Foundations of the theory of open quantum systems September 15, 2020–May 11, 2021, MIPT  MI RAS, Moscow
The course discusses the theory of open quantum systems and can serve as
a supplement to the standard courses of quantum mechanics, usually
focused on the description of reversible dynamics of an isolated system.
But it is only assumed that students are familiar only with linear
algebra and mathematical analysis, and the necessary elements of quantum
mechanics in the course will be presented. The theory of open quantum
systems is the theoretical basis of modern spectroscopy, quantum optics,
quantum measurement theory, quantum thermodynamics and has wide range of
physical applications. The presented theory is also inseparable from
quantum theory of information. From the mathematical point of view, the
course is close to the theory of Markov processes with a finite number
of states, but considers its noncommutative analog. The course will
describe the properties and methods of solution and derivation of the
GoriniKossakowskiSudarshanLindblad equation which is the basic
approach for describing the dynamics of open quantum systems. In
addition, the basic physical examples of finite open quantum systems
will be considered and their properties described. During the course,
students will be asked a number of tasks that will develop the skill of
applying the knowledge gained in the course to specific physical problems.
Spring Semester Schedule of 2020/2021:
Time: Tuesday 10:00 – 11:25
First lecture: 9 February
Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 0751520191614).
RSS: Forthcoming seminars
Seminar organizer
Teretenkov Aleksandr Evgenevich
Institutions
Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center 

Foundations of the theory of open quantum systems, Moscow, September 15, 2020–May 11, 2021 


May 11, 2021 (Tue) 

1. 
Lecture 12. Mean field master equations A. E. Teretenkov May 11, 2021 10:00, Moscow, MIPT  MI RAS






May 4, 2021 (Tue) 

2. 
Lecture 11. Quantum Boltzmann equation A. E. Teretenkov May 4, 2021 10:00, Moscow, MIPT  MI RAS






April 27, 2021 (Tue) 

3. 
Lecture 10. Example of timeconvolutionless master equation A. E. Teretenkov April 27, 2021 10:00, Moscow, MIPT  MI RAS






April 20, 2021 (Tue) 

4. 
Lecture 9. Timeconvolutionless master equation A. E. Teretenkov April 20, 2021 10:00, Moscow, MIPT  MI RAS






April 13, 2021 (Tue) 

5. 
Lecture 8. Caldeira–Leggett model. Nakajima–Zwanzig projection method A. E. Teretenkov April 13, 2021 10:00, Moscow, MIPT  MI RAS






April 6, 2021 (Tue) 

6. 
Lecture 7. Exactly solvable model of multilevel system with several reservoirs A. E. Teretenkov April 6, 2021 10:00, Moscow, MIPT  MI RAS






March 23, 2021 (Tue) 

7. 
Lecture 6. Pseudomode approach A. E. Teretenkov March 23, 2021 10:00, Moscow, MIPT  MI RAS






March 16, 2021 (Tue) 

8. 
Lecture 5. Quadratic dynamics avareged over Poisson process. Spinboson in rotating wave approximation A. E. Teretenkov March 16, 2021 10:00, Moscow, MIPT  MI RAS






March 9, 2021 (Tue) 

9. 
Lecture 4. Fermionic quadratic GKSL generators A. E. Teretenkov March 9, 2021 10:00, Moscow, MIPT  MI RAS






March 2, 2021 (Tue) 

10. 
Lecture 3. Gaussian solutions. Different forms of equations for moments dynamics A. E. Teretenkov March 2, 2021 10:00, Moscow, MIPT  MI RAS






February 16, 2021 (Tue) 

11. 
Lecture 2. First and second moments dynamics for quadratic generator A. E. Teretenkov February 16, 2021 10:00, Moscow, MIPT  MI RAS






February 9, 2021 (Tue) 

12. 
Lecture 1. Linear and quadratic forms in bosonic creation and annihilation operators A. E. Teretenkov February 9, 2021 10:00, Moscow, MIPT  MI RAS






December 15, 2020 (Tue) 

13. 
Lecture 13. Other limits leading to GKSL equation A. E. Teretenkov December 15, 2020 10:00, Moscow, MIPT  MI RAS






December 8, 2020 (Tue) 

14. 
Lecture 12. Quantum detailed balance A. E. Teretenkov December 8, 2020 10:00, Moscow, MIPT  MI RAS






December 1, 2020 (Tue) 

15. 
Lecture 11. Weak coupling limit A. E. Teretenkov December 1, 2020 10:00, Moscow, MIPT  MI RAS






November 24, 2020 (Tue) 

16. 
Lecture 10. GKSL equations arising as averaging over classical stochastic processes A. E. Teretenkov November 24, 2020 10:00, Moscow, MIPT  MI RAS






November 17, 2020 (Tue) 

17. 
Lecture 9. Monotonicity of quantum relative entropy A. E. Teretenkov November 17, 2020 10:00, Moscow, MIPT  MI RAS






November 10, 2020 (Tue) 

18. 
Lecture 8. The generator of oneparametric completely positive trace preserving semigroup A. E. Teretenkov November 10, 2020 10:00, Moscow, MIPT  MI RAS






October 27, 2020 (Tue) 

19. 
Lecture 7. Completely positive maps. ChoiJamiolkowski correspondence. Kraus and Stinespring representations A. E. Teretenkov October 27, 2020 10:00, Moscow, MIPT  MI RAS






October 20, 2020 (Tue) 

20. 
Lecture 6. GKSL and constraints on relaxation times relations. Mollow spectrum. Generalized Bloch equations A. E. Teretenkov October 20, 2020 10:00, Moscow, MIPT  MI RAS






October 13, 2020 (Tue) 

21. 
Lecture 5. 2level system under external field. Dissipation in equilibrium reservoir and pure dephasing A. E. Teretenkov October 13, 2020 10:00, Moscow, MIPT  MI RAS






October 6, 2020 (Tue) 

22. 
Lecture 4. Multitime correlation function. Lamb equation and optical potential. Unitary dynamics of qbit A. E. Teretenkov October 6, 2020 10:00, Moscow, MIPT  MI RAS






September 29, 2020 (Tue) 

23. 
Lecture 3. Pauli equation. Classical timecontinuous Markov chains and monotonicity of relative entropy A. E. Teretenkov September 29, 2020 10:00, Moscow, MIPT  MI RAS






September 22, 2020 (Tue) 

24. 
Lecture 2. GKSL equation. Shroedinger and Heisenberg representations for irreversible dynamics. Description of decoherence and transfer. Lorentz spectrum A. E. Teretenkov September 22, 2020 10:00, Moscow, MIPT  MI RAS






September 15, 2020 (Tue) 

25. 
Lecture 1. States and observables in quantum mechanics. Selective and nonselective measurements. Unitary dynamics A. E. Teretenkov September 15, 2020 10:00, Moscow, MIPT  MI RAS





