I am interested in \u201cquantum engineering\u201d: application of quantum mechanics. I do theory, and like elegant mathematics geometry, and animations.<\/p>\n\n\n\n
You may enjoy the visualizations even if the mathematics and physics does not really interest you.<\/p>\n\n\n\n
The motion of small organisms and microbots is dominated by viscosity and inertia is largely irrelevant. This makes this mode of locomotion foreighn and unituitive. Its mathematical appeal comes from the fact that it is geometric in character.<\/p>\n\n\n\n
Pushmepulyou versus three linked sphere<\/a><\/p>\n\n\n\n Pushmepulyou<\/strong>: The three linked spheres is an elegant model of a microswimmer invented by Njafy and Golestanian. Inspiredd by their work, David Oaknin, Oded Kenneth and I invented Pushmepulyou. By pressing START you will see a swimming competition between the two swimmers. For more informatio see<\/a>.<\/p>\n\n\n\n Symmetric Purcell swimmer<\/a><\/p>\n\n\n\n Purcell swimmer<\/strong>: Perhaps the most important caricature of a micro-swimmer is the one invented by Purcell. It is made of three linked rods and mimics a flagellum, it also illustrates the unintuitive nature of the motion at low Reynolds numbers and it is a challenge to guess (given the stroke) it will swim. It is also very hard to analyze mathematically. Together with my student, Oren Raz, we invented a symmmetric version of Purcell swimmer which is intuitive and that removes some of the mystery. For more see<\/a>.<\/p>\n\n\n\n Cats always fall on their feet and they do so without relying angular momentum. Rotations at zero zangular momentum look surprising, but they are possible if a body is deformable. The image of a cat in the animation above shows how a sequence of non-commuting deformations lead to a rotation. This is a simple example of holonomy. The mathematical description is quite pretty and geometric and there is huge literature on this problem. For my work see<\/a>.<\/p>\n\n\n\n Swimming on a sphere<\/a><\/p>\n\n\n\n Baron von Munchhausen claimed to have pulled himself, and his horse, out of a swamp by pulling on his hair. This is a tall story because it conflicts with Newton’s laws. However, as Jack wisdom noted it is not such a tall stroy in a curved space. Wisdom was interested in swimming away from blach holes. Together with Oded Kenneth we developed a theory of swimming of deformable bodies in isotropic and homogeneous spcaces. In the animation above, the same stroke propagates the swimmer in opposite directions because the curvature of the ambient space is opposite.<\/p>\n\n\n\n Swimming on a surface with negative curvature<\/a><\/p>\n\n\n\n The colored Hofstadter butterfly shown below is pretty fractal, pictures that arises from the solution of an simple looking single linear equation that is a model of the quantum Hall effect. The picture was made by my student Daniel Osadchy as part of his MSc. A Matlab code for making the picture is available from his home page<\/a>. and it is called a hofstadter butterly because Douglas Hofstadter, the author of the best seller “Goedel Escher Bach” made the black and white version of the butterfly back in 1976. The colors in the diagram represent intgeres known mathematically as Chern number and physically as the quantized values of the Hall conductance. These integers were not known in 1976: The Hall effect was only discovered in 1980 by Klaus von Klitzing, who recieved a Nobel prize for it. David Thouless and coauthors, TKNN, studied the Hosftader model in this context and showed that the Hall conductance is related to Chern numbers. For more, see<\/a>.<\/p>\n\n\n\nFalling cats<\/h3>\n\n\n\n
Baron von Munchhausen or Swimming in empty curved space<\/h3>\n\n\n\n
Hofstadter butterflies and the Quantum Hall effect<\/h3>\n\n\n\n
Optimal swimming strokes for microswimmers<\/h3>\n\n\n\n
