mathematical theory of open quantum systems, quantum master equations, quantum key distribution, quantum networks, mathematical foundations of statistical mechanics, quantum information
UDC:
517.958, 530.145
Subject:
1. Mathematical foundations of theory of open quantum systems: derivation of quantum master equations, asymptotic properties of solutions of the Gorini–Kosssakowski–Sudarshan–Lindblad (GKSL) equation, applications to quantum biology and quantum thermodynamics. The general focus is on mathematically rigorous results on challenging problems in theoretical physics.
2. Quantum key distribution: security proofs of quantum key distribution with imperfect devices (i.e., for the practical case), quantum networks.
The most important results:
In the field of mathematical foundations of statistical mechanics and irreversibility:
The existence of microscopic (singular) solutions of the nonlinear integro-differential Boltzmann–Enskog kinetic equation has been proved (with M. Pulvirenti and S. Simonella). These solutions were discovered by N. N. Bogolyubov on the physical level of rigour and are important for understanding the correspondence between the reversible microscopic dynamics and irreversible macroscopic dynamics.
In the field of quantum key distribution:
Security of the most widely used BB84 protocol with detection-efficiency mismatch has been proved. This case is practical and significantly more mathematically challenging. The main mathematical difficulty was to obtain estimates for quantum entropic quantities in an infinite-dimensional space. This result is included in the list of the most important achievements of the Russian scientists in the field of mathematics in 2020.
In the field of mathematical foundations of the theory of open quantum systems:
Based on the perturbation theory, the local approach to quantum master equations has been rigorously justified (with I. V. Volovich). This result is important because the local approach is simple and widely used in theoretical physics, but had not rigorous justification.
The unified quantum master equation for the weak system-bath coupling regime beyond the secular approximation has been rigorously derived. This was a known fundamental problem in this field.
Biography
Graduated from Moscow Engineering Physics Institute with honours in 2006 (Faculty of Cybernetics, Department of System Analysis). Post-graduate education in the Steklov Mathematical Institute of Russian Academy of Sciences (Department of Mathematical Physics, supervisor Prof. Igor Volovich). Ph.D. (2009), habilitation (2020). Now I am a leading researcher in the Steklov Mathematical Institute of Russian Academy of Sciences (Department of Mathematical Physics), professor of Moscow Institute of Physics and Technology and of National University of Science and Technology MISIS. In 2023–2025, I work in the project "Quantum networks: Correlations and Communication" in the Heinrich Heine University Düsseldorf (working group of Prof. Dagmar Bruß).
Laureate of grants of the presidential program for young scientists in Russia. Scientific results on quantum key distribution have been included in the list of the most important achievements of the Russian scientists in the field of mathematics in 2020. Award of the Government of Moscow for Young Scientists in Mathematics, Mechanics, and Computer Science in 2022 for the proof of security of quantum cryptography with practical devices.
Teaching: courses on quantum computations, quantum key distribution, information theory and mathematical modelling. I have supervised four masters theses.
Main publications:
A. S. Trushechkin, M. Merkli, J. D. Cresser, J. Anders, “Open quantum system dynamics and the mean force Gibbs state”, AVS Quantum Sci., 4 (2022), 012301 , 23 pp., arXiv: 2110.01671;
A. Trushechkin, “Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case”, Quantum, 6 (2022), 771 , 29 pp., arXiv: 2004.07809;
A. Trushechkin, “Unified Gorini–Kossakowski–Lindblad–Sudarshan quantum master equation beyond the secular approximation”, Phys. Rev. A, 103:6 (2021), 062226 , 12 pp., arXiv: 2103.12042
M. Pulvirenti, S. Simonella, A. Trushechkin, “Microscopic solutions of the Boltzmann-Enskog equation in the series representation”, Kinet. Relat. Models, 11:4 (2018), 911–931 , arXiv: 1802.05926
A. S. Trushechkin, I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks”, EPL, 113:3 (2016), 30005 , 6 pp., arXiv: 1509.05754
A. S. Trushechkin, “Kinetic State and Emergence of Markovian Dynamics in Exactly Solvable Models of Open Quantum Systems”, Proc. Steklov Inst. Math., 324 (2024), 187–212
2.
A. Trushechkin, “Long-term behaviour in an exactly solvable model of pure decoherence and the problem of Markovian embedding”, Mathematics, 12:1 (2024), 1 , 18 pp., arXiv: 2311.16010;
A. S. Trushechkin, M. Merkli, J. D. Cresser, J. Anders, “Open quantum system dynamics and the mean force Gibbs state”, AVS Quantum Sci., 4 (2022), 012301 , 23 pp., arXiv: 2110.01671;
A. Trushechkin, “Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case”, Quantum, 6 (2022), 771 , 29 pp., arXiv: 2004.07809;
D. A. Kronberg, E. O. Kiktenko, A. S. Trushechkin, A. K. Fedorov, “Comments on the Paper “Are There Enough Decoy States to Ensure Key Secrecy in Quantum Cryptography?” by S. N. Molotkov, K. S. Kravtsov, and M. I. Ryzhkin and on the Erratum to This Paper”, J. Exp. Theor. Phys., 134:5 (2022), 533–535
7.
L. Accardi, B. Dragovich, S. V. Kozyrev, A. S. Trushechkin, “Preface”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2202002 , 1 pp. ;
8.
G. M. Timofeev, A. S. Trushechkin, “Hamiltonian of mean force in the weak-coupling and high-temperature approximations and re ned quantum master equations”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2243021 , 24 pp., arXiv: 2204.00599;
A. Trushechkin, “Quantum master equations and steady states for the ultrastrong-coupling limit and the strong-decoherence limit”, Phys. Rev. A, 106:4 (2022), 042209 , 20 pp., arXiv: 2109.01888;
A. S. Trushechkin, E. O. Kiktenko, D. A. Kronberg, A. K. Fedorov, “Security of the decoy state method for quantum key distribution”, Phys. Usp., 64:1 (2021), 88–102
11.
A. S. Trushechkin, “Derivation of the Redfield Quantum Master Equation and Corrections to It by the Bogoliubov Method”, Proc. Steklov Inst. Math., 313 (2021), 246–257 , arXiv: 2108.03128
12.
A. Trushechkin, “Unified Gorini–Kossakowski–Lindblad–Sudarshan quantum master equation beyond the secular approximation”, Phys. Rev. A, 103:6 (2021), 062226 , 12 pp., arXiv: 2103.12042
A. S. Trushechkin, “On the operational meaning and practical aspects of using the security parameter in quantum key distribution”, Quantum Electron., 50:5 (2020), 426–439
14.
A. S. Trushechkin, “On the proof of existence of microscopic solutions to the Boltzmann–Enskog kinetic equation”, Phys. Part. Nucl., 51:4 (2020), 791–796
2019
15.
M. K. Bochkov, A. S. Trushechkin, “Security of quantum key distribution with detection-efficiency mismatch in the single-photon case: Tight bounds”, Phys. Rev. A, 99:3 (2019), 32308 , 15 pp., arXiv: 1810.04663
A. S. Trushechkin, “Dynamics of Reservoir Observables within the Zwanzig Projection-Operator Method in the Theory of Open Quantum Systems”, Proc. Steklov Inst. Math., 306 (2019), 257–270
17.
V. E. Rodimin, E. O. Kiktenko, V. V. Usova, M. Y. Ponomarev, T. V. Kazieva, A. V. Miller, A. S. Sokolov, A. A. Kanapin, A. V. Losev, A. S. Trushechkin, M. N. Anufriev, N. O. Pozhar, V. L. Kurochkin, Y. V. Kurochkin, A. K. Fedorov, “Modular quantum key distribution setup for research and development applications”, J. Russian Laser Research, 40:3 (2019), 221–229 , arXiv: 1612.04168
A. Trushechkin, “Calculation of coherences in Förster and modified Redfield theories of excitation energy transfer”, J. Chem. Phys., 151:7 (2019), 074101 , arXiv: 1902.00554
A. S. Trushechkin, “Higher-order corrections to the Redfield equation with respect to the system-bath coupling based on the hierarchical equations of motion”, Lobachevskii J. Math., 40:10 (2019), 1606–1618 , arXiv: 1905.05068
A. S. Trushechkin, “Decoherence and coherence preservation in the solutions of the GKSL equation in the theory of open quantum systems”, Math. Notes, 106:6 (2019), 986–993
2018
21.
A. S. Trushechkin, P. A. Tregubov, E. O. Kiktenko, Yu. V. Kurochkin, A. K. Fedorov, “Quantum-key-distribution protocol with pseudorandom bases”, Phys. Rev. A, 97:1 (2018), 12311 , 15 pp., arXiv: 1706.00611
A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271
23.
