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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Improved spatial resolution for spot sampling in thermal desorption atomic force microscopy – mass spectrometry via rapid heating functions

The key to advancing materials is to understand and control their structure and chemistry. However, thorough chemical characterization is challenging since existing techniques characterize only a few properties of the specimen, thereby necessitating multiple measurement platforms to acquire the necessary information. The multimodal combination of atomic force microscopy (AFM) and mass spectrometry (MS) transcends existing analytical capabilities for nanometer scale spatially resolved correlation of the chemical and physical properties of a sample surface. One such hybrid system employs heated AFM cantilevers for thermal desorption (TD) sampling of molecules from a surface and subsequent gas phase ionization and detection of the liberated species by MS. Here in this paper, we report on the use of voltage pulse trains to tailor cantilever heating such that spot sampling size was reduced and mass spectral signal was improved compared to constant voltage, static heating of the cantilever. Desorption efficiency (DE), defined as the quotient of the mass spectral signal intensity and the volume of the desorption crater, was used to judge the effectiveness of a particular tailored heating function. To guide the development and optimization of the heating functions and aid in interpreting experimental results, a 1D finite element model was developed that predicted the cantilever response to different heating functions. Three tailored heating functions that used different combinations, magnitudes, and durations of rectangular voltage pulses, were used for surface spot sampling. The resultant sampling spot size and DE were compared to the same metrics obtained with the conventional method that uses a single voltage pulse. Using a model system composed of a thin film of ink containing pigment yellow 74 as a model system, desorption craters shrunk from 2 μm, using the conventional approach, to 310 nm using the optimum tailored heating function. This same pulsed heating function produced a 381× improvement in the DE and an 8× improvement in spatial resolution compared to the conventional heating approach showing that signal/amount of material sampled was improved significantly by this new cantilever heating strategy.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Evidence for non-electrostatic interactions between a pyrophosphate-functionalized uranyl peroxide nanocluster and iron (hydr)oxide minerals

We report the terminal oxygen atoms of the pyrophosphate groups in the uranyl peroxide nanocluster U 24 Pp 12 ([(UO 2 ) 24 (O 2 ) 24 (P 2 O 7 ) 12 ] 48- ) are not fully satisfied by bond valence considerations and can become protonated. This functionality could allow for specific interactions with mineral surfaces, as opposed to the electrostatically-driven interactions observed between non-functionalized uranyl peroxide nanoclusters and mineral surfaces. The sorption of U 24 Pp 12 to goethite and hematite was studied using batch sorption experiments as a function of U 24 Pp 12 concentration, mineral concentration, and pH. A suite of spectroscopic techniques, scanning electron microscopy, and electrophoretic mobility measurements were used to examine the minerals before and after reaction with U 24 Pp 12 , leading to a proposed conceptual model for U 24 Pp 12 interactions with goethite. The governing rate laws were determined and compared to those previously determined for a non-functionalized uranyl peroxide nanocluster. The rate of uranyl peroxide nanocluster sorption depends on the charge density and functionalized component of the uranyl peroxide cage. Electrophoretic mobility and attenuated total reflectance Fourier transform infrared spectroscopy analyses show that an inner-sphere complex forms between the U 24 Pp 12 cluster and the goethite surface through the terminal pyrophosphate groups, leading to a proposed conceptual model in which U 24 Pp 12 interacts with the triply-coordinated reactive sites on the (110) plane of goethite. Finally, these results demonstrate that the behavior of U 24 Pp 12 at the iron (hydr)oxide-water interface is unique relative to interactions of the uranyl ion and non-functionalized uranyl peroxide nanoclusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Computational insights into the interaction of water with the UiO-66 metal–organic framework and its functionalized derivatives

