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Posted in April 2010

Advanced Statistical Mechanics

As mentioned, I will be giving a different course starting spring 2011: Advanced Statistical Mechanics. Today I have made some decisions concerning the structure. One of the goals is to provide backward compatibility with the course of Jos Thijssen sucsessfully given for a number of years.

Book: I decided to go for most popular books for a course of the kind: those of Mehrar Kardar. This was not a simple decision since the books are thick, written in a more scolastic style than I’d like, provide the coverage that is more broad than interesting, and cost seventy-nine silver pounds. Many teachers that use the books complain about inconventional notations. Still the books are adopted in most prestigious American universities. So finally I got in terms with those.

Topics: since the books are too thick, one has to make a selection of topics. The present selection of Jos Thijssen is very logical and will be taken as a basis. However, owing to unavoidable taste differences I’d rather resize the relative volume of the topics. For instance, I’d like very much to talk about the correspondence between classical 1d stat-mechanics and 0d quantum mechanics, while ideal gases do not appeal to me that much.



Christ is risen!

Blessed Easter to you, dear reader. I’d like to make an exception from no-image rule for this blog and let you see my favourite icon of Resurrection. This icon is situated in a small russian-orthodox chapel in Dachau, Germany, and refers to Easter celebration on May 8th, 1945.


Good Friday, Holy Saturday

Just attended Matins of Holy Saturday, celebrated Friday evening. Wish I had words.

From Troparia

The One, who of old hid the pursuing tyrant in the waves of the sea, the children of those he saved have hidden beneath the earth; but let us, like the young maidens, sing to the Lord; for he has been greatly glorified.’

Lord, my God, I will sing a song for your departure, a funeral hymn for you who by your burial opened up for me the entrances to life, and by your death put Death and Hell to death.

All things above the world and all below the earth quaked with fear at your death, as they saw you on the throne above and below in a tomb; for beyond understanding you appeared as a one dead, you the source of life.

That you might fill all things with your glory, you went down into the lowest parts of the earth; for my substance, which is in Adam was not hidden from you, and by being buried you make me, who had been corrupted, new, O Lover of humankind.


Measuring entanglement

I cannot believe it myself, and it is hardly thustworthy to write about it on April 1, but please take it for a fact. I have attempted to experimentally quantify entanglement of photon pairs today. I did not do any experiments for more than thirty years.

Val Zwiller is to blame. When asked to provide an experimental setup for undegraduate lab practice, he could not come with any fresh idea. So he’s just slightly modified a setup of pioneering experiment of Alian Aspect who has quantified the violation of Bell inequality in 1981. He has invited me and Leo Kouwenhoven to "inagurate" – that’s how he put it – the experimental setup. 

At 16:00 I was at his office. We brisky got to the measurement room. On the way Val asked me with soft heartfelt tone: " Do you believe in entanglement? Do you believe in non-locality?" This gave me a thrilling impression of being a part of important rite: he sounded like a priest asking faithful about their readiness. "I do. I do believe." I responded, trying to match the tone. I wanted to add that I believe in quantum mechanics, but, given the nature of the rite (where a participant should demonstrate a ritual doubt and sucsessfully overcome it by direct measurement) this would not sound polite. 

Me and Leo have been supervised by Julia Cramer and another young lady. The setup was placed in two large plastic boxes alike my children use to store old toys. One box housed a blue laser, non-linear crystal to chop a blue photon into an entangled pair of red ones. The two go by two fibers to the second box where their polarizations have been rotated by changeable angles and finally get to photon counters. The computer gave coincidence counts, those depending on the rotation angles. The math to be made afterwards, and its significance is explained in

There were about twenty curious people in the room, all irradiating excess heat. Val has attibuted the chaotic work of the setup to this mere circumstance. He kept re-tuning the fibers in the production box. He did it quickly and efficiently. I was turning polarizers. Leo read data and wrote it up. One needs to measure at four different positions of the polarizers. So we got 16 readings. After the experiment everybody was cheering while I had to do the math.

We did not manage to prove (our faithful devotion to ) quantum mechanics this time. This would happen if the final answer would exceed classical boundary of 2. Yet we got 1.91: Almost. Not bad for the first time.

Thanks very much, Val, Julia and all others involved: this was a wonderful and entertaining experience for me, and it will be fun for many generations of students.


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