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Готові списки джерел за темами / Microlocal and semiclassical analysis

Добірка наукової літератури з теми "Microlocal and semiclassical analysis"

Автор: Grafiati

Опубліковано: 7 липня 2024

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Статті в журналах з теми "Microlocal and semiclassical analysis":

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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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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Анотація:

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.

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Дисертації з теми "Microlocal and semiclassical analysis":

1

Prouff, Antoine. "Correspondance classique-quantique et application au contrôle d'équations d'ondes et de Schrödinger dans l'espace euclidien." Electronic Thesis or Diss., université Paris-Saclay, 2024. https://theses.hal.science/tel-04634673.

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Les équations des ondes et de Schrödinger modélisent une grande variété de phénomènes ondulatoires, tels que la propagation de la lumière, les vibrations d'un objet ou l'évolution temporelle d'une particule quantique. Dans ces modèles, l'asymptotique des hautes énergies peut être décrite par des équations de la mécanique classique, comme l'optique géométrique. Dans cette thèse, nous étudions plusieurs applications de la correspondance classique-quantique à des problèmes de contrôle des équations des ondes et de Schrödinger dans l'espace euclidien, en utilisant des méthodes d'analyse microlocale.Dans les deux premières parties, nous étudions l'équation des ondes amorties et l'équation de Schrödinger avec un potentiel confinant dans l'espace euclidien. Nous donnons des conditions nécessaires et suffisantes de stabilité uniforme pour la première, et d'observabilité pour la seconde. Ces conditions font intervenir la dynamique classique sous-jacente qui consiste en une optique géométrique tordue par la présence du potentiel.Nous analysons ensuite dans une troisième partie la correspondance classique-quantique dans un cadre général qui contient les deux problèmes mentionnés ci-dessus. Nous démontrons une version du théorème d'Egorov dans le formalisme des métriques sur l'espace des phases et du calcul de Weyl--Hörmander. On présente différents cadres d'application de ce théorème pour des équations de Schrödinger, de demi-ondes et de transport
Wave and Schrödinger equations model a variety of phenomena, such as propagation of light, vibrating structures or the time evolution of a quantum particle. In these models, the high-energy asymptotics can be approximated by classical mechanics, as geometric optics. In this thesis, we study several applications of this principle to control problems for wave and Schrödinger equations in the Euclidean space, using microlocal analysis.In the first two chapters, we study the damped wave equation and the Schrödinger equation with a confining potential in the euclidean space. We provide necessary and sufficient conditions for uniform stability in the first case, or observability in the second one. These conditions involve the underlying classical dynamics which consists in a distorted version of geometric optics, due to the presence of the potential.Then in the third part, we analyze the quantum-classical correspondence principle in a general setting that encompasses the two aforementioned problems. We prove a version of Egorov's theorem in the Weyl--Hörmander framework of metrics on the phase space. We provide with various examples of application of this theorem for Schrödinger, half-wave and transport equations

2

Le, Floch Yohann. "Théorie spectrale inverse pour les opérateurs de Toeplitz 1D." Phd thesis, Université Rennes 1, 2014. http://tel.archives-ouvertes.fr/tel-01065441.

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Dans cette thèse, nous prouvons des résultats de théorie spectrale, directe et inverse, dans la limite semi-classique, pour les opérateurs de Toeplitz autoadjoints sur les surfaces. Pour les opérateurs pseudo-différentiels, les résultats en question sont déjà connus, et il est naturel de vouloir les étendre aux opérateurs de Toeplitz. Les conditions de Bohr-Sommerfeld usuelles, qui caractérisent les valeurs propres proches d'une valeur régulière du symbole principal, ont été obtenues il y a quelques années seulement pour les opérateurs de Toeplitz. Notre contribution consiste en l'extension de ces conditions près de valeurs critiques non dégénérées. Nous traitons le cas d'une valeur critique elliptique à l'aide d'une technique de forme normale ; l'opérateur modèle est la réalisation de l'oscillateur harmonique sur l'espace de Bargmann, dont le spectre est bien connu. Dans le cas d'une valeur critique hyperbolique, la forme normale ne suffit plus et nous complétons l'étude en faisant appel à des arguments dus à Colin de Verdière et Parisse, à qui l'on doit le résultat analogue dans le cas pseudo-différentiel. Enfin, nous établissons un résultat de théorie spectrale inverse pour les opérateurs de Toeplitz autoadjoints sur les surfaces ; plus précisément, nous montrons que sous certaines hypothèses génériques, la connaissance du spectre à l'ordre deux dans la limite semi-classique permet de retrouver le symbole principal à symplectomorphisme près. Ce résultat s'appuie en grande partie sur l'écriture des règles de Bohr-Sommerfeld.

3

Tarkhanov, Nikolai, and Nikolai Vasilevski. "Microlocal analysis of the Bochner-Martinelli integral." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/3001/.

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In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.

4

Schultka, Konrad. "Microlocal analyticity of Feynman integrals." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20161.

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Wir geben eine rigorose Konstruktion von analytisch-regularisierten Feynman-Integralen im D-dimensionalen Minkowski-Raum als meromorphe Distributionen in den externen Impulsen, sowohl in der Impuls- als auch in der parametrischen Darstellung. Wir zeigen, dass ihre Pole durch die üblichen Power-counting Formeln gegeben sind, und dass ihr singulärer Träger in mikrolokalen Verallgemeinerungen der (+alpha)-Landauflächen enthalten ist. Als weitere Anwendungen geben wir eine Konstruktion von dimensional regularisierten Integralen im Minkowski-Raum und beweisen Diskontinuitätsformeln für parametrische Amplituden.
We give a rigorous construction of analytically regularized Feynman integrals in D-dimensional Minkowski space as meromorphic distributions in the external momenta, both in the momentum and parametric representation. We show that their pole structure is given by the usual power-counting formula and that their singular support is contained in a microlocal generalization of the alpha-Landau surfaces. As further applications, we give a construction of dimensionally regularized integrals in Minkowski space and prove discontinuity formula for parametric amplitudes.

5

Ramaseshan, Karthik. "Microlocal analysis of the doppler transform on R³ /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5739.

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6

Welch, Barry Alan. "Semiclassical analysis of vibroacoustic systems." Thesis, University of Southampton, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.433930.

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7

Webber, James. "Radon transforms and microlocal analysis in Compton scattering tomography." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/radon-transforms-and-microlocal-analysis-in-compton-scattering-tomography(c1ad3583-01ce-4147-8576-2e635090cb15).html.

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In this thesis we present new ideas and mathematical insights in the field of Compton Scattering Tomography (CST), an X-ray and gamma ray imaging technique which uses Compton scattered data to reconstruct an electron density of the target. This is an area not considered extensively in the literature, with only two dimensional gamma ray (monochromatic source) CST problems being analysed thus far. The analytic treatment of the polychromatic source case is left untouched and while there are three dimensional acquisition geometries in CST which consider the reconstruction of gamma ray source intensities, an explicit three dimensional electron density reconstruction from Compton scatter data is yet to be obtained. Noting this gap in the literature, we aim to make new and significant advancements in CST, in particular in answering the questions of the three dimensional density reconstruction and polychromatic source problem. Specifically we provide novel and conclusive results on the stability and uniqueness properties of two and three dimensional inverse problems in CST through an analysis of a disc transform and a generalized spindle torus transform. In the final chapter of the thesis we give a novel analysis of the stability of a spindle torus transform from a microlocal perspective. The practical application of our inversion methods to fields in X-ray and gamma ray imaging are also assessed through simulation work.

8

Conrady, Florian. "Semiclassical analysis of loop quantum gravity." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=982087144.

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9

Conrady, Florian. "Semiclassical analysis of loop quantum gravity." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2006. http://dx.doi.org/10.18452/15549.

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In dieser Dissertation untersuchen und entwickeln wir neue Methoden, die dabei helfen sollen eine effektive semiklassische Beschreibung der kanonischen Loop-Quantengravitation und der Spinfoam-Gravitation zu bestimmen. Einer kurzen Einführung in die Loop-Quantengravitation folgen drei Forschungsartikel, die die Resultate der Doktorarbeit präsentieren. Im ersten Artikel behandeln wir das Problem der Zeit und einen neuen Vorschlag zur Implementierung von Eigenzeit durch Randbedingungen an Pfadintegrale: wir untersuchen eine konkrete Realisierung dieses Formalismus für die freie Skalarfeldtheorie. Im zweiten Artikel übersetzen wir semiklassische Zustände der linearisierten Gravitation in Zustände der Loop-Quantengravitation. Deren Eigenschaften deuten an, wie sich Semiklassizität im Loop-Formalismus manifestiert, and wie man dies benützen könnte, um semiklassische Entwicklungen herzuleiten. Im dritten Teil schlagen wir eine neue Formulierung von Spinfoam-Modellen vor, die vollständig Triangulierungs- und Hintergrund-unabhängig ist: mit Hilfe einer Symmetrie-Bedingung identifizieren wir Spinfoam-Modelle, deren Triangulierungs-Abhängigkeit auf natürliche Weise entfernt werden kann.
In this Ph.D. thesis, we explore and develop new methods that should help in determining an effective semiclassical description of canonical loop quantum gravity and spin foam gravity. A brief introduction to loop quantum gravity is followed by three research papers that present the results of the Ph.D. project. In the first article, we deal with the problem of time and a new proposal for implementing proper time as boundary conditions in a sum over histories: we investigate a concrete realization of this formalism for free scalar field theory. In the second article, we translate semiclassical states of linearized gravity into states of loop quantum gravity. The properties of the latter indicate how semiclassicality manifests itself in the loop framework, and how this may be exploited for doing semiclassical expansions. In the third part, we propose a new formulation of spin foam models that is fully triangulation- and background-independent: by means of a symmetry condition, we identify spin foam models whose triangulation-dependence can be naturally removed.

10

Teloni, Daniele. "Semiclassical analysis of systems of Schrödinger equations." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19239/.

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The scalar Schrödinger equation models the probability density distribution for a particle to be found in a point x given a certain potential V(x) forming a well with respect to a fixed energy level E_0. Formally two real inversion points a,b exist such that V(a)=V(b)=E_0, V(x)<0 in (a,b) and V(x)>0 for xb. Following the work made by D.Yafaev and performing a WKB approximation we obtain solutions defined on specific intervals. The aim of the first part of the thesis is to find a condition on E, which belongs to a neighbourhood of E_0, such that it is an eigenvalue of the Schrödinger operator, obtaining in this way global and linear dependent solutions in L2. In quantum mechanics this condition is known as Bohr-Sommerfeld quantization. In the second part we define a Schrödinger operator referred to two potential wells and we study the quantization conditions on E in order to have a global solution in L2xL2 with respect to the mutual position of the potentials. In particular their wells can be disjoint,can have an intersection, can be included one into the other and can have a single point intersection. For these cases we refer to the works of A.Martinez, S. Fujiié, T. Watanabe, S. Ashida.

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Книги з теми "Microlocal and semiclassical analysis":

1

Martinez, André. An Introduction to Semiclassical and Microlocal Analysis. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-4495-8.

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2

Zworski, Maciej. Semiclassical analysis. Providence, R.I: American Mathematical Society, 2012.

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3

Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. Microlocal analysis and asymptotic analysis. [Kyoto]: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2004.

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4

Bony, Jean Michel, Gerd Grubb, Lars Hörmander, Hikosaburo Komatsu, and Johannes Sjöstrand. Microlocal Analysis and Applications. Edited by Lamberto Cattabriga and Luigi Rodino. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0085120.

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5

Garnir, H. G., ed. Advances in Microlocal Analysis. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4606-4.

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6

Kashiwara, Masaki. Introduction to microlocal analysis. Gene ve: L'Enseignement mathe matique, Universite de Gene ve, 1986.

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7

NATO Advanced Study Institute on Advances in Microlocal analysis (1985 Castelvecchio Pascoli, Italy). Advances in microlocal analysis. Dordrecht: D. Reidel Pub. Co., 1986.