The UiO-66 metal–organic framework (MOF) has been identified as a promising hydrophilic material for water harvesting. Recent studies show that its water uptake ability at low relative humidity (RH) can be improved by incorporating hydrophilic functional groups into the framework. In this work, we provide computational insights into the adsorption of water in UiO-66 and its functionalized derivatives to reveal the role played by different adsorption sites and functional groups in the adsorption mechanism. We started by developing molecular models for UiO-66, UiO-66-NH 2 , UiO-66-OH, and UiO-66-(OH) 2 compatible with the MB-pol data-driven many-body potential of water. We then benchmarked these models against ab initio data. Here we used these models to perform molecular dynamics simulations and calculate radial distribution functions, IR spectra, and two-dimensional density distribution maps for water in the MOFs. These results consistently show that the μ 3 -OH sites are the preferential interaction sites for water in UiO-66 and all its variants, and the formation of localised water clusters inside the octahedral pores is responsible for the abrupt step in the experimental adsorption isotherms. Furthermore, the presence of functional groups in the framework allows water to cluster in the octahedral pores at lower RH, thus making the MOF a more efficient water harvester. Overall, this study provides molecular-level insights into the pore filling process of UiO-66 and its functionalized derivatives, which are needed for the design of efficient water harvesting materials based on MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Planck 2013 results. IV. Low Frequency Instrument beams and window functions

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). Knowledge of the beam profiles is necessary for determining the transfer function to go from the observed to the actual sky anisotropy power spectrum. The main beam distortions affect the beam window function, complicating the reconstruction of the anisotropy power spectrum at high multipoles, whereas the sidelobes affect the low and intermediate multipoles. The in-flight assessment of the LFI main beams relies on the measurements performed during Jupiter observations. By stacking the datafrom multiple Jupiter transits, the main beam profiles are measured down to-20 dB at 30 and 44 GHz, and down to-25 dB at 70 GHz. The main beam solid angles are determined to better than 0.2% at each LFI frequency band. The Planck pre-launch optical model is conveniently tuned to characterize the main beams independently of any noise effects. This approach provides an optical model whose beams fully reproduce the measurements in the main beam region, but also allows a description of the beams at power levels lower than can be achieved by the Jupiter measurements themselves. The agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band. The simulated beams are used for the computation of the window functions for the effective beams. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer bandshapes. The total uncertainties in the effective beam window functions are: 2% and 1.2% at 30 and 44 GHz, respectively (at ℓ ≈ 600), and 0.7% at 70 GHz (at ℓ ≈ 1000).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Stiffness and strength of oxygen-functionalized graphene with vacancies

The 2D elastic modulus (E{sup 2D}) and strength (σ{sup 2D}) of defective graphene sheets containing vacancies, epoxide, and hydroxyl functional groups are evaluated at 300 K by atomistic simulations. The fraction of vacancies is controlled in the range 0% to 5%, while the density of functional groups corresponds to O:C ratios in the range 0% to 25%. In-plane modulus and strength diagrams as functions of vacancy and functional group densities are generated using models with a single type of defect and with combinations of two types of defects (vacancies and functional groups). It is observed that in models containing only vacancies, the rate at which strength decreases with increasing the concentration of defects is largest, followed by models containing only epoxide groups and those with only hydroxyl groups. The effect on modulus of vacancies and epoxides present alone in the model is similar, and much stronger than that of hydroxyl groups. When the concentration of defects is large, the combined effect of the functional groups and vacancies cannot be obtained as the superposition of individual effects of the two types of defects. The elastic modulus deteriorates faster (slower) than predicted by superposition in systems containing vacancies and hydroxyl groups (vacancies and epoxide groups)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The screening effects of the screened exchange hybrid functional in surface systems: A case study on the CO/Pt(111) problem

