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Academic literature on the topic 'Gaussian approximation potentials'

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Published: 9 March 2023
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Journal articles on the topic "Gaussian approximation potentials"

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Bartók, Albert P., and Gábor Csányi. "Gaussian approximation potentials: A brief tutorial introduction." International Journal of Quantum Chemistry 115, no. 16 (April 27, 2015): 1051–57. http://dx.doi.org/10.1002/qua.24927.

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Klawohn, Sascha, James R. Kermode, and Albert P. Bartók. "Massively parallel fitting of Gaussian approximation potentials." Machine Learning: Science and Technology 4, no. 1 (February 16, 2023): 015020. http://dx.doi.org/10.1088/2632-2153/aca743.

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Abstract We present a data-parallel software package for fitting Gaussian approximation potentials (GAPs) on multiple nodes using the ScaLAPACK library with MPI and OpenMP. Until now the maximum training set size for GAP models has been limited by the available memory on a single compute node. In our new implementation, descriptor evaluation is carried out in parallel with no communication requirement. The subsequent linear solve required to determine the model coefficients is parallelised with ScaLAPACK. Our approach scales to thousands of cores, lifting the memory limitation and also delivering substantial speedups. This development expands the applicability of the GAP approach to more complex systems as well as opening up opportunities for efficiently embedding GAP model fitting within higher-level workflows such as committee models or hyperparameter optimisation.
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Bartók, Albert P., and Gábor Csányi. "Erratum: Gaussian approximation potentials: A brief tutorial introduction." International Journal of Quantum Chemistry 116, no. 13 (April 21, 2016): 1049. http://dx.doi.org/10.1002/qua.25140.

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Hiroshima, Fumio. "A Scaling Limit of a Hamiltonian of Many Nonrelativistic Particles Interacting with a Quantized Radiation Field." Reviews in Mathematical Physics 09, no. 02 (February 1997): 201–25. http://dx.doi.org/10.1142/s0129055x97000075.

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This paper presents a scaling limit of Hamiltonians which describe interactions of N-nonrelativistic charged particles in a scalar potential and a quantized radiation field in the Coulomb gauge with the dipole approximation. The scaling limit defines effective potentials. In one-nonrelativistic particle case, the effective potentials have been known to be Gaussian transformations of the scalar potential [J. Math. Phys.34 (1993) 4478–4518]. However it is shown that the effective potentials in the case of N-nonrelativistic particles are not necessary to be Gaussian transformations of the scalar potential.
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John, S. T., and Gábor Csányi. "Many-Body Coarse-Grained Interactions Using Gaussian Approximation Potentials." Journal of Physical Chemistry B 121, no. 48 (November 29, 2017): 10934–49. http://dx.doi.org/10.1021/acs.jpcb.7b09636.

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FUKUKAWA, K., Y. FUJIWARA, and Y. SUZUKI. "GAUSSIAN NONLOCAL POTENTIALS FOR THE QUARK-MODEL BARYON–BARYON INTERACTIONS." Modern Physics Letters A 24, no. 11n13 (April 30, 2009): 1035–38. http://dx.doi.org/10.1142/s021773230900053x.

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Gaussian nonlocal potentials for the quark-model baryon–baryon interactions are derived by using the Gauss-Legendre quadrature for the special functions. The reliability of the approximation is examined with respect to the phase shifts and the deuteron binding energy. The potential is accurate enough if one uses seven-point Gauss-Legendre quadrature.
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SÉNÉCHAL, DAVID. "CHAOS IN THE HERMITIAN ONE-MATRIX MODEL." International Journal of Modern Physics A 07, no. 07 (March 20, 1992): 1491–506. http://dx.doi.org/10.1142/s0217751x9200065x.

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The recursion coefficients Ri, which appear in the orthogonal polynomial method of solution for the Hermitian one-matrix model, are determined numerically for values of N up to a thousand. For some cases a chaotic behavior appears in some range, preventing a smooth flow from odd to even multicrititical models. This behavior is studied both for single-well and multiwell potentials. For multiwell potentials, the coefficients Ri generically tend toward more than one function in the N→∞ limit, and this structure is analyzed for small i using the Gaussian approximation.
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Demiroğlu, İlker, Yenal Karaaslan, Tuğbey Kocabaş, Murat Keçeli, Álvaro Vázquez-Mayagoitia, and Cem Sevik. "Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials." Journal of Physical Chemistry C 125, no. 26 (June 24, 2021): 14409–15. http://dx.doi.org/10.1021/acs.jpcc.1c01888.

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Exl, Lukas, Norbert J. Mauser, and Yong Zhang. "Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation." Journal of Computational Physics 327 (December 2016): 629–42. http://dx.doi.org/10.1016/j.jcp.2016.09.045.

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OLSEN, R. A., and F. RAVNDAL. "EFFECTIVE POTENTIALS FOR ϕ4-THEORY IN 2+1 DIMENSIONS." Modern Physics Letters A 09, no. 28 (September 14, 1994): 2623–35. http://dx.doi.org/10.1142/s021773239400246x.

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Spontaneous symmetry breaking in ϕ4-theory in 2+1 dimensions is investigated using the Gaussian approximation. The theory stays in the symmetric phase at zero temperature as long as the bare coupling constant is below a critical value λc. When λ>λc the symmetric phase is again stable when the temperature is above a transition temperature T(λ). The obtained results are compared with the predictions of the standard one-loop effective potential.
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Dissertations / Theses on the topic "Gaussian approximation potentials"

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DRAGONI, DANIELE. "Energetics and thermodynamics of α-iron from first-principles and machine-learning potentials." Doctoral thesis, École Polytechnique Fédérale de Lausanne, 2016. http://hdl.handle.net/10281/231122.

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Iron is a material of fundamental importance in the industrial and economic processes of our society as it is the major constituent of steels. With advances in computational science, much progress has been made in the understanding of the microscopic mechanisms that determine the macroscopic properties of such material at ordinary or extreme conditions. Ab initio quantum mechanical calculations based on density-functional theory (DFT), in particular, proved to be a unique tool for this purpose. Nevertheless, in order to study large enough systems up to length- and time-scales comparable with those accessible in experiments, interatomic potentials are needed. These are typically based on functional forms driven by physical intuition and fitted on experimental data at zero/low temperature and/or on available first-principles data. Despite their vast success, however, their low flexibility limits their systematic improvement upon database extension. Moreover, their accuracy at intermediate and high temperature remains questionable. In this thesis, we first survey a selection of embedded atom method (EAM) potentials to understand their strengths and limitations in reproducing experimental thermodynamic, vibrational and elastic properties of bcc iron at finite temperature. Our calculations show that, on average, all the potentials rapidly deviate from experiments as temperature is increased. At the same time, they suggest that, despite an anomalous rapid softening of its C44 shear constant, the Mendelev03 parameterization is the most accurate among those considered in this work. As a second step, we compute the same finite-temperature properties from DFT. We verify our plane-wave spin-polarized pseudopotential implementation against selected zero temperature all-electron calculations, thus highlighting the difficulties of the semi-local generalized gradient approximation exchange and correlation functional in describing the electronic properties of iron. On the other hand, we demonstrate that after accounting for the vibrational degrees of freedom, DFT provides a good description of the thermal behavior of thermodynamic and elastic properties of α-iron up to a good fraction of the Curie temperature without the explicit inclusion of magnetic transverse degrees of freedom. Electronic entropy effects are also analyzed and shown to be of secondary importance. Finally, we attempt at generating a set of highly flexible Gaussian approximation potentials (GAP) for bcc iron that retain ab initio accuracy both at zero and finite temperature. To this end, we use a non-linear, non-parametric Gaussian-process regression, and construct a training database of total energies, stresses and forces taken from first-principles molecular dynamics simulations. We cover approximately 105 local atomic environments including pristine and defected bulk systems, and surfaces with different crystallographic orientations. We then validate the different GAP models against DFT data not directly included in the dataset, focusing on the prediction of thermodynamic, vibrational, and elastic properties and of the energetics of bulk defects.
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Morgan, David C. "A Gaussian approximation to the effective potential." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26500.

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This thesis investigates some of the properties of a variational approximation to scalar field theories: a trial wavefunctional which has a gaussian form is used as a ground state ansatz for an interacting scalar field theory - the expectation value of the Hamiltonian in this state is then minimized. This we call the Gaussian Approximation; the resulting effective potential we follow others by calling the Gaussian Effective Potential (GEP). An equivalent but more general finite temperature formalism is then reviewed and used for the calculations of the GEP in this thesis. Two scalar field theories are described: ϕ⁴ theory in four dimensions (ϕ⁴₄) and ϕ⁶ theory in three dimensions (ϕ⁶₃). After showing what the Gaussian Approximation does in terms of Feynman diagrams, renormalized GEP's are calculated for both theories. Dimensional Regularization is used in the renormalization and this this is especially convenient for the GEP in ϕ⁶₃ theory because it becomes trivially renor-malizable. It is noted that ϕ⁶₃ loses its infrared asymptotic freedom in the Gaussian Approximation. Finally, it is shown how a finite temperature GEP can be calculated by finding low and high temperature expansions of the temperature terms in ϕ⁶₃ theory.
Science, Faculty of
Physics and Astronomy, Department of
Graduate
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Bartók-Pártay, Albert. "Gaussian approximation potential : an interatomic potential derived from first principles Quantum Mechanics." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608570.

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Books on the topic "Gaussian approximation potentials"

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Bartόk-Pártay, Albert. The Gaussian Approximation Potential. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9.

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The Gaussian approximation potential: An interatomic potential derived from first principles quantum mechanics. Heidelberg: Springer, c2010., 2010.

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Bartók-Pártay, Albert. The Gaussian Approximation Potential: An Interatomic Potential Derived from First Principles Quantum Mechanics. Springer, 2012.

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Bartók-Pártay, Albert. The Gaussian Approximation Potential: An Interatomic Potential Derived from First Principles Quantum Mechanics. Springer, 2011.

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Akemann, Gernot. Random matrix theory and quantum chromodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0005.

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This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian unitary ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions, and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in quantum chromodynamics with three colors in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered, including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. This chapter also provides some open random matrix problems.
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Book chapters on the topic "Gaussian approximation potentials"

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Bartók-Pártay, Albert. "Interatomic Potentials." In The Gaussian Approximation Potential, 33–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_4.

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Bartók-Pártay, Albert. "Introduction." In The Gaussian Approximation Potential, 1–3. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_1.

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Bartók-Pártay, Albert. "Representation of Atomic Environments." In The Gaussian Approximation Potential, 5–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_2.

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Bartók-Pártay, Albert. "Gaussian Process." In The Gaussian Approximation Potential, 23–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_3.

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Bartók-Pártay, Albert. "Computational Methods." In The Gaussian Approximation Potential, 51–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_5.

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Bartók-Pártay, Albert. "Results." In The Gaussian Approximation Potential, 57–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_6.

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Bartók-Pártay, Albert. "Conclusion and Further Work." In The Gaussian Approximation Potential, 83–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_7.

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Bartók-Pártay, Albert. "Appendices." In The Gaussian Approximation Potential, 85–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14067-9_8.

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Barker, James, Johannes Bulin, Jan Hamaekers, and Sonja Mathias. "LC-GAP: Localized Coulomb Descriptors for the Gaussian Approximation Potential." In Scientific Computing and Algorithms in Industrial Simulations, 25–42. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62458-7_2.

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Wudka, José. "Gaussian Approximations and Renormalization of Effective Potentials in 1+1 vs Higher Dimensions." In Variational Calculations In Quantum Field Theory, 120–26. WORLD SCIENTIFIC, 1988. http://dx.doi.org/10.1142/9789814390187_0011.

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Conference papers on the topic "Gaussian approximation potentials"

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Drühl, Kai J. "Solutions of the Raman wave equation for focused pump beams." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.tua7.

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We solve the wave equation for stimulated Raman and Brillouin scattering from Gaussian pump beams by a transformation to a system of coexpanding and contracting coordinates in which the pump beam has constant radius. The resulting equation has a quadratic potential term and is equivalent to the Schrödinger equation for a harmonic oscillator in two dimensions. If the typical gain length is small compared to the Rayleigh range of the pump, the decrease of pump intensity away from the center will lead to strong narrowing of the amplified Stokes beam. The pump intensity distribution can then be expanded to second order in the radius about the center. In this approximation the wave equation can be solved exactly by Gaussians for arbitrary Gaussian initial Stokes fields. A lowest-order mode is found whose radius is narrower than the pump radius by about the inverse fourth root of the gain. For almost all initial Gaussian fields the amplified Stokes beam develops into this stationary mode. By transforming back to laboratory coordinates simple closed-form expressions for Stokes beam divergence and apparent location of the waist are found. Results agree very well with numerical calculations and recent experimental observations.
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Fedorov, M. V., and J. Peatross. "Strong-Field Dipole Emission of an Ionized Electron in the Vicinity of a Coulomb Potential." In High Resolution Fourier Transform Spectroscopy. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/hrfts.1994.mc9.

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We have calculated three-dimensionally in the first Born approximation the interaction with a Coulomb potential of an electronic wave packet oscillating in a strong field. The initial wave packet was chosen to be a Gaussian with a 1/e2 probability-density radius of ro = 1.92ao (ao=Borh radius) which has an overlap of 98% with the hydrogen 1s state. The wave packet was expanded in terms of the Volkov states, and in the zeroth-order approximation it was considered to become suddenly free of the Coulomb potential, evolving in the strong oscillating electric field. The first-order correction to the electron motion was evaluated based on a perturbative treatment of the interaction with the Coulomb potential. Implicit in the calculation are the assumptions of the barrier-suppression ionization (BSI) model1 and the wave-packet-spreading photoionization model.2 The conditions for applicability of this approach are examined.
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Maignan, Aude, and Tony Scott. "Quantum Clustering Analysis: Minima of the Potential Energy Function." In 9th International Conference on Signal, Image Processing and Pattern Recognition (SPPR 2020). AIRCC Publishing Corporation, 2020. http://dx.doi.org/10.5121/csit.2020.101914.

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Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a 𝜎 value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size 𝜎, there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach “per block”. This technique decreases the number of particles (or samples) by approximating some groups of particles to weighted particles. These findings are not only useful to the quantum clustering problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics and other applications.
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Gallatin, Gregg M., and Phil Gould. "Laser focusing of atomic beams." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.thbb4.

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Recently, the focusing of an atomic beam using a laser has been considered by Balykin and Letokhov.1 Their calculations explicitly assume the thin lens approximation. Here, using path integral techniques, we derive the focal length and lowest-order aberrations of the laser atomic beam lens as a function of both laser and atomic beam parameters without making the thin lens approximation. Starting from the basic form of the potential energy for an atom in a laser beam, the propagation kernel is derived for the TEM(01)* or donut mode beam. From this result the focal length and lowest-order aberrations can be found for any atomic beam profile. We consider in particular a Gaussian atomic beam. Both the full 3-D propagation kernel and its paraxial approximation are discussed. We show how the paraxial case can be obtained from the 3-D case via a stationary phase approximation of the propagation equation.
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Kocák, Tomáš, and Aurélien Garivier. "Epsilon Best Arm Identification in Spectral Bandits." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/363.

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We propose an analysis of Probably Approximately Correct (PAC) identification of an ϵ-best arm in graph bandit models with Gaussian distributions. We consider finite but potentially very large bandit models where the set of arms is endowed with a graph structure, and we assume that the arms' expectations μ are smooth with respect to this graph. Our goal is to identify an arm whose expectation is at most ϵ below the largest of all means. We focus on the fixed-confidence setting: given a risk parameter δ, we consider sequential strategies that yield an ϵ-optimal arm with probability at least 1-δ. All such strategies use at least T*(μ)log(1/δ) samples, where R is the smoothness parameter. We identify the complexity term T*(μ) as the solution of a min-max problem for which we give a game-theoretic analysis and an approximation procedure. This procedure is the key element required by the asymptotically optimal Track-and-Stop strategy.
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Wang, B. X., and C. Y. Zhao. "Polarized Radiative Transfer in Anisotropic Disordered Media With Short-Range Order." In ASME 2017 Heat Transfer Summer Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/ht2017-5051.

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The aim of this study is to present a general method to investigate radiative transfer in disordered media with a subwave-length, anisotropic short-range order and provide a fundamental understanding on the interplay between polarized radiative transfer and microstructural anisotropy as well short-range order. We show the anisotropy of short-range order, described by an anisotropic correlation length in Gaussian random permittivity model, induces a significant anisotropy of radiative properties. Here the photon scattering mean free path is derived using the Feynman diagrammatic expansion of self-energy, and the transport mean free path and phase function are calculated based on the diagrammatic representation of the irreducible vertex in the Bethe-Salpeter equation. We further consider the transport of polarized light in such media by directly solving Bethe-Salpeter equation (BSE) for photons, without the use of traditional vector radiative transfer equation (VRTE). The present method advantageously allows us to elegantly relate anisotropic structural parameters to polarized radiative transport properties and obtain more fundamental physical insights, because the approximations in all steps of our derivation are given explicitly with reasonable explanations from the exact ab-initio BSE. Moreover, through a polarization eigen-channel expansion technique for intensity tensor, we show that values of transport mean free path in different polarization eigen-channels are rather different, which are also strongly affected by structural anisotropy and short-range order. As a conclusion, this study depicts some fundamental physical features of polarized radiative transfer in disordered media, and is also valuable for potential applications of utilizing anisotropic short-range order in disordered media in manipulation of polarized radiative transfer.
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