Weblog Yuli Nazarov
Paper to commemorate Markus Buttiker
who has passed away on Oct 4, 2013 in the age of 63. There will be a special issue of Physica E devoted to his memory.
From the conclusions:
“In conclusion, we have provided a technical and comprehensive introduction to the Keldysh action formalism for a multi-terminal scatterer with special emphasis on superconducting leads. We have derived a very general and compact formula and have elaborated on simple important examples to demonstrate the variety of its applications.
I did this to commemorate Markus Buttiker, the pioneer of scattering approach to quantum transport, one of the fathers of this big, prosperous and fruitfully developing research field. I admire not only his research merits: throughout 25 years of our acquaintance I was appreciating much his daring to remain himself, to keep his own research style, research topics and idea sets in times where the close following of a quickly changing scientific fashion seemed to be a must. He was also a charming personality and a good friend.”
The paper can be found here.
Survey Advanced Quantum Mechanics 2
The semester is over – well, almost, we need to prepare the exams, yet it all will happen very soon. The end of the semester was pretty busy so I had no mood neither time for the blog. I shall only do what I ought to – to publish the results of the last survey on Advanced Quantum Mechanics course made on 1-6-2015, during one of the last lectures. Students by this time had very certain opinion about the course, were rather critical, yet could appreciate the good parts of it. That I can also judge from a big number of the students (52) who are going to take the exam.
Ok, questions and answers:
In my opinion, the content of this course is relevant to my education (from -2 to 2) 1.4
This course corresponds well to my prior knowledge (from -2 to 2) 0.8
In relation to the amount of credit points, the actual study load of this course was much higher (from -2 to 2) 0
The lecturer explain the subject matter clearly (from -2 to 2) 0.3
The lecturer discuss the subject matter in a stimulating way (from -2 to 2) 0.2
The instructors give sufficient feedback on student presentations (from -2 to 2 ) 1.53 here we have improved a lot !
The problem-solving sessions are interesting and useful (from -2 to 2 ) -0.22 we need to restructure the problem-solving sessions
English mark for the teacher (from 0 to 10 ) 6.7
English mark for the instructors (from 0 to 10 ) 8.3 good
The lecturer should present the material with more examples . OK
The problem-solving sessions should be with more discussions. OK
This course is well organised (supply of information, scheduling) (from -2 to 2 ) 1.4 much improvement!
I will go on with the course and come to the examination. Majority answered undoubtedly.
What mark do you expect to get at the exam? 6.9
Do you use the book? Majority uses it regulary
The overal mark:
lectures 6.6
problem-solving sessions 6.1 have to do something about
the whole course 7.2 could be better
we wouldn’t mind to score more, yet it’s not a big problem
I have also interesting remarks from the students, to be posted later.
Exact correspondence between Renyi entropy flows and physical flows
has been published today.
Reference: Mohammad H. Ansari and Yuli V. Nazarov, Phys. Rev. B 91, 174307 (2015)
Link: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.174307
DOI: http://dx.doi.org/10.1103/PhysRevB.91.174307
Nanofront proposal granted
This happens from time to time with the submitted proposals. The proposal title is “Quantum mixtures of topological and non-topological states realized with superconducting junctions”. I will announce a PhD position soon.
Silence and ERC Advanced Grant proposal
I didn’t write much to the blog for almost a couple of months. An excuse for this is I’ve been busy preparing an important grant proposal. Not that it really took every minute of my working time – yet for me it is psychologically difficult to prepare proposals, and any unrelated activity eventually gives a feeling of guilt – whatever irrational it may be.
Anyway, I’m almost done and will submit the proposal soon. It is in development of the recent ideas about topological properties of superconducting junctions. Below is the title and the abstract.
Higher-dimensional topological solids realized with multi-terminal superconducting junctions (HITSUPERJU)
Recently I revealed a deep operational analogy between an exotic material and an electronic device, i.e. between a 3-dimensional topological solid and a 4-terminal superconducting junction. Specifically, the 3d Weyl singularities revealed in the energy spectrum of this quantum device give rise to quantized trans-conductance in two leads that is typical for 2-dimensional topological Quantum Hall materials. The quantized value can be tuned with the third control phase.
I propose to capitalize on this breakthrough by realizing artificial n-dimensional (topological) solid materials by (n+1)-terminal superconducting junctions. This seemed to be fundamentally forbidden so far. In particular, in the framework of one research direction I will address the realization of higher Chern numbers. The edges and interfaces are important in topological solids, they need to be structured. For the artificial topological materials made with multi-terminal superconducting junctions such structuring is impossible in geometric coordinate space. However, the fact that the charge and superconducting phase are quantum-conjugated quantities provide the unique possibility for the structuring in multi-dimensional charge space that I will access in the framework of another direction. These two research directions will be supplemented by a more technical effort devoted to computational (quantum) dynamics of multi-terminal superconducting junctions.
The proposed way to “conquer” higher dimensions for condensed matter physics is of clear fundamental importance. Exciting applications are at the horizon, too. The exotic quantum states under consideration can be topologically protected and thus useful for quantum information processing. Quantized trans-resistance as well as other topological invariants may be important in metrology. More generally, the research proposed will boost the whole field of electronic devices wherever topology guarantees the discrete stability of device characteristics.
Strong effects of weak ac driving in short superconducting junctions
has been published in PRB couple of days ago.
URL: http://link.aps.org/doi/10.1103/PhysRevB.91.104522
DOI: 10.1103/PhysRevB.91.104522
You can find the preprint here.
Abstract:
We study a short superconducting junction subject to a dc and ac phase bias. The ac modulation changes the occupation of the Andreev bound states formed at the constriction by transitions between bound states and the continuum. In a short junction, the non-equilibrium Andreev bound state population may relax through processes that conserve parity of the occupation number on the same bound state and processes that do not conserve it. We argue that the parity conserving processes occur on a much faster time scale. In this case, even a weak driving may lead to a large deviation of the supercurrent from its equilibrium value. We show that this effect is accompanied by a quasiparticle current which may lead to a measurable charge imbalance in the vicinity of the junction. Furthermore, we study the time evolution of the supercurrent after switching off the ac drive. On a time scale where parity relaxation is negligible, the supercurrent relaxes to a stationary non-equilibrium state. Finally, we briefly outline the regime of ultraweak driving where the ac-induced processes occur on a time scale comparable to parity relaxation.
Self-evaluation AQM: the results of the survey
About a month ago I ask the students to answer some questions regarding the course. We’ve used this feedback. Now the semester break has started: I have time to derive and publish the exact results.
In my opinion, the content of this course is relevant to my education (from -2 to 2) 1.66 good
This course corresponds well to my prior knowledge (from -2 to 2) 0.83 lower than we expected, though not bad
In relation to the amount of credit points, the actual study load of this course was much higher (from -2 to 2) 0.33 very good
The lecturer explain the subject matter clearly (from -2 to 2) 0.33 mmm, point to improve
The lecturer discuss the subject matter in a stimulating way (from -2 to 2) 1.0 rather good
The instructors give sufficient feedback on student presentations (from -2 to 2 ) 0.66 we can improve
The problem-solving sessions are interesting and useful (from -2 to 2 ) 0.88 as expected
English mark for the teacher (from 0 to 10 ) 6.8 mmm…
English mark for the instructors (from 0 to 10 ) 8.0 good
The lecturer should present the material with more examples . OK
The problem-solving sessions should be with more discussions. OK
This course is well organised (supply of information, scheduling) (from -2 to 2 ) 0.9 expected
I will go on with the course and come to the examination. Majority answered undoubtedly or most likely.
What mark do you expect to get at the exam? 7 well, not very ambitious 🙂
Do you use the book? Much worse than expected! A quarter use it regulary, a quater – sometimes. No, that is not good.
The overal mark:
lectures 7.5
problem-solving sessions 6.9
the whole course 7.5
we wouldn’t mind to score more, yet it’s not a big problem
I will make another survey shortly after the semester break.
Sixth lecture Quantum Transport
the last one before the semester break. We did Coulomb blockade and I believe we did it good). I’m pretty slow this year, there’s a delay of one lecture, so the the deadline for home work about Coulomb blockade was actually earlier than the lecture(. I feel guilty, yet could not do anything about except the better semester planning six month ago. I have to really hurry up after the semester break.
Evaluation from VvTP
The VvTP, our student society, has a contact group that evaluates the courses given and provides a feedback for the teachers. This is what I got on Wednesday:
Advanced Quantum Mechanics:
Nazarov is very enthusiastic about the content of the course. He is following the book very closely: that’s a very good thing. The book is very good. Students like this, there is a clear structure in the course. A bit more examples would be nice though, to have some practical view. The problems are very compatible with the book and lectures. Students say that it takes a long time making them, because you really have to understand the content.
The presentations which the students have to prepare are quite good. It would be appreciated if the focus of the course would be a bit more practical in the lectures. Students like the way Nazarov did a survey himself. They appreciated the fact that he is clearly trying to improve his way of teaching. A possible improvement would be to give a quick summary of the content covered at the end of each lecture.’
Actually, it’s pretty encouraging evaluation, thank you). I promise to give the summary every lecture. But, well, my memory is not as good as it used to be X years ago. Perhaps I need to ask assistance from the audience? 🙂
Quantum Transport:
‘12 students attending in total. The homework is pretty nice. The course is about applications, but the lectures are not that much into it. Maybe there could be some more exercises to practice and get a better insight.‘
A bit surprised that the course is about the applications: but well, it’s rather a compliment 🙂 I hated home work, especially extensive one, when I was a student. Good, perhaps next year I can make more of it.
Seventh lecture Advanced Quantum Mechanics
Can’t believe I got so far before the semester break: we have sucsesfully quantized the classical fields! The stuff is still rather technical and boring, yet in the second half we’ve discussed fancy effects of zero-point energy, vacuum fluctuations and uncertainties. It was on time: wish I am so good next time, I expect more difficulties)).