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The Stratospheric Observatory for Infrared Astronomy (SOFIA) has recently concluded a set of engineering flights for Observatory performance evaluation. These in-flight opportunities are viewed as a first comprehensive assessment of the Observatory's performance and are used to guide future development activities, as well as to identify additional Observatory upgrades. Pointing stability was evaluated, including the image motion due to rigid-body and flexible-body telescope modes as well as possible aero-optical image motion. We report on recent improvements in pointing stability by using an active mass damper system installed on the telescope. Measurements and characterization of the shear layer and cavity seeing, as well as image quality evaluation as a function of wavelength have also been performed. Additional tests targeted basic Observatory capabilities and requirements, including pointing accuracy, chopper evaluation and imager sensitivity. This paper reports on the data collected during these flights and presents current SOFIA Observatory performance and characterization., Comment: 13 pages, 13 figure, and 2 tables; accepted by ApJS

There was an error in the Funding statement. The correct funding is: "Supported by the NIH grants R01 AR047825 and R01 AI07055. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript."

We study general quantum waveguides and establish explicit effective Hamiltonians for the Laplacian on these spaces. A conventional quantum waveguide is an $${\epsilon}$$ -tubular neighbourhood of a curve in $${\mathbb{R}^3}$$ and the object of interest is the Dirichlet Laplacian on this tube in the asymptotic limit $${\epsilon\ll1}$$ . We generalise this by considering fibre bundles M over a complete d-dimensional submanifold $${B\subset\mathbb{R}^{d+k}}$$ with fibres diffeomorphic to $${F\subset\mathbb{R}^k}$$ , whose total space is embedded into an $${\epsilon}$$ -neighbourhood of B. From this point of view, B takes the role of the curve and F that of the disc-shaped cross section of a conventional quantum waveguide. Our approach allows, among other things, for waveguides whose cross sections F are deformed along B and also the study of the Laplacian on the boundaries of such waveguides. By applying recent results on the adiabatic limit of Schrodinger operators on fibre bundles we show, in particular, that for small energies the dynamics and the spectrum of the Laplacian on M are reflected by the adiabatic approximation associated with the ground state band of the normal Laplacian. We give explicit formulas for the accordingly effective operator on L 2(B) in various scenarios, thereby improving and extending many of the known results on quantum waveguides and quantum layers in $${\mathbb{R}^3}$$ .

The thermal impact of magmatic underplating at various crustal levels is studied along a traverse through the Ivrea‐Verbano Zone and Strona‐Ceneri Zone in northern Italy. Geochronological and petrologic data are compared to a two‐dimensional thermal‐kinematic model. Field data and numerical simulation show the strong disturbance of the temperature field in the lower and intermediate crust in relation to magmatic underplating leading to granulite‐ to amphibolite‐facies metamorphism as well as reequilibration of mineral chemical and isotopic systems. Magmatic underplating leaves a crust with an apparently heterogeneous tectonometamorphic evolution, as information on the earlier history is preserved only at upper crustal levels.

We consider the Schr\"odinger operator in two dimensions with a periodic potential and a strong constant magnetic field perturbed by slowly varying non-periodic scalar and vector potentials, $\phi(\epsilon x)$ and $A(\epsilon x)$, for $\epsilon\ll 1$. For each isolated family of magnetic Bloch bands we derive an effective Hamiltonian that is unitarily equivalent to the restriction of the Schr\"odinger operator to a corresponding almost invariant subspace. At leading order, our effective Hamiltonian can be interpreted as the Peierls substitution Hamiltonian widely used in physics for non-magnetic Bloch bands. However, while for non-magnetic Bloch bands the corresponding result is well understood, for magnetic Bloch bands it is not clear how to even define a Peierls substitution Hamiltonian beyond a formal expression. The source of the difficulty is a topological obstruction: magnetic Bloch bundles are generically not trivializable. As a consequence, Peierls substitution Hamiltonians for magnetic Bloch bands turn out to be pseudodifferential operators acting on sections of non-trivial vector bundles over a two-torus, the reduced Brillouin zone. Part of our contribution is the construction of a suitable Weyl calculus for such pseudos. As an application of our results we construct a new family of canonical one-band Hamiltonians $H^B_{\theta,q}$ for magnetic Bloch bands with Chern number $\theta\in \mathbb{Z}$ that generalizes the Hofstadter model $H^B_{\rm Hof} = H^B_{0,1}$ for a single non-magnetic Bloch band. It turns out that $H^B_{\theta,q}$ is isospectral to $H^{q^2B}_{\rm Hof}$ for any $\theta$ and all spectra agree with the Hofstadter spectrum depicted in his famous black and white butterfly. However, the resulting Chern numbers of subbands, corresponding to Hall conductivities, depend on $\theta$ and $q$, and thus the models lead to different colored butterflies., Comment: 39 pages, 4 figures. Final version to appear in Analysis & PDE

We show how to relate the full quantum dynamics of a spin-1/2 particle on R^d to a classical Hamiltonian dynamics on the enlarged phase space R^d x S^2 up to errors of second order in the semiclassical parameter. This is done via an Egorov-type theorem for normal Wigner-Weyl calculus for R^d [Lei10,Fol89] combined with the Stratonovich-Weyl calculus for SU(2) [VGB89]. For a specific class of Hamiltonians, including the Rabi- and Jaynes-Cummings model, we prove an Egorov theorem for times much longer than the semiclassical time scale. We illustrate the approach for a simple model of the Stern-Gerlach experiment., 24 pages

We demonstrate that a highly excited quantum electromagnetic mode strongly interacting with a single qubit exhibits several distinct resonances in addition to the Bloch-Siegert resonance condition that arises in the interaction with classical radiation. The resonance phenomena are associated with non-classical effects: Collapse of Rabi oscillations, splitting of the photon wave packet, and field-qubit entanglement. The analysis is based on a semiclassical phase-space flow of 2-by-2 matrices and becomes exact when the photon number tends to infinity. The flow equations are solved perturbatively and numerically, showing that the resonant detuning of the field and qubit frequencies lie on two branches in the leading order, that further split into distinct curves in higher orders., Comment: 17 pages, 3 figures

Preface.- Semiclassical and adiabatic limits.- Singular spaces.- Spectral and scattering theory.- Wave propagation and topological applications.

The Stratospheric Observatory for Infrared Astronomy (SOFIA) has recently concluded a set of engineering flights for Observatory performance evaluation. These in-flight opportunities have been viewed as a first comprehensive assessment of the Observatory's performance and will be used to address the development activity that is planned for 2012, as well as to identify additional Observatory upgrades. A series of 8 SOFIA Characterization And Integration (SCAI) flights have been conducted from June to December 2011. The HIPO science instrument in conjunction with the DSI Super Fast Diagnostic Camera (SFDC) have been used to evaluate pointing stability, including the image motion due to rigid-body and flexible-body telescope modes as well as possible aero-optical image motion. We report on recent improvements in pointing stability by using an Active Mass Damper system installed on Telescope Assembly. Measurements and characterization of the shear layer and cavity seeing, as well as image quality evaluation as a function of wavelength have been performed using the HIPO+FLITECAM Science Instrument configuration (FLIPO). A number of additional tests and measurements have targeted basic Observatory capabilities and requirements including, but not limited to, pointing accuracy, chopper evaluation and imager sensitivity. SCAI activities included in-flight partial Science Instrument commissioning prior to the use of the instruments as measuring engines. This paper reports on the data collected during the SCAI flights and presents current SOFIA Observatory performance and characterization.

The NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA) employs a 2.5-meter reflector telescope in a Boeing 747SP. The telescope is housed in an open cavity and is subjected to aeroacoustic and inertial disturbances in flight. To meet pointing requirements, SOFIA must achieve a pointing stability of approximately 0.5 arcseconds RMS. An active damping control system is being developed for SOFIA to reduce image jitter and image degradation due to resonance of the telescope assembly. Our paper discusses the history of the active damping design for SOFIA, from early concepts to the current implementation which has recently completed a ground and flight testing for proof-of-concept. We describe some milestones in the analysis and testing of the telescope assembly which guided the development of the vibration control system. The control synthesis approach and current implementation of the active damping control system is presented. Finally, we summarize the performance observed in early flight tests and the steps that are currently foreseen to completing the development of this system.

We consider the time dependent Schrodinger equation on a fibre bundle in the adiabatic limit. We allow the fibres to have a boundary, in which case we impose Dirichlet conditions. In particular this allows us to understand, in a general setting, results obtained in the context of quantum waveguides (see the review [2]), in which case the bundle is usually a solid cylinder or a square.

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an $\epsi$-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation., Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was removed

Sensing of infectious danger by toll-like receptors (TLRs) on macrophages causes not only a reprogramming of the transcriptome but also changes in the cytoskeleton important for cell spreading and motility. Since manual determination of cell contact areas from fluo-, rescence micrographs is very time-consuming and prone to bias, we have developed and tested algorithms for automated measurement of macrophage spreading. The two-step method combines identification of cells by nuclear staining with DAPI and cell surface staining of the integrin CD11b. Automated image analysis correlated very well with manual annotation in resting macrophages and early after stimulation, whereas at later time points the automated cell segmentation algorithm and manual annotation showed slightly larger variation. The method was applied to investigate the impact of genetic or pharmacological inhibition of known TLR signaling components. Deficiency in the adapter protein Myd88 strongly reduced spreading activity at the late time points, but had no impact early after LPS-stimulation. A similar effect was observed upon pharmacological inhibition of MEK1, the kinase activating the mitogen-activated protein kinases (MAPK) ERK1/2, indicating that ERK1/2 mediates Myd88-dependent macrophages spreading. In contrast, macrophages lacking the MAPK p38 were impaired in the initial spreading response but responded normally 8-24 h after stimulation. The dichotomy of p38 and ERK1/2 MAPK effects on early and late macrophage spreading raises the question which of the respective substrate proteins mediate(s) cytoskeletal remodeling and spreading. The automated measurement of cell spreading described here increases the objectivity and greatly reduces the time required for such investigations and is therefore expected to facilitate larger throughput analysis of macrophage spreading, e.g., in siRNA knockdown screens.

We consider the Pauli-Fierz Hamiltonian with dynamical nuclei and investigate the transitions between the resonant electronic energy levels under the assumption that there are no free photons in the beginning. Coupling the limits of small fine structure constant and of heavy nuclei allows us to prove the validity of the Born-Oppenheimer approximation at leading order and to provide a simple formula for the rate of spontaneous decay., To appear in Commun. Math. Phys

The Stratospheric Observatory for Infrared Astronomy (SOFIA) is an airborne observatory for astronomical observations at wavelengths ranging from 0.3-1600 µm. It consists of a telescope with an effective aperture of 2.5 m, which is mounted in a heavily modified Boeing 747SP. The aircraft features an open port cavity that gives the telescope an unobstructed view of the sky. Hence the optical system is subject to both aerodynamic loads from airflow entering the cavity, and to inertial loads introduced by motion of the airborne platform. A complex suspension assembly was designed to stabilize the telescope. Detailed end-to-end simulations were performed to estimate image stability based on the mechatronic design, the expected loads, and optical influence parameters. In December 2010 SOFIA entered its operational phase with a series of Early Science flights, which have relaxed image quality requirements compared to the full operations capability. At the same time, those flights are used to characterize image quality and image stability in order to validate models and to optimize systems. Optimization of systems is not based on analytical models, but on models derived from system identification measurements that are performed on the actual hardware both under controlled conditions and operational conditions. This paper discusses recent results from system identification measurements, improvements to image stability, and plans for the further enhancement of the system.

We show how to translate recent results on effective Hamiltonians for quantum systems constrained to a submanifold by a sharply peaked potential to quantum systems on thin Dirichlet tubes. While the structure of the problem and the form of the effective Hamiltonian stays the same, the difficulties in the proofs are different., Comment: 6 pages, 1 figure

The NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA) employs a 2.5-meter reflector telescope in a Boeing 747SP. The telescope is housed in an open cavity and will be subjected to aeroacoustic and inertial disturbances. The image stability goal for SOFIA is 0.2 arc-seconds (RMS). Throughout the development phase of the project, analytical models were employed to predict the image stability performance of the telescope, and to evaluate pointing performance improvement measures. These analyses clearly demonstrated that key aspects which determined performance were: 1) Disturbance environment and relevant load-paths 2) Telescope modal behavior 3) Sensor and actuator placement 4) Control algorithm design The SOFIA program is now entering an exciting phase in which the characteristics of the telescope and the cavity environment are being verified through ground and airborne testing. A modal survey test (MST) was conducted in early 2008 to quantify the telescope modal behavior. We will give a brief overview of analytical methods which have been employed to assess/improve the pointing stability performance of the SOFIA telescope. In this context, we will describe the motivation for the MST, and the pre-test analysis which determined the modes of interest and the required MST sensor/shaker placement. A summary will then be given of the FEM-test correlation effort, updated end-to-end simulation results, and actual data coming from telescope activation test flights.

We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to earlier works we consider at the same time the effects of variations in the constraining potential and the effects of interior and exterior geometry which appear at different energy scales and thus provide, for the first time, a complete picture ranging over all interesting energy scales. We show that the leading order contribution to the effective Hamiltonian is the adiabatic potential given by an eigenvalue of the confining potential well-known in the context of adiabatic quantum wave guides. At next to leading order we see effects from the variation of the normal eigenfunctions in form of a Berry connection. We apply our results to quantum wave guides and provide an example for the occurrence of a topological phase due to the geometry of a quantum wave circuit, i.e. a closed quantum wave guide., Comment: 19 pages, 4 figures

Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schrödinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory.

We consider a system of N non-relativistic spinless quantum particles (``electrons'') interacting with a quantized scalar Bose field (whose excitations we call ``photons''). We examine the case when the velocity v of the electrons is small with respect to the one of the photons, denoted by c (v/c= epsilon << 1). We show that dressed particle states exist (particles surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and the velocity dependent Darwin interaction and a mass renormalization at order (v/c)^{2}. Beyond that order the effective dynamics are expected to be dissipative. The main mathematical tool we use is adiabatic perturbation theory. However, in the present case there is no eigenvalue which is separated by a gap from the rest of the spectrum, but its role is taken by the bottom of the absolutely continuous spectrum, which is not an eigenvalue. Nevertheless we construct approximate dressed electrons subspaces, which are adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln (v/c)^{-1}}. We also give an explicit expression for the non adiabatic transitions corresponding to emission of free photons. For the radiated energy we obtain the quantum analogue of the Larmor formula of classical electrodynamics., 67 pages, 2 figures, version accepted for publication in Communications in Mathematical Physics

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering., Comment: 17 pages, no figures

We study the large scale evolution of a scalar lattice excitation which satisfies a discrete wave-equation in three dimensions. We assume that the dispersion relation associated to the elastic coupling constants of the wave-equation is acoustic, i.e., it has a singularity of the type |k| near the vanishing wave vector, k=0. To derive equations that describe the macroscopic energy transport we introduce the Wigner transform and change variables so that the spatial and temporal scales are of the order of epsilon. In the continuum limit, which is achieved by sending the parameter epsilon to 0, the Wigner transform disintegrates into three different limit objects: the transform of the weak limit, the H-measure and the Wigner-measure. We demonstrate that these three limit objects satisfy a set of decoupled transport equations: a wave-equation for the weak limit of the rescaled initial data, a dispersive transport equation for the regular limiting Wigner measure, and a geometric optics transport equation for the H-measure limit of the initial data concentrating to k=0. A simple consequence of our result is the complete characterization of energy transport in harmonic lattices with acoustic dispersion relations., 34 pages, 2 figures

We use recent results on precise coupling terms in the optimal supera- diabatic basis in order to determine exponentially small transition probabilities in the adiabatic limit of time-dependent two-level systems. As examples, we discuss the Landau-Zener and the Rosen-Zener models.