The screened exchange (sX) hybrid functional has been widely used in computational material science. Although it has widely been studied in bulk systems, less is known about its functional behavior in surface systems which are crucial to many technologies such as materials synthesis and nano-electronic devices. Assessing the screening dependent functional behaviors in the surface systems is therefore important for its application in such systems. In this work, we investigate the screening effects of the sX in CO adsorption on Pt(111) surface. The differences between the sX and Heyd-Scuseria-Ernzerhof (HSE06) hybrid functionals, and the effects of screening parameters are studied. The screening has two effects: first, the HOMO-LUMO gap is screening dependent. This affects the site preference most significantly. In this work, atop adsorption of CO/Pt(111) is predicted by the hybrid functionals with screened exchange potential. The sX(1.44) gives the largest HOMO-LUMO gap for the isolated CO molecule. The adsorption energy difference between the atop and fcc site is also the largest by the sX(1.44) which is explained by the reduced metal d states to the CO 2π* state back-donation, with stronger effect for the fcc adsorption than for the atop adsorption; second, the adsorption energy is screening dependent. This can be seen by comparing the sX(2.38) and HSE06 which have different screening strengths. They show similar surface band structures for the CO adsorption but different adsorption energies, which is explained by the stronger CO 5σ state to the metal d states donation or the effectively screened Pauli repulsion. This work underlines the screening strength as a main difference between sX and HSE06, as well as an important hybrid functional parameter for surface calculation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Weight-lattice discretization of Weyl-orbit functions

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight lattice, so that digitized data on the fundamental region can be Fourier-analyzed. The discretized orbit function has arguments that are redundant if related by the affine Weyl group, while its labels, the Weyl-orbit representatives, invoke the dual affine Weyl group. Here we discretize the orbit functions in a novel way, by using the weight lattice. A cleaner theory results with symmetry between the arguments and labels of the discretized orbit functions. Orthogonality of the new discretized orbit functions is proved, and leads to the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For one type of orbit function, the matrix coincides with the Kac-Peterson modular S matrix, important for Wess-Zumino-Novikov-Witten conformal field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Work function and surface stability of tungsten-based thermionic electron emission cathodes

Materials that exhibit a low work function and therefore easily emit electrons into vacuum form the basis of electronic devices used in applications ranging from satellite communications to thermionic energy conversion. W–Ba–O is the canonical materials system that functions as the thermionic electron emitter commercially used in a range of high-power electron devices. However, the work functions, surface stability, and kinetic characteristics of a polycrystalline W emitter surface are still not well understood or characterized. In this study, we examined the work function and surface stability of the eight lowest index surfaces of the W–Ba–O system using density functional theory methods. We found that under the typical thermionic cathode operating conditions of high temperature and low oxygen partial pressure, the most stable surface adsorbates are Ba–O species with compositions in the range of Ba 0.125 O–Ba 0.25 O per surface W atom, with O passivating all dangling W bonds and Ba creating work function-lowering surface dipoles. Wulff construction analysis reveals that the presence of O and Ba significantly alters the surface energetics and changes the proportions of surface facets present under equilibrium conditions. In conclusion, analysis of previously published data on W sintering kinetics suggests that fine W particles in the size range of 100-500 nm may be at or near equilibrium during cathode synthesis and thus may exhibit surface orientation fractions well described by the calculated Wulff construction.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Structural, electronic, and dynamical properties of liquid water by ab initio molecular dynamics based on SCAN functional within the canonical ensemble

We perform ab initio molecular dynamics (AIMD) simulation of liquid water in the canonical ensemble at ambient conditions using the strongly constrained and appropriately normed (SCAN) meta-generalized-gradient approximation (GGA) functional approximation and carry out systematic comparisons with the results obtained from the GGA-level Perdew-Burke-Ernzerhof (PBE) functional and Tkatchenko-Scheffler van der Waals (vdW) dispersion correction inclusive PBE functional. We analyze various properties of liquid water including radial distribution functions, oxygen-oxygen-oxygen triplet angular distribution, tetrahedrality, hydrogen bonds, diffusion coefficients, ring statistics, density of states, band gaps, and dipole moments. We find that the SCAN functional is generally more accurate than the other two functionals for liquid water by not only capturing the intermediate-range vdW interactions but also mitigating the overly strong hydrogen bonds prescribed in PBE simulations. We also compare the results of SCAN-based AIMD simulations in the canonical and isothermal-isobaric ensembles. Our results suggest that SCAN provides a reliable description for most structural, electronic, and dynamical properties in liquid water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Finding the “lost-time” in detonator function

Exploding bridgewire (EBW) detonators were invented during the Manhattan Project over 75 years ago. Initially developed for precise timing and reproducibility, they continue to be used in many applications. Despite widespread use and reliability, their mechanism for function remains controversial. They provide precision timing, yet their function is described in terms of a “lost time” accounting for nearly half of the function time. Buried in understanding the EBW function is the mystery of how an incoherent impulse such as powering a bridgewire yields the coherent energy output of a detonation. Even the general phenomena by which release of chemical energy in a crystalline organic explosive becomes associated with the sonic plane of a steady detonation wave remain uncertain. Here, we investigate the EBW function with a suite of diagnostics and show that stationary heating occurs during the “lost-time.” We use x-ray radiography to observe the propagation of a shock wave from bridgewire vaporization and establish that the origin of the radially emanating detonation wave is spatially separated from the initial shock. Utilizing the observed temperature as a boundary condition in our explosive response models yields a thermal ignition consistent with the “lost-time” and detonation location consistent with previous work. With these findings, we define a direct thermal initiation mechanism for the EBW function consistent with previous integral observations and explain the displacement of initiation from the bridgewire burst in time and space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Plasma thermal transport with a generalized 8-moment distribution function

Moment equations that model plasma transport require an ansatz distribution function to close the system of equations. The resulting transport is sensitive to the specific closure used, and several options have been proposed in the literature. Two different 8-moment distribution functions can be generalized to form a single-parameter family of distribution functions. The transport coefficients resulting from this generalized distribution function can be expressed in terms of this free parameter. This provides the flexibility of matching the 8-moment model to some validating result at a given magnetization value, such as Braginskii’s transport, or the more recent results of Davies et al. [Physics of Plasma, 28, 012305 (2021)]. Here, this process can be thought of as solving for the 8-moment distribution function that matches the value of a transport coefficient given by a Chapman-Enskog expansion, while retaining the improved physical properties, such as finite propagation speeds and time dependence which belong to the hyperbolic moment models. Since the presented generalized distribution function only has a single free parameter, only a single transport coefficient can be matched at a time. However, this generalization process may be extended to provide multiple free parameters. The focus of this Brief Communication is on the dramatically improved thermal conductivity of the proposed model compared to the two base moment models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Understanding the effect of density functional choice and van der Waals treatment on predicting the binding configuration, loading, and stability of amine-grafted metal organic frameworks

Metal organic frameworks (MOFs) are crystalline, three-dimensional structures with high surface areas and tunable porosities. Made from metal nodes connected by organic linkers, the exact properties of a given MOF are determined by node and linker choice. MOFs hold promise for numerous applications, including gas capture and storage. M2(4,4′-dioxidobiphenyl-3,3′-dicarboxylate)—henceforth simply M2(dobpdc), with M = Mg, Mn, Fe, Co, Ni, Cu, or Zn—is regarded as one of the most promising structures for CO2 capture applications. Further modification of the MOF with diamines or tetramines can significantly boost gas species selectivity, a necessity for the ultra-dilute CO2 concentrations in the direct-air capture of CO2. There are countless potential diamines and tetramines, paving the way for a vast number of potential sorbents to be probed for CO2 adsorption properties. The number of amines and their configuration in the MOF pore are key drivers of CO2 adsorption capacity and kinetics, and so a validation of computational prediction of these quantities is required to suitably use computational methods in the discovery and screening of amine-functionalized sorbents. In this work, we study the predictive accuracy of density functional theory and related calculations on amine loading and configuration for one diamine and two tetramines. In particular, we explore the Perdew–Burke–Ernzerhof (PBE) functional and its formulation for solids (PBEsol) with and without the Grimme-D2 and Grimme-D3 pairwise corrections (PBE+D2/3 and PBEsol+D2/3), two revised PBE functionals with the Grimme-D2 and Grimme-D3 pairwise corrections (RPBE+D2/3 and revPBE+D2/3), and the nonlocal van der Waals correlation (vdW-DF2) functional. We also investigate a universal graph deep learning interatomic potential’s (M3GNet) predictive accuracy for loading and configuration. These results allow us to identify a useful screening procedure for configuration prediction that has a coarse component for quick evaluation and a higher accuracy component for detailed analysis. Our general observation is that the neural network-based potential can be used as a high-level and rapid screening tool, whereas PBEsol+D3 gives a completely qualitatively predictive picture across all systems studied, and can thus be used for high accuracy motif predictions. We close by briefly exploring the predictions of relative thermal stability for the different functionals and dispersion corrections.

Chemistry↗
DOE OSTI2016

Functional remediation components: A conceptual method of evaluating the effects of remediation on risks to ecological receptors

Governmental agencies, regulators, health professionals, tribal leaders, and the public are faced with understanding and evaluating the effects of cleanup activities on species, populations, and ecosystems. While engineers and managers understand the processes involved in different remediation types such as capping, pump and treat, and natural attenuation, there is often a disconnect between (1) how ecologists view the influence of different types of remediation, (2) how the public perceives them, and (3) how engineers understand them. The overall goal of the present investigation was to define the components of remediation types (= functional remediation). Objectives were to (1) define and describe functional components of remediation, regardless of the remediation type, (2) provide examples of each functional remediation component, and (3) explore potential effects of functional remediation components in the post-cleanup phase that may involve continued monitoring and assessment. Functional remediation components include types, numbers, and intensity of people, trucks, heavy equipment, pipes, and drill holes, among others. Several components may be involved in each remediation type, and each results in ecological effects, ranging from trampling of plants, to spreading invasive species, to disturbing rare species, and to creating fragmented habitats. In some cases remediation may exert a greater effect on ecological receptors than leaving the limited contamination in place. A goal of this conceptualization is to break down functional components of remediation such that managers, regulators, and the public might assess the effects of timing, extent, and duration of different remediation options on ecological systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Electroweak fragmentation functions for dark matter annihilation

Electroweak corrections can play a crucial role in dark matter annihilation. The emission of gauge bosons, in particular, leads to a secondary flux consisting of all Standard Model particles, and may be described by electroweak fragmentation functions. To assess the quality of the fragmentation function approximation to electroweak radiation in dark matter annihilation, we have calculated the flux of secondary particles from gauge-boson emission in models with Majorana fermion and vector dark matter, respectively. For both models, we have compared cross sections and energy spectra of positrons and antiprotons after propagation through the galactic halo in the fragmentation function approximation and in the full calculation. Fragmentation functions fail to describe the particle fluxes in the case of Majorana fermion annihilation into light fermions: the helicity suppression of the lowest-order cross section in such models cannot be lifted by the leading logarithmic contributions included in the fragmentation function approach. However, for other classes of models like vector dark matter, where the lowest-order cross section is not suppressed, electroweak fragmentation functions provide a simple, model-independent and accurate description of secondary particle fluxes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

The angle-averaged squeezed limit of nonlinear matter N-point functions

Assuming Gaussian initial conditions, we show that in a certain, angle-averaged squeezed limit the N-point function of matter is related to the response of the matter power spectrum to a long-wavelength density perturbation, P{sup −1}d{sup nP}(k|δ{sub L})/dδ{sub L}{sup n}|{sub δ{sub L=0}}, with n=N−2. By performing N-body simulations with a homogeneous overdensity superimposed on a flat Friedmann-Robertson-Lemaȋtre-Walker (FRLW) universe using the separate universe approach, we obtain measurements of the nonlinear matter power spectrum response up to n=3, which is equivalent to measuring the fully nonlinear matter 3- to 5-point function in this squeezed limit. The sub-percent to few percent accuracy of those measurements is unprecedented. We then test the hypothesis that nonlinear N-point functions at a given time are a function of the linear power spectrum at that time, which is predicted in an Einstein-de Sitter (EdS) universe by standard perturbation theory (SPT) and its variants that are based on the ideal pressureless fluid equations. Specifically, we compare the responses computed from the separate universe simulations and simulations with a rescaled initial (linear) power spectrum amplitude. We find discrepancies of 10% at k≅ 0.2–0.5 h Mpc{sup −1} for 5- to 3-point functions at z=0. The discrepancy occurs at higher wavenumbers at z=2. Thus, theoretical predictions that are insensitive to the growth history, such as SPT and its variants assuming EdS, even when carried out to arbitrarily high order, are guaranteed to fail to describe matter N-point functions (N>2) around that scale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Disconnected covariance of 2-point functions in large-scale structure

