The following "Actual problems of applied mathematics" seminar will be held on May 21

The next seminar "Actual problems of applied mathematics" will be held on May 21 at 5 pm (UTC+7).
Seminar heads: RAS academician I. A. Taimanov, RAS corresponding member S. I. Kabanikhin, RAS corresponding member A. E. Mironov, Doctor of Sciences (Mathematics and Physics) M. A. Shishlenin.
Seminar secretary: N. M. Prokhoshin (

Mikhail Katsnelson (Radboud University Nijmegen, the Netherlands) will present his talk "Semiclassical dynamics of charge carriers in graphene".

After a general introduction to the physics of massless Dirac fermions in graphene and their exotic properties (first of all, chiral or Klein tunneling — passing through arbitrarily high and wide potential barriers), I will present a semiclassical theory of these phenomena. For the case of a one-dimensional potential barrier, a homogeneous asymptotic approximation can be developed, which gives a very accurate analytical solution for an arbitrary shape of the barrier [1, 2]. Then, I will move on to a discussion of electronic optics in graphene, namely, the Veselago electron lens theory, including consideration of wavefront catastrophes [3,4]. I will also briefly consider the general theory of the propagation of Dirac fermions in a two-dimensional potential relief [5], as a special case of the semiclassical approximation for matrix Hamiltonians. Finally, I will briefly describe the features of chiral tunneling for the case of bilayer graphene [6].

  1. T. Tudorovskiy, K. J. A. Reinders, M. I. Katsnelson, Phys. Scripta T 146, 014010 (2012).
  2. K. J. A. Reijnders, T. Tudorovskiy, M. I. Katsnelson, Ann. Phys. (NY) 333, 155 (2013).
  3. K. J. A. Reijnders, M. I. Katsnelson, Phys, Rev. B 95, 115310 (2017).
  4. K. J. A. Reijnders, M. I. Katsnelson, Phys, Rev. B 96, 045305 (2017).
  5. K. J. A. Reijnders, D. S. Minenkov, M. I. Katsnelson, S. Yu. Dobrokhotov, Ann. Phys. (NY) 397, 65 (2018).
  6. V. Kleptsyn, A. Okunev, I. Schurov, D. Zubov, M. I. Katsnelson, Phys, Rev. B 92, 165407 (2015).
In order to participate in the seminar, on May 21 after 4:45 pm (UTC+7) you should connect to the Zoom conference via the following link or manually using the Zoom conference ID 897 7646 2466 and password 549526.

Please pay attention to the following rules of attending an online lecture:
  • As a security measure, it is highly advisable to connect using your real name. 
  • You are free to join the discussion after the end of a talk. However, during a speech please keep your microphone turned off. 
  • For the convenience of the speaker, we recommend writing your questions in the chat in advance.