![Colored Hofstadter buttterfly: High resolution image. <\/a> Courtesy of D. Osadchy<\/li>\n\n\n\nWebb based app for testing separability of quantum states: States separator<\/a>,<\/a> a project carried by N. Shalev and O. Messer (Instructions for use: https:\/\/github.com\/omesser\/stateseparator\/blob\/main\/CONTRIBUTING.md<\/a>)<\/li>\n<\/ul>\n\n\n\nLectures (pdf):<\/h2>\n\n\n\n\nQuantum Games<\/a>, the Hebrew university of Jerusalem, November 2024<\/li>\n\n\n\nQuantum games: The Mermin-Peres magic square<\/a>, July 2023<\/li>\n\n\n\nQuantum: Threats and promises<\/a>, Quantum session for social sciences and humanities, Haifa University, June 2023<\/li>\n\n\n\n2022 Nobel Prize<\/a>, Technion Physics colloquium, May 2023<\/li>\n\n\n\nBorn rule for Lindblad evolutions<\/a>, Lecture at the Quantum Computing conference, Kfar Bloom, 2022<\/li>\n\n\n\nAn invitation to Zak phase<\/a>, Korea-Israel meeting, the Academy of Science, Jerusalem 2022<\/li>\n\n\n\nRisorgimento della vita felice<\/a>, Zurich, 2022<\/li>\n\n\n\nAn introduction to Zak phase: Fun with 2×2 matrices<\/a>, Strasbourg 2022<\/li>\n\n\n\nShor in short<\/a>, Haifa University 2022<\/li>\n\n\n\nA century of adiabaticity<\/a>, Rutgers, 2020<\/li>\n\n\n\nShor algorithm in times of Corona<\/a>, Lecture at the Diller Summer school 2020 (Slides in English, video in Hebrew)<\/li>\n\n\n\nBraiding flluxes in Pauli Hamiltonians<\/a>, Shanghai 2019<\/li>\n\n\n\nHall conductance for large interacting systems<\/a>, Nordita 2019<\/li>\n\n\n\nQuantum computers and Shor algorithm: Crash course<\/a>, \u05e8\u05e4\u05d0”\u05dc 2019<\/li>\n\n\n\nOdd viscosity: Hall viscosity for the neophyte<\/a>, WIS 2018<\/li>\n\n\n\nThe geometry of 1,2 and n qubits,<\/a> Torun, Poland 2018<\/li>\n\n\n\nGeometry of qubits<\/a>, Haifa, 2018<\/li>\n\n\n\nFlexible Ring Interferometers<\/a>, Smilansky Fest, Rehovot, 2016.<\/li>\n\n\n\nVignettes, Barry Simon Fest<\/a>, Montreal 2016<\/li>\n\n\n\n4 Lectures on Adiabatic Quantum Transport<\/a>, La Sapienza, Rome, 2016<\/li>\n\n\n\nBar-Ilan Colloquium: Tutorial on Fredholm index interpretation of the Quantum Hall effect<\/a> (2016)<\/li>\n\n\n\nAdiabatic transport in Open Systems<\/a> (Koln 2015)<\/li>\n\n\n\nTwo tutorial lectures on the Quantum Hall Effect, Chern numbers<\/a>, Fredholm Index<\/a>, ESI, Vienna (2014)<\/li>\n\n\n\nBraiding fluxes in Pauli Hamiltonians, (Hebrew University<\/a>, 2016) SISSA (2014)<\/a>, Montreal, (2014)<\/a><\/li>\n\n\n\nEntanglement for pedestrians, Colloquium, Weizmann (2014)<\/a><\/li>\n\n\n\nAdiabatic response in open systems<\/a>, Kfar Blum (2012)<\/li>\n\n\n\nTransport in open systems<\/a>, KITP, (2011)<\/li>\n\n\n\nThe Baron and the Cat<\/a> KITP, (2011)<\/li>\n\n\n\nJerusalem winter school<\/a> 2010<\/li>\n\n\n\nSwimming in curved space (Technion 2011)<\/li>\n\n\n\nGeometry of response in open systems (CRM Montreal 2011)<\/li>\n\n\n\nVisualizing 2 qubits<\/a> (Caltech 2011)<\/li>\n\n\n\nGeometry of transport in open systems (Caltech, Harvard, MIT 2011)<\/li>\n<\/ul>\n\n\n\nLecture notes:<\/h2>\n\n\n\n\nQuantum information<\/a><\/li>\n\n\n\nElectrodynamics<\/a><\/li>\n\n\n\nClassical Thermodynamics<\/a> (draft)<\/li>\n\n\n\nLagrangian and Hamiltonian Mechanics<\/a><\/li>\n<\/ul>\n\n\n\nRecent Graduate students and thesis:<\/h2>\n\n\n\n\nAmit Tsabary, Dissipation in Linear and Nonlinear Models of Quantum Systems<\/a>, 2017<\/li>\n\n\n\nRotem Berman, Swimming and alignment in low Reynolds numbers<\/a>, 2014<\/li>\n\n\n\nMichael Shalyt, Control of a 2-Level System to Reduce Colored Noise<\/a>, 2013.<\/li>\n\n\n\nLev Kvitny, Entanglement in Quantum States<\/a>, 2011.<\/li>\n\n\n\nEli Meirom, Entanglement in Radiative caascades<\/a>, 2008.<\/li>\n\n\n\nOren Raz, Swimming, Pumping and Gliding at Low Reynolds Number<\/a>, 2007.<\/li>\n\n\n\nGili Bisker, The world of two qubits<\/a>, 2007<\/li>\n<\/ul>\n\n\n\nWikipedia<\/h2>\n\n\n\n\n\u05d9\u05d4\u05d5\u05e9\u05e2 \u05d6\u05e7<\/a><\/li>\n\n\n\n\u05d4\u05e0\u05e1 \u05e7\u05e8\u05d5\u05da<\/a><\/li>\n\n\n\n\u05d0\u05e9\u05e8 \u05e4\u05e8\u05e1<\/a><\/li>\n\n\n\n\u05d3\u05d1 \u05d0\u05d1\u05e8\u05d5\u05df<\/a><\/li>\n\n\n\n\u05d0\u05e4\u05e7\u05d8 \u05e1\u05e0\u05d9\u05d0\u05e7<\/a><\/li>\n\n\n\nSagnac effect<\/a><\/li>\n\n\n\nStokes’ paradox<\/a>, Yacov Nir Breitstein, project<\/li>\n\n\n\nState separator<\/a>,<\/a> a web app for testing separability, contributed entry to Quantum entaglement,<\/a> O. Messer, project<\/li>\n<\/ul>\n\n\n\nAnimations:<\/h2>\n\n\n\nMicroswimmers:<\/h3>\n\n\n\nThe motion of small organisms and microbots is dominated by viscosity and inertia is largely irrelevant. This makes this mode of locomotion foreighn and unituitive. Its mathematical appeal comes from the fact that it is geometric in character.<\/p>\n\n\n\nPushmepulyou versus three linked sphere<\/a><\/p>\n\n\n\nPushmepulyou<\/strong>: The three linked spheres is an elegant model of a microswimmer invented by Njafy and Golestanian. Inspiredd by their work, David Oaknin, Oded Kenneth and I invented Pushmepulyou. By pressing START you will see a swimming competition between the two swimmers. For more informatio see<\/a>.<\/p>\n\n\n\nSymmetric Purcell swimmer<\/a><\/p>\n\n\n\nPurcell swimmer<\/strong>: Perhaps the most important caricature of a micro-swimmer is the one invented by Purcell. It is made of three linked rods and mimics a flagellum, it also illustrates the unintuitive nature of the motion at low Reynolds numbers and it is a challenge to guess (given the stroke) it will swim. It is also very hard to analyze mathematically. Together with my student, Oren Raz, we invented a symmmetric version of Purcell swimmer which is intuitive and that removes some of the mystery. For more see<\/a>.<\/p>\n\n\n\nFalling cats<\/h3>\n\n\n\nCats always fall on their feet and they do so without relying angular momentum. Rotations at zero zangular momentum look surprising, but they are possible if a body is deformable. The image of a cat in the animation above shows how a sequence of non-commuting deformations lead to a rotation. This is a simple example of holonomy. The mathematical description is quite pretty and geometric and there is huge literature on this problem. For my work see<\/a>.<\/p>\n\n\n\nBaron von Munchhausen or Swimming in empty curved space<\/h3>\n\n\n\nSwimming on a sphere<\/a><\/p>\n\n\n\nBaron von Munchhausen claimed to have pulled himself, and his horse, out of a swamp by pulling on his hair. This is a tall story because it conflicts with Newton’s laws. However, as Jack wisdom noted it is not such a tall stroy in a curved space. Wisdom was interested in swimming away from blach holes. Together with Oded Kenneth we developed a theory of swimming of deformable bodies in isotropic and homogeneous spcaces. In the animation above, the same stroke propagates the swimmer in opposite directions because the curvature of the ambient space is opposite.<\/p>\n\n\n\nSwimming on a surface with negative curvature<\/a><\/p>\n\n\n\nHofstadter butterflies and the Quantum Hall effect<\/h3>\n\n\n\nThe colored Hofstadter butterfly shown below is pretty fractal, pictures that arises from the solution of an simple looking single linear equation that is a model of the quantum Hall effect. The picture was made by my student Daniel Osadchy as part of his MSc. A Matlab code for making the picture is available from his home page<\/a>. and it is called a hofstadter butterly because Douglas Hofstadter, the author of the best seller “Goedel Escher Bach” made the black and white version of the butterfly back in 1976. The colors in the diagram represent intgeres known mathematically as Chern number and physically as the quantized values of the Hall conductance. These integers were not known in 1976: The Hall effect was only discovered in 1980 by Klaus von Klitzing, who recieved a Nobel prize for it. David Thouless and coauthors, TKNN, studied the Hosftader model in this context and showed that the Hall conductance is related to Chern numbers. For more, see<\/a>.<\/p>\n\n\n\nOptimal swimming strokes for microswimmers<\/h3>\n\n\n\n\n\nWhat determines the size and shape of an optimal stroke of microswimmers? In the animation the one sees that the stroke ends when the shape developes a cusp. Together with Gat and Kenneth we gave a detailed analysis of the problem of two dimensional swimmers using conformal techniques. For more see<\/a><\/p>\n<\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"I am interested in \u201cquantum engineering\u201d: application of quantum mechanics. I do theory, and like elegant mathematics geometry, and animations. You may enjoy the visualizations even if the mathematics and physics does not really interest you. Publications: Podcast Video lectures: Zoom Lectures: Video course (Hebrew): (Semi-) Popular: Blog App Lectures (pdf): Lecture notes: Recent Graduate …<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"content-sidebar","footnotes":""},"class_list":{"1":"page","2":"type-page","5":"entry"},"yoast_head":"\nHome page of Prof. Yossi Avron - Technion<\/title>\n<meta name=\"description\" content=\"Yosi Avron's web site at the Technion: publications, teaching materials, personal information and more\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/phsites.technion.ac.il\/avron\/\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/phsites.technion.ac.il\\\/avron\\\/\",\"url\":\"https:\\\/\\\/phsites.technion.ac.il\\\/avron\\\/\",\"name\":\"Home page of Prof. Yossi Avron - 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