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Trushechkin Anton Sergeevich

Total publications: 27
Scientific articles: 27
in MathSciNet: 9
in zbMATH: 7
in Web of Science: 14
in Scopus: 13
Cited articles: 12
Citations in Math-Net.Ru: 16
Citations in MathSciNet: 6
Citations in Web of Science: 23
Citations in Scopus: 22
Presentations: 51

Number of views:
This page:4657
Abstract pages:2496
Full texts:334
References:312
Trushechkin Anton Sergeevich
Candidate of physico-mathematical sciences (2009)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 5.07.1983
E-mail:
Keywords: mathematical physics, quantum mechanics, statistical mechanics, open quantum systems, quantum thermodynamics, quantum information, quantum mechanics in bounded domains, quantum cryptography.
UDC: 517.958, 530.145

Subject:

1. Open quantum systems, quantum thermodynamics. A systematic perturbation expansion for corrections to the so called local approach master equation was proposed. Using this improvement of the local approach, an expression for the heat flux for a particular model was derived and it is shown that it is consistent with the second law of thermodynamics (in contrast to the original local approach master equation). A general definitions for the entropy production as well as its adiabatic and non-adiabatic contributions in Markovian quantum system were proposed, theorems about their positivity were proved.

2. Quantum control, manipulations with qubits. The problem of optimal acceleration of the Landau–Zener transitions (used, in particular, for manipulations with qubits) by non-selective quantum measurements was solved. The solution was based on combination of analytic asymptotic methods and numerical methods.

3. Quantum dynamics in bounded domains. In this field, coherent quantum states for a particle on a circle and in the infinite well was constructed. Theorems about their behaviour on all time scales in the special semiclassical limit were proved. They give detailed information about all stages of evolution of quantum wave packets: semiclassical motion, collapses, revivals, as well as intermediate stages. In particular, a mathematical justification of the asymptotic flattening of the spatial distribution of probability was obtained. Earlier such a flattening was known merely from the numerical calculations. Also families of squeezed quantum states on an interval are constructed, their asymptotic properties of localization were researched. Estimations for the dispersions of the position and momentum of the particle on an interval were obtained. In particular, these estimations can be applied to the nanoscale systems.

4. Kinetic equations. In this field, a rigorous justification for microscopic (singular) solutions of the nonlinear integro-differential Boltzmann–Enskog kinetic equation was given. These solutions were discovered by N.N.Bogolyubov. Exact smooth soliton-like solutions of the generalized Enskog equation were found.

5. Quantum cryptography. In this field, a general model of quantum key distrubution based on the concepts of Turing machine and quantum chanