-parameter scaling theory in a domain where the higher transmission cumulants may be neglected. We compare our results with earlier results for transmission cumulants in the weak localization domain based on the phase randomization hypothesis.

The cumulants of the logarithm of the conductance (lng) in the localized regime in the one-dimensional Anderson model are calculated exactly in the second Born approximation for weak disorder. Only the first two cumulants turn out to ne non-zero since the third and fourth cumulants vanish identically and the higher cumulants are of higher order in the disorder. The variance and the mean of lng vary linearly with length $L$ while their ratio is proportional to the inverse localization length. The resulting exact log-normal distribution of conductance thus corresponds to a special form of two-parameter scaling. This contradicts the standard one-parameter scaling in the random phase approximation.

This paper extends an earlier analytical scattering matrix treatment of conductance and localization in coupled two- and three Anderson chain systems for weak disorder when evanescent states are present at the Fermi level. Such states exist typically when the interchain coupling exceeds the width of propagating energy bands associated with the various transverse eigenvalues of the coupled tight-binding systems. We calculate reflection- and transmission coefficients in cases where, besides propagating states, one or two evanescent states are available at the Fermi level for elastic scattering of electrons by the disordered systems. We observe important qualitative changes in these coefficients and in the related localization lengths due to ineffectiveness of the evanescent modes for transmission and reflection in the various scattering channels. In particular, the localization lengths are generally significantly larger than the values obtained when evanescent modes are absent. Effects associated with disorder mediated coupling between propagating and evanescent modes are shown to be suppressed by quantum interference effects, in lowest order for weak disorder.

We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L^{-1}_c=N.\xi^{-1}$ for the considered systems with $N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disorder. The inverse localization length is defined from the exponential decay of the two-probe Landauer conductance, which is determined from an earlier transfer matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact expressions above differ qualitatively from Dorokhov's localization length identified as the length scaling parameter in his scaling description of the distribution of the participation ratio. For N=3 we also discuss the case where the coupled chains are arranged on a strip rather than periodically on a tube. From the transfer matrix treatment we also obtain reflection coefficients matrices which allow us to find mean free paths and to discuss their relation to localization lengths in the two- and three channel systems.

We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic boundary conditions between the chains. The finite disordered wires are connected to ideal leads and the localization length is defined from the Landauer conductance in terms of the transmission coefficients matrix. The transmission- and reflection amplitudes in properly defined quantum channels are obtained from S-matrices constructed from transfer matrices in Bloch wave bases for the various quasi-1D systems. Our exact analytic expressions for localization lengths for weak disorder reduce to the Thouless expression for 1D systems in the limit of vanishing interchain hopping. For weak interchain hopping the localization length decreases with respect to the 1D value in all three cases. In the three-channel cases it increases with interchain hopping over restricted domains of large hopping.

The invariant imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered 1D chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection (transmission) coefficients of Anderson chains of N and N-1 atoms embedded in infinite non-disordered chains. We show that various available analytical and numerical results for reflection phase distributions in the Anderson- and invariant imbedding models are in good qualitative agreement, as expected from the above equivalence of these models. We also discuss the distribution of reflection phases and of reflection delay times for an Anderson model with a simple distribution of on-site potentials characterizing extreme strong disorder., Comment: 6 pages, RevTex

We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux, using he one-band tight-binding model for a ring of N-sites with random site energies. The secular equation for the eigenenergies expressed in terms of transfer matrices in the site representation is solved exactly to second order in a perturbation theory for weak disorder and fluxes differing from half-integer multiples of the elementary flux quantum. From the equilibrium currents associated with the one-electron eigenstates we derive closed analytic expressions for the disorder averaged persistent current for even and odd numbers, Ne, of electrons in the ground state. Explicit discussion for the half-filled band case confirms that the persistent current is flux periodic as in the absence of disorder, and that its amplitude is generally suppressed by the effect of the disorder. In comparison to previous results, based on an approximate analysis of the secular equation, the current suppression by disorder is strongly enhanced by a new flux-dependent factor., Comment: 15 pages, LaTex 2e

We present an analytical study of the Lyapunov exponent for electronic states in a disordered tight-binding ring, with N sites of spacing c, in the presence of a non-hermitian field component h, for weak disorder. This system has been proposed by Hatano and Nelson (HN) as a model for the depinning of flux lines bound to columnar defects in a superconducting cylindrical shell in a transverse magnetic field proportional to h. We calculate the Lyapunov exponent to second order in the disorder in the domain of complex energies in an ordered ring in a non-hermitian field. The result exhibits an important antisymmetry property of the Lyapunov exponent, which reflects the directionality of the non-hermitian localization. By combining the results for the Lyapunov exponent with a previous calculation of the complex eigenvalues for weak disorder, we show that the localization length of the complex eigenenergy states is generally larger than the circumference (Nc) of the ring. This supports the initial suggestion of HN that these eigenstates are delocalized. Our perturbative treatment of the disorder when applied for an open chain embedded in an infinite non-disordered chain recovers the Thouless formula for the zero-field localization length., Comment: 15 pages, LaTex 2e