M. Pulvirenti, S. Simonella, A. Trushechkin, “Microscopic solutions of the Boltzmann-Enskog equation in the series representation”, Kinet. Relat. Models, 11:4 (2018), 911–931 , arXiv: 1802.05926
E. O. Kiktenko, N. O. Pozhar, M. N. Anufriev, A. S. Trushechkin, R. R. Yunusov, Yu. V. Kurochkin, A. I. Lvovsky, A. K. Fedorov, “Quantum-secured blockchain”, Quantum Sci. Technol., 3:3 (2018), 35004 , 8 pp., arXiv: 1705.09258
P. A. Tregubov, A. S. Trushechkin, “Quantum Stream Ciphers: Impossibility of Unconditionally Strong Algorithms”, J. Math. Sci. (N. Y.), 252:1 (2021), 90–103
2018
26.
A. K. Fedorov, E. O. Kiktenko, A. S. Trushechkin, “Symmetric blind information reconciliation and hash-function-based verification for quantum key distribution”, Lobachevskii J. Math., 39:7 (2018), 992–996 , arXiv: 1705.06664
A. S. Trushechkin, “On general production of entropy in open Markov quantum systems”, Journal of Mathematical Sciences, 241:2 (2019), 191–209
28.
E. A. Markevich, A. S. Trushechkin, “Quantum branch-and-bound algorithm and its application to the travelling salesman problem”, Journal of Mathematical Sciences, 241:2 (2019), 168–184
2017
29.
A. S. Trushechkin, E. O. Kiktenko, A. K. Fedorov, “Practical issues in decoy-state quantum key distribution based on the central limit theorem”, Phys. Rev. A, 96:2 (2017), 022316 , 7 pp., arXiv: 1702.08531
E. O. Kiktenko, N. O. Pozhar, A. V. Duplinskiy, A. A. Kanapin, A. S. Sokolov, S. S. Vorobey, A. V. Miller, V. E. Ustimchik, M. N. Anufriev, A. S. Trushechkin, R. R. Yunusov, V. L. Kurochkin, Yu. V. Kurochkin, A. K. Fedorov, “Demonstration of a quantum key distribution network in urban fibre-optic communication lines”, Quantum Electron., 47:9 (2017), 798–802
31.
E. O. Kiktenko, A. S. Trushechkin, S. S. W. Lim, Y. V. Kurochkin, A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution”, Physical Review Applied, 8 (2017), 44017 , 12 pp., arXiv: 1612.03673
A. Trushechkin, “Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions”, J. Math. Phys., 58:6 (2017), 62102 , 16 pp., arXiv: 1607.07572
A. S. Trushechkin, I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks”, EPL, 113:3 (2016), 30005 , 6 pp., arXiv: 1509.05754
E. Kiktenko, A. Trushechkin, Yu. Kurochkin, A. Fedorov, “Post-processing procedure for industrial quantum key distribution systems”, JPCS, 741:1 (2016), 12081 , 6 pp.
A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274
37.
A. S. Trushechkin, “Microscopic and soliton-like solutions of the Boltzmann–Enskog and generalized Enskog equations for elastic and inelastic hard spheres”, Kinetic and Related Models, 7:4 (2014), 755–778 , arXiv: 1307.4741
A. S. Trushechkin, “On a rigorous definition of microscopic solutions of the Boltzmann–Enskog equation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(30) (2013), 270–278
39.
A. S. Trushechkin, “Functional mechanics and kinetic equations”, Quantum Bio-Informatics V (Tokyo University of Science, Japan, 5–12 March 2011), QP-PQ: Quantum Probability and White Noise analysis, 30, World Scientific, Singapore, 2013, 339–350
I. V. Volovich, A. S. Trushechkin, “Asymptotic properties of quantum dynamics in bounded domains at various time scales”, Izv. Math., 76:1 (2012), 39–78 , arXiv: 1304.2332
41.
A. S. Trushechkin, “Derivation of the particle dynamics from kinetic equations”, p-Adic Numbers, Ultrametic Analysis and Applications, 4:2 (2012), 130–142 , arXiv: 1201.3607
A. S. Trushechkin, “Boltzmann equation and $H$-theorem in the functional formulation of classical mechanics”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 158–164
43.
A. S. Trushechkin, “Derivation of the Boltzmann equation and entropy production in functional mechanics”, p-Adic Numbers, Ultrametric Analysis, and Applications, 3:3 (2011), 225–235 , arXiv: 1108.3847
2010
44.