Optimal analyses using the 2-point functions of large-scale structure probes require accurate covariance matrices. A covariance matrix of the 2-point function comprises the disconnected part and the connected part. While the connected covariance only becomes important on small scales, the disconnected covariance is dominant on large scales, where the survey window has a significant impact. In this work, we develop an analytical method to compute the disconnected covariance, accounting for the window effect. Derived under the flat-sky approximation, our formalism is applicable to wide surveys by swapping in the curved-sky window functions. Our method works for both the power spectrum and the correlation function, and applies to the covariances of various probes including the multipoles and the wedges of 3D clustering, the angular and the projected statistics of clustering and shear, as well as the cross covariances between different probes. We verify the analytic covariance against the sample covariance from the galaxy mock simulations in two test cases: (1) the power spectrum multipole covariance, and (2) the joint covariance of the projected correlation function and the correlation function multipoles. Our method achieve good agreement with the mocks, while at a negligible computational cost. Unlike mocks, our analytic covariance is free of sampling noise, which often leads to numerical problems and the need to inflate the errors. In addition, our method can use the best-fit power spectrum as input, in contrast to the standard procedure of using a fiducial model that may deviate significantly from the truth. We also show that a naive diagonal power spectrum covariance underestimates the signal-to-noise ratio compared to our analytic covariance. The code that accompanies this paper is available at https://github.com/eelregit/covdisc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Orbit tomography of energetic particle distribution functions

Both fast ions and runaway electrons are described by distribution functions, the understanding of which are of critical importance for the success of future fusion devices such as ITER. Typically, energetic particle diagnostics are only sensitive to a limited subsection of the energetic particle phase-space which is often insufficient for model validation. However, previous publications show that multiple measurements of a single spatially localized volume can be used to reconstruct a distribution function of the energetic particle velocity-space by using the diagnostics' velocity-space weight functions, i.e. velocity-space Tomography. In this work we use the recently formulated orbit weight functions to remove the restriction of spatially localized measurements and present orbit tomography, which is used to reconstruct the 3D phase-space distribution of all energetic particle orbits in the plasma. Through a transformation of the orbit distribution, the full energetic particle distribution function can be determined in the standard {energy, pitch, r, z}-space. We benchmark the technique by reconstructing the fast-ion distribution function of an MHD-quiescent DIII-D discharge using synthetic and experimental FIDA measurements. We also use the method to study the redistribution of fast ions during a sawtooth crash at ASDEX upgrade using FIDA measurements. Lastly, a comparison between the orbit tomography and velocity-space tomography is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Liouville theory, AdS 2 string, and three-point functions

This is a write-up of the lectures given in Young Researchers Integrability School 2017. The main goal is to explain the connection between the ODE/IM correspondence and the classical integrability of strings in AdS. As a warm up, we first discuss the classical three-point function of the Liouville theory. The starting point is the well-known fact that the classical solutions to the Liouville equation can be constructed by solving a Schrodinger-like differential equation. We then convert it into a set of functional equations using a method similar to the ODE/IM correspondence. The classical three-point functions can be computed directly from these functional equations, and the result matches with the classical limit of the celebrated DOZZ formula. We then discuss the semi-classical three-point function of strings in AdS 2 and show that one can apply a similar idea by making use of the classical integrability of the string sigma model on AdS 2 . Furthermore, the result is given in terms of the "massive" generalization of Gamma functions, which show up also in string theory on pp-wave backgrounds and the twistorial generalization of topological string.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