We study the motion of electrons in a periodic background potential (usually resulting from a crystalline solid). For small velocities one would use either the non-magnetic or the magnetic Bloch hamiltonian, while in the relativistic regime one would use the Dirac equation with a periodic potential. The dynamics, with the background potential included, is perturbed either through slowly varying external electromagnetic potentials or through a slow deformation of the crystal. In either case we discuss how the Hilbert space of states decouples into almost invariant subspaces and explain the effective dynamics within such a subspace.

In Section 3 of his paper (N. Gisin, Phys. Lett. A 210 (1996) 151), Gisin argues that a ``careless application of generalized quantum measurements can violate Bell's inequality even for mixtures of product states.'' However, the observed violation of the CHSH inequality is not in fact due to the application of generalized quantum measurements, but rather to a misapplication of the inequality itself -- to conditional expectations in which the conditioning depends upon the measurements under consideration.

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye., Comment: 24 pages

We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schroedinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a node of the wavefunction, where the law of motion is ill-defined. The aim is to show, under suitable assumptions on the initial wavefunction and the potential, global existence of almost all solutions. We provide a simpler and more transparent proof of the known global existence result for spinless Schroedinger particles and extend the result to particles with spin, to the presence of magnetic fields, and to Dirac wavefunctions. Our main new result are conditions on the current vector field on configuration-space-time which are sufficient for almost-sure global existence., 18 pages

We review the foundations of the scattering formalism for one-particle potential scattering and discuss the generalisation to the simplest case of many non-interacting particles. We point out that the “straight path motion” of the particles, which is achieved in the scattering regime, is at the heart of the crossing statistics of surfaces, which should be thought of as detector surfaces. We prove the relevant version of the many-particle flux across surfaces theorem and discuss what needs to be proven for the foundations of scattering theory in this context.

For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special Hamiltonians we explicitly determine the asymptotic behavior of the exponentially small coupling term for generic two-state systems with real-symmetric Hamiltonian. The superadiabatic coupling term takes a universal form and depends only on the location and the strength of the complex singularities of the adiabatic coupling function. As shown in [BeTe1], first order perturbation theory in the superadiabatic representation then allows to describe the time-development of exponentially small adiabatic transitions and thus to rigorously confirm Michael Berry's [Ber] predictions on the universal form of adiabatic transition histories., Comment: 30 pages, 1 figure

Let V Γ be a lattice periodic potential and A and Φ external electromagnetic potentials which vary slowly on the scale set by the lattice spacing. It is shown that the Wigner function of a solution of the Schrodinger equation with Hamiltonian operator \(H = \tfrac{1}{2}{{( - i{{\nabla }_{x}} - A(\varepsilon x))}^{2}} + {{V}_{\Gamma }}(x) + \phi (\varepsilon x)\) propagates along the flow of the semiclassical model of solid states physics up to an error of order e. If e-dependent corrections to the flow are taken into account, the error is improved to order e 2. We also discuss the propagation of the Wigner measure. The results are obtained as corollaries of an Egorov type theorem proved in [PST3].

3.1 Almost invariant subspaces 3.2 Mapping to the reference space 3.3 Effective dynamics 3.3.1 Expanding the effective Hamiltonian 3.4 Semiclassical limit for effective Hamiltonians 3.4.1 Semiclassical analysis for matrix-valued symbols 3.4.2 Geometrical interpretation: the generalized Berry connection 3.4.3 Semiclassical observables and an Egorov theorem

5.1 The periodic Hamiltonian 5.2 Adiabatic perturbation theory for Bloch bands 5.2.1 The almost invariant subspace 5.2.2 The intertwining unitaries 5.2.3 The effective Hamiltonian 5.3 Semiclassical dynamics for Bloch electrons