A. S. Trushechkin, “Irreversibility and the role of an instrument in the functional formulation of classical mechanics”, Theoret. and Math. Phys., 164:3 (2010), 1198–1201
2009
45.
I. V. Volovich, A. S. Trushechkin, “Squeezed Quantum States on an Interval and Uncertainty Relations for Nanoscale Systems”, Proc. Steklov Inst. Math., 265 (2009), 276–306 , arXiv: 1304.6277
46.
A. S. Trushechkin, I. V. Volovich, “Functional classical mechanics and rational numbers”, P-Adic Numbers, Ultrametric Analysis and Applications, 1:4 (2009), 365–371 , arXiv: 0910.1502
A. S. Trushechkin, “Quantum mechanics on compact manifolds and nanosystems: uncertainty relations, coherent states and semiclassical limit”, Sveske fizichkikh nauka Series A: Conferences, 2009, no. A1, 457–462
2008
48.
A. S. Trushechkin, I. V. Volovich, “On standards and specifications in quantum cryptography”, International Journal of Quantum Information, 6:2 (2008), 347–367 , arXiv: quant-ph/0508035
A. S. Trushechkin, “Kvantovye kogerentnye sostoyaniya i sootnosheniya neopredelënnostei dlya nanoskopicheskikh sistem”, Vestnik Samarskogo gosudarstvennogo universiteta, 2008, no. 8/1(67), 254–273
2006
50.
A. S. Trushechkin, I. V. Volovich, “On quantum cryptography and number theory”, p-adic mathematical physics. 2nd international conference (Belgrade, Serbia and Montenegro, 15–21 September 2005), AIP Conference Proceedings, 826, American Institute of Physics (AIP), Melville, NY, 2006, 345–354
2005
51.
I. V. Volovich, A. S. Trushechkin, “On a model of the quantum key distribution”, Dokl. Math., 72:2 (2005), 795–797 , arXiv: quant-ph/0504156
Presentations in Math-Net.Ru
1.
Seminar 11. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" November 20, 2024 18:00
2.
Seminar 10. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" November 13, 2024 18:00
3.
Seminar 9. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" November 6, 2024 18:00
4.
Квантовые коды коррекции ошибок A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" October 30, 2024 18:00
5.
Квантовая верификация местоположения A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" September 18, 2024 18:00
Rate of the pure decoherence A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" September 28, 2022 18:45
40.
Pure decoherence: full and partial A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" September 21, 2022 18:45
41.
Mathematical formalism of quantum mechanics A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" September 14, 2022 18:45
"Information paradox" for open quantum systems A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" December 1, 2021 18:45
Seminar 15. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" May 26, 2021 18:00
81.
Seminar 14. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" May 19, 2021 18:00
Seminar 13. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" May 12, 2021 18:00
Seminar 12. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" April 28, 2021 18:00
Seminar 11. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" April 21, 2021 18:00
Seminar 10. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" April 14, 2021 18:00
Seminar 9. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" April 7, 2021 18:00
Seminar 8. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" March 31, 2021 18:00
Seminar 7. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" March 24, 2021 18:00
Seminar 6. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" March 17, 2021 18:00
Seminar 5. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" March 10, 2021 18:00
101.
Seminar 4. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" March 3, 2021 18:00
Seminar 3. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" February 24, 2021 18:00
104.
Seminar 2. Quantum mathematical physics I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" February 17, 2021 18:00
Seminar 1. Quantum mathematical physics V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin, I. V. Volovich Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" February 10, 2021 18:00
Семинар 11. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" July 8, 2020 18:00
Семинар 8. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" April 22, 2020
132.
Семинар 7. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" April 15, 2020
133.
Семинар 6. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" April 8, 2020
134.
Семинар 5. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" March 11, 2020 18:00
135.
Семинар 4. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" March 4, 2020 18:00
136.
Семинар 3. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" February 26, 2020 18:00
137.
Семинар 2. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" February 19, 2020 18:00
138.
Семинар 1. Квантовая математическая физика I. V. Volovich, V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin Seminar by I. V. Volovich, V. V. Kozlov, S. V. Kozyrev and A. S. Trushechkin "Quantum Mathematical Physic" February 12, 2020 18:00
Perturbation theory for open quantum systems A. S. Trushechkin Conference «Contemporary Mathematics and its applications» dedicated to the results of research supported by the Russian Science Foundation grant 14-50-00005 November 19, 2018 16:30
Perturbation theory for open quantum systems I. V. Volovich, A. S. Trushechkin Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2017 November 29, 2017 14:15
2024
Contact us: