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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 non-commutative analog. The course will describe the properties and methods of solution and derivation of the Gorini-Kossakowski-Sudarshan-Lindblad 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. 075-15-2019-1614).

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 time-convolutionless master equation
A. E. Teretenkov
April 27, 2021 10:00, Moscow, MIPT - MI RAS
  

April 20, 2021 (Tue)
4. Lecture 9. Time-convolutionless 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 multi-level 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. Spin-boson 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 one-parametric 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. Choi-Jamiolkowski 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. 2-level 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. Multi-time correlation function. Lamb equation and optical potential. Unitary dynamics of q-bit
A. E. Teretenkov
October 6, 2020 10:00, Moscow, MIPT - MI RAS
  

September 29, 2020 (Tue)
23. Lecture 3. Pauli equation. Classical time-continuous 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 non-selective measurements. Unitary dynamics
A. E. Teretenkov
September 15, 2020 10:00, Moscow, MIPT - MI RAS
  
 
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