Department of
Physics
415 Taub (Arts and Humanities)
Technion,
email: avronj@tx.technion.ac.il
972-4-829 3853 (Taub office)
054-759 2348 (cell)
972-4-834 0545 (home)
972-4-834 0717 (fax,
home)
Technion
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Directions
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Topological quantum numbers,
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אודיסיאה: טלפורטציה קוונטית
Animations:
The animations below can be downloaded from here. Right click and choose Save target as... Flash files (*.swf) run from a browser.
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Purcell swimmer
Bacteria and microbots live in a world without
inertia. Swimming in this world is a challenge for those of us whose physical
intuition developed in a world where inertia dominates. Oren Raz, my grad
student, made the simulation above showing a simpler version of Purcell
celebrated swimmer. As you can see, the net motion results from cancellations
and this is why this is a poor swimmer.
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Entanglement Entanglement is one of the things that make quantum mechanics weird. The simplest quantum system that exhibits entanglement is two qubits. Together with Oded Kenneth and my student Gili Bisker we developed a geometric description of the 16 dimensional world of two qubits. The tetrahedron in the diagram represents the equivalence class of the quantum states and the octahedron gives the separable states. The states outside the octahedron and inside the tetrahedron are the entangled state. The cube represents the entanglement witnesses.
Swimming in curved space Baron von Munchausen claimed to have rescued himself from drowning in a swamp by pulling on his hair. J. Wisdom noted that this is not such a tall story if the Baron lived in a curved space where it is possible to move without momentum. This is an analog of a cat falling on its feet and so turns with no angular momentum. I did some joint work on this together with Oded Kenneth. Two movies of swimmers in curved space below were made by my student Oren Raz. Note that a stroke leads to forward swimming on the sphere gives backward swimming on the inside of the torus
A swimming competition between the three linked spheres (invented by Najafi and Golestanian) and Pushmepullyou (due to Oaknin, Keneth and myself). Pushmepullyou easily wins the competition. You may worry that the competition is rigged and Pushmepullyou wins because it has more power. Actually the opposite is true. Pushmepullyou uses much less power than the three linked spheres. It is so efficient that it beats the efficiency of microorganisms that use beating flagella to swim. Pushmepullyou has some resemblance to a swimming mode of Euglena known as metaboly. For more details see article.
Press start button
on picture to start the competition
Toroidal fullerenes: J. Berger and I toyed with the idea that carbon would may form toroidal molecules. Here is one candidate that looks pretty stable with 120 carbon atoms. To appreciate the 3d aspect of the figure, place the cursor on the figure and drag, the molecule will rotate. You can read more about how to construct toroidal carbon molecules and how to test their stability in my papers with J. Berger
Hofstadter
Butterflies: The integer quantum Hall effect leads to interesting fractal
phase diagrams. The center picture below shows the
phase diagram of the Azbel-Harper-Hofstadter model.
The colors represent the Hall conductances, which are
all integers. The horizontal axis is the density of electrons and the vertical
axis is the strenth os the
magnetic field. This picture served as a cover page of Physics Today which also
runs an expository article on the integer quantum Hall effect by Ruedi
Seiler, Danniel Osadchy and myself. The Japanese text on the right is the
translation of the article which appeared in Parity. The picture was made by my
student Daniel Osadchy as part of his M.Sc. thesis.
lick picture to get article
Quantum swimmers
Swimming in a one dimensional Fermi sea at zero
temperature is quantized. Moreover, it is possible to swim without
dissipation. This work was done together with Daviv Oaknin and Boris
Gutkin whose picture is given below. If you click on Boris's picture you'll get
the Science article the reports on this
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Click picture of Boris Gutkin to get Science report on quantum swimmer |
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