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8

Takahiro, Kawai, Fujita Keiko, and Kyōto Daigaku. Sūri Kaiseki Kenkyūjo., eds. Microlocal analysis and complex Fourier analysis. River Edge, NJ: World Scientific, 2002.

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9

Rodino, Luigi, ed. Microlocal Analysis and Spectral Theory. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5626-4.

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10

Beals, Michael, Richard B. Melrose, and Jeffrey Rauch, eds. Microlocal Analysis and Nonlinear Waves. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4613-9136-4.

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Частини книг з теми "Microlocal and semiclassical analysis":

1

Ivrii, Victor. "Introduction to Semiclassical Microlocal Analysis." In Springer Monographs in Mathematics, 21–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-12496-3_2.

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2

Ivrii, Victor. "Complete Differentiable Semiclassical Spectral Asymptotics." In Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 607–18. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30561-1_35.

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3

Ivrii, Victor. "Bethe-Sommerfeld Conjecture in Semiclassical Settings." In Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 619–39. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30561-1_36.

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4

Ivrii, Victor. "Standard Local Semiclassical Spectral Asymptotics near the Boundary." In Microlocal Analysis, Sharp Spectral Asymptotics and Applications I, 623–741. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30557-4_7.

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5

Paul, T. "Recent Results in Semiclassical Approximation with Rough Potentials." In Microlocal Methods in Mathematical Physics and Global Analysis, 49–52. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0466-0_11.

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6

Datchev, Kiril, and András Vasy. "Propagation Through Trapped Sets and Semiclassical Resolvent Estimates." In Microlocal Methods in Mathematical Physics and Global Analysis, 7–10. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0466-0_2.

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7

Ivrii, Victor. "Standard Local Semiclassical Spectral Asymptotics near the Boundary. Miscellaneous." In Microlocal Analysis, Sharp Spectral Asymptotics and Applications I, 742–800. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30557-4_8.

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8

Hassell, Andrew, and Victor Ivrii. "Spectral Asymptotics for the Semiclassical Dirichlet to Neumann Operator." In Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 468–94. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30561-1_29.

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9

Ivrii, Victor. "Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators." In Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 583–606. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30561-1_34.

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10

Alazard, Thomas, and Claude Zuily. "Microlocal Analysis." In Universitext, 61–73. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50284-3_5.

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Тези доповідей конференцій з теми "Microlocal and semiclassical analysis":

1

Chang, Kung-ching, Yu-min Huang, and Ta-tsien Li. "Nonlinear Analysis and Microlocal Analysis." In International Conference at the Nankai Institute of Mathematics. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814537841.

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2

Cheney, Margaret, and Brett Borden. "Microlocal analysis of GTD-based SAR models." In Defense and Security, edited by Edmund G. Zelnio and Frederick D. Garber. SPIE, 2005. http://dx.doi.org/10.1117/12.602982.

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3

Marti, Jean-André. "Sheaf theory and regularity. Application to local and microlocal analysis." In Linear and Non-Linear Theory of Generalized Functions and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc88-0-17.

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4

Tsobanjan, Artur, Jerzy Kowalski-Glikman, R. Durka, and M. Szczachor. "Semiclassical Analysis of Constrained Quantum Systems." In THE PLANCK SCALE: Proceedings of the XXV Max Born Symposium. AIP, 2009. http://dx.doi.org/10.1063/1.3284397.

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Franco, Daniel Heber Teodoro. "Paley-Wiener-Schwartz Theorem and Microlocal Analysis of Singularities in Theory of Tempered Ultrahyperfunctions." In Fifth International Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2007. http://dx.doi.org/10.22323/1.031.0047.

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Yang, Jaw-Yen, Li-Hsin Hung, Sheng-Hsin Hu, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Simulation of MicroChannel Flows Using a Semiclassical Lattice Boltzmann Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241532.

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Czuma, Pawel, and Pawel Szczepański. "Analysis of light generation in 2D photonic crystal laser: semiclassical approach." In SPIE Proceedings, edited by Wieslaw Wolinski, Zdzislaw Jankiewicz, and Ryszard S. Romaniuk. SPIE, 2006. http://dx.doi.org/10.1117/12.726656.

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