OPEN QUANTUM SYSTEMS

Entry requirements:

•  Master’s degree / equivalent in a related field
•  B2 level of English
•  Good track record of publications related to the topic of the intended research
•  Strong research proposal 1,500 - 3,500 words

Research supervisor:
Alexander Teretenkov
PhD

Supervisor’s research interests:
I study a wide range of problems in the theory of open quantum systems. But there are several topics which I am especially interested in:

•  Exactly solvable Gorini-Kossakowski-Sudarshan-Lindblad equations, especially the generalizations of the equations with generators which are quadratic in creation and annihilation operators.
•  Exactly solvable models of non-Markovian quantum evolutions, especially by pseudo mode method generalizations.
•  Perturbative derivation of master equations both by projective and stochastic limit methods, especially in the case when it could be done for all the orders of perturbation theory.

Research highlights:

• The theory of open quantum systems is a theoretical basis of modern spectroscopy, quantum optics, quantum measurement theory, quantum thermodynamics and has a wide range of physical applications. It belongs to the intersection of cutting edges of physics and mathematics. There is a very wide and active community providing a great number of conferences, seminars and grant possibilities.
• Supervisor’s specific requirements:
•  Basic knowledge of theory of open quantum systems (circa Chapters 2-3 in H.P.Breuer and F.P. Pettruchione’s book “Theory of open quantum systems”).
•  Basic but solid skills in usual mathematical subjects: linear algebra, ordinary and partial differential equations, probability theory, stochastic processes, and in usual physical subjects: electrodynamics, quantum mechanics, statistical physics.

Main publications:

•  A. E. Teretenkov, “Irreversible quantum evolution with quadratic generator: Review”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 22:4 (2019), 19300019.
•  A. E. Teretenkov, “Dynamics of Moments for Quadratic GKSL Generators”, Math. Notes, 106:1 (2019), 151–155.
•  A. E. Teretenkov, “Non-Markovian evolution of multilevel system interacting with several reservoirs. Exact and approximate”, Lobachevskii J. Math., 40:10 (2019), 1587–1605.
•  S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, I. V. Volovich, “Flows in nonequilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021.
•  A. M. Chebotarev, A. E. Teretenkov, “Singular value decomposition for the Takagi factorization of symmetric matrices”, Appl. Math. Comput., 234 (2014), 380–384. Web cite: http://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=76513