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Journal articles on the topic 'Microlocal and semiclassical analysis'

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Author: Grafiati

Published: 7 July 2024

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1

Vasy, András, and Jared Wunsch. "Semiclassical second microlocal propagation of regularity and integrable systems." Journal d'Analyse Mathématique 108, no. 1 (May 2009): 119–57. http://dx.doi.org/10.1007/s11854-009-0020-5.

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2

Sales, Jorge Henrique de Oliveira, and Rômulo Damasclin Chaves dos Santos. "An essay on semiclassical analysis for microlocal singularities, turbulence intensity and integration of singularities by Schrödinger equation in probabilistic behavior." OBSERVATÓRIO DE LA ECONOMÍA LATINOAMERICANA 22, no. 5 (May 20, 2024): e4751. http://dx.doi.org/10.55905/oelv22n5-127.

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Abstract:

The Schrödinger equation governs the probabilistic behavior of quantum particles through the wave function. Microlocal singularities denote regions with significantly high probability density or abrupt changes therein. By visualizing the probability distribution in time and space, we discern regions with higher probability density, indicative of potential microlocal singularities. These regions probably correspond to areas with a greater probability of particle presence. Such analysis aligns with Theorem 1, predicting characteristics of microlocal singularities of wave functions. Furthermore, Theorem 2 postulates that semiclassical path integrals along these singularities contribute significantly to solving the Schrödinger equation. Interpreting the temporal evolution of the probability density in the probability distribution visualization reveals the propagation of the particle over time. Regions of high density mean likely presence of particles at specific times, aligning with the predictions of Theorem 2. Consequently, the analysis of the contribution of high-density regions to the temporal evolution of the wave function resembles semi-classical path integral calculations. Thus, our findings demonstrate that visualization of probability distributions obtained from the numerical resolution of the Schrödinger equation allows a comprehensive interpretation of the behavior of quantum particles, consistent with the theorems.

3

SAFAROV, YURI. "AN INTRODUCTION TO SEMICLASSICAL AND MICROLOCAL ANALYSIS (Universitext) By ANDRÉ MARTINEZ: 190 pp., £49.00 (US$59.95), ISBN 0-387-95344-2 (Springer, New York, 2002)." Bulletin of the London Mathematical Society 35, no. 05 (August 13, 2003): 716–17. http://dx.doi.org/10.1112/s002460930324933x.

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4

Vasy, András, and Jared Wunsch. "Erratum to: “semiclassical second microlocal propagation of regularity and integrable systems”." Journal d'Analyse Mathématique 115, no. 1 (June 2011): 389–91. http://dx.doi.org/10.1007/s11854-011-0033-8.

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5

Herbin, Erick, and Jacques Lévy-Véhel. "Stochastic 2-microlocal analysis." Stochastic Processes and their Applications 119, no. 7 (July 2009): 2277–311. http://dx.doi.org/10.1016/j.spa.2008.11.005.

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6

Pilipović, Stevan. "Microlocal analysis of ultradistributions." Proceedings of the American Mathematical Society 126, no. 1 (1998): 105–13. http://dx.doi.org/10.1090/s0002-9939-98-04357-3.

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7

Sjöstrand, Johannes. "Resonances and microlocal analysis." International Journal of Quantum Chemistry 31, no. 5 (May 1987): 733–37. http://dx.doi.org/10.1002/qua.560310505.

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8

Martinez, André, and Vania Sordoni. "Microlocal WKB Expansions." Journal of Functional Analysis 168, no. 2 (November 1999): 380–402. http://dx.doi.org/10.1006/jfan.1999.3460.

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9

Delort, Jean-Marc. "Semiclassical microlocal normal forms and global solutions of modified one-dimensional KG equations." Annales de l'Institut Fourier 66, no. 4 (2016): 1451–528. http://dx.doi.org/10.5802/aif.3041.

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10

Salo, Mikko. "Applications of Microlocal Analysis in Inverse Problems." Mathematics 8, no. 7 (July 18, 2020): 1184. http://dx.doi.org/10.3390/math8071184.

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Abstract:

This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.

11

Dyatlov, Semyon, and Maciej Zworski. "Microlocal analysis of forced waves." Pure and Applied Analysis 1, no. 3 (July 17, 2019): 359–84. http://dx.doi.org/10.2140/paa.2019.1.359.

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12

ten Kroode, A. P. E., D. J. Smit, and A. R. Verdel. "A microlocal analysis of migration." Wave Motion 28, no. 2 (September 1998): 149–72. http://dx.doi.org/10.1016/s0165-2125(98)00004-3.

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13

Wang, Ya-Guang. "Microlocal analysis in nonlinear thermoelasticity." Nonlinear Analysis: Theory, Methods & Applications 54, no. 4 (August 2003): 683–705. http://dx.doi.org/10.1016/s0362-546x(03)00095-6.

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14

Globevnik, Josip, and Eric Todd Quinto. "Morera theorems via microlocal analysis." Journal of Geometric Analysis 6, no. 1 (March 1996): 19–30. http://dx.doi.org/10.1007/bf02921565.

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15

Anantharaman, Nalini, Clotilde Fermanian-Kammerer, and Fabricio Macià. "Semiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures." American Journal of Mathematics 137, no. 3 (2015): 577–638. http://dx.doi.org/10.1353/ajm.2015.0020.

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16

Hoepfner, Gustavo, and Luis F. Ragognette. "A new microlocal analysis of hyperfunctions." Journal of Functional Analysis 281, no. 4 (August 2021): 109065. http://dx.doi.org/10.1016/j.jfa.2021.109065.

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17

Abbott, Steve, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze, and Johannes Sjostrand. "Spectral Theory, Microlocal Analysis, Singular Manifolds." Mathematical Gazette 82, no. 494 (July 1998): 348. http://dx.doi.org/10.2307/3620458.

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18

Marti, J. A. "𝒢L-microlocal analysis of generalized functions." Integral Transforms and Special Functions 17, no. 2-3 (February 2006): 119–25. http://dx.doi.org/10.1080/10652460500437732.

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19

Marhuenda, F. "Microlocal analysis of some isospectral deformations." Transactions of the American Mathematical Society 343, no. 1 (January 1, 1994): 245–75. http://dx.doi.org/10.1090/s0002-9947-1994-1181185-0.

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20

Benamou, Jean-David, Francis Collino, and Olof Runborg. "Numerical microlocal analysis of harmonic wavefields." Journal of Computational Physics 199, no. 2 (September 2004): 717–41. http://dx.doi.org/10.1016/j.jcp.2004.03.014.

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21

W. Webber, James, and Sean Holman. "Microlocal analysis of a spindle transform." Inverse Problems & Imaging 13, no. 2 (2019): 231–61. http://dx.doi.org/10.3934/ipi.2019013.

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22

Hörmann, Günther, Ljubica Oparnica, and Dušan Zorica. "Microlocal analysis of fractional wave equations." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 97, no. 2 (September 12, 2016): 217–25. http://dx.doi.org/10.1002/zamm.201600036.

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23

Iagolnitzer, D. "Microlocal analysis and phase-space decompositions." Letters in Mathematical Physics 21, no. 4 (April 1991): 323–28. http://dx.doi.org/10.1007/bf00398330.

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24

Benmeriem, Khaled, and Fatima Zohra Korbaa. "Generalized Roumieu ultradistributions and their microlocal analysis." Novi Sad Journal of Mathematics 46, no. 2 (July 13, 2016): 181–200. http://dx.doi.org/10.30755/nsjom.04658.

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25

Uchida, Motoo. "Microlocal analysis of diffraction by a corner." Annales scientifiques de l'École normale supérieure 25, no. 1 (1992): 47–75. http://dx.doi.org/10.24033/asens.1643.

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26

Stolk, Christiaan C. "MICROLOCAL ANALYSIS OF THE SCATTERING ANGLE TRANSFORM." Communications in Partial Differential Equations 27, no. 9-10 (January 12, 2002): 1879–900. http://dx.doi.org/10.1081/pde-120016131.

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27

Quinto, Eric Todd. "Mean value extension theorems and microlocal analysis." Proceedings of the American Mathematical Society 131, no. 10 (February 12, 2003): 3267–74. http://dx.doi.org/10.1090/s0002-9939-03-06926-0.

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28

Nolan, Clifford J., and Margaret Cheney. "Microlocal Analysis of Synthetic Aperture Radar Imaging." Journal of Fourier Analysis and Applications 10, no. 2 (March 1, 2004): 133–48. http://dx.doi.org/10.1007/s00041-004-8008-0.

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29

Tarkhanov, Nikolai, and Nikolai Vasilevski. "Microlocal Analysis of the Bochner-Martinelli Integral." Integral Equations and Operator Theory 57, no. 4 (December 26, 2006): 583–92. http://dx.doi.org/10.1007/s00020-006-1469-6.

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30

Webber, James W., and Eric Todd Quinto. "Microlocal Analysis of a Compton Tomography Problem." SIAM Journal on Imaging Sciences 13, no. 2 (January 2020): 746–74. http://dx.doi.org/10.1137/19m1251035.

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31

Felea, Raluca, Romina Gaburro, Allan Greenleaf, and Clifford Nolan. "Microlocal analysis of Doppler synthetic aperture radar." Inverse Problems & Imaging 13, no. 6 (2019): 1283–307. http://dx.doi.org/10.3934/ipi.2019056.

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32

Fürdös, Stefan. "Geometric microlocal analysis in Denjoy–Carleman classes." Pacific Journal of Mathematics 307, no. 2 (September 4, 2020): 303–51. http://dx.doi.org/10.2140/pjm.2020.307.303.

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33

Donoho, David, and Gitta Kutyniok. "Microlocal Analysis of the Geometric Separation Problem." Communications on Pure and Applied Mathematics 66, no. 1 (August 6, 2012): 1–47. http://dx.doi.org/10.1002/cpa.21418.

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34

King, Emily J., Gitta Kutyniok, and Xiaosheng Zhuang. "Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis." Journal of Mathematical Imaging and Vision 48, no. 2 (February 21, 2013): 205–34. http://dx.doi.org/10.1007/s10851-013-0422-y.

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35

Taylor, Michael. "Microlocal Weyl formula on contact manifolds." Communications in Partial Differential Equations 45, no. 5 (November 12, 2019): 392–413. http://dx.doi.org/10.1080/03605302.2019.1689400.

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36

Cappiello, Marco, and René Schulz. "Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions." Complex Variables and Elliptic Equations 61, no. 4 (January 12, 2016): 538–61. http://dx.doi.org/10.1080/17476933.2015.1106481.

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37

Stolk, Christiaan C. "Microlocal analysis of a seismic linearized inverse problem." Wave Motion 32, no. 3 (September 2000): 267–90. http://dx.doi.org/10.1016/s0165-2125(00)00043-3.

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38

Balança, Paul, and Erick Herbin. "2-microlocal analysis of martingales and stochastic integrals." Stochastic Processes and their Applications 122, no. 6 (June 2012): 2346–82. http://dx.doi.org/10.1016/j.spa.2012.03.011.

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39

Haller, Simon. "Microlocal Analysis of Generalized Pullbacks of Colombeau Functions." Acta Applicandae Mathematicae 105, no. 1 (July 22, 2008): 83–109. http://dx.doi.org/10.1007/s10440-008-9266-7.

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40

Calvetti, Daniela, and Erkki Somersalo. "Microlocal sequential regularization in imaging." Inverse Problems & Imaging 1, no. 1 (2007): 1–11. http://dx.doi.org/10.3934/ipi.2007.1.1.

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41

Gonçalves, Helena F., Susana D. Moura, and Júlio S. Neves. "On trace spaces of 2-microlocal type spaces." Journal of Functional Analysis 267, no. 9 (November 2014): 3444–68. http://dx.doi.org/10.1016/j.jfa.2014.07.016.

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42

Raymond, N. "Breaking a magnetic zero locus: Asymptotic analysis." Mathematical Models and Methods in Applied Sciences 24, no. 14 (October 16, 2014): 2785–817. http://dx.doi.org/10.1142/s0218202514500377.

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Abstract:

This paper deals with the spectral analysis of the Laplacian in the presence of a magnetic field vanishing along a broken line. Denoting by θ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when θ goes to 0. The investigation strongly uses a coherent state decomposition and a microlocal analysis of the eigenfunctions.

43

Webber, James W., and Eric Todd Quinto. "Microlocal Analysis of Generalized Radon Transforms from Scattering Tomography." SIAM Journal on Imaging Sciences 14, no. 3 (January 2021): 976–1003. http://dx.doi.org/10.1137/20m1357305.

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44

Dyatlov, Semyon, and Maciej Zworski. "Dynamical zeta functions for Anosov flows via microlocal analysis." Annales scientifiques de l'École normale supérieure 49, no. 3 (2016): 543–77. http://dx.doi.org/10.24033/asens.2290.

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45

Franco, Daniel H. T., and José L. Acebal. "Microlocal Analysis and Renormalization in Finite Temperature Field Theory." International Journal of Theoretical Physics 46, no. 2 (January 4, 2007): 383–98. http://dx.doi.org/10.1007/s10773-006-9239-4.

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46

Ramaseshan, Karthik. "Microlocal Analysis of the Doppler Transform on R 3." Journal of Fourier Analysis and Applications 10, no. 1 (January 1, 2004): 73–82. http://dx.doi.org/10.1007/s00041-004-8004-4.

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47

Hoepfner, G., and R. Medrado. "The FBI transforms and their use in microlocal analysis." Journal of Functional Analysis 275, no. 5 (September 2018): 1208–58. http://dx.doi.org/10.1016/j.jfa.2018.05.022.

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48

Dapić, N., S. Pilipović, and D. Scarpalézos. "Microlocal analysis of Colombeau’s generalized functions: Propagation of singularities." Journal d'Analyse Mathématique 75, no. 1 (December 1998): 51–66. http://dx.doi.org/10.1007/bf02788691.

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49

Guo, Kanghui, and Demetrio Labate. "Microlocal analysis of edge flatness through directional multiscale representations." Advances in Computational Mathematics 43, no. 2 (October 12, 2016): 295–318. http://dx.doi.org/10.1007/s10444-016-9486-8.

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50

Nguyen, Linh V., and Tuan A. Pham. "Microlocal analysis for spherical Radon transform: two nonstandard problems." Inverse Problems 35, no. 7 (June 19, 2019): 074001. http://dx.doi.org/10.1088/1361-6420/ab15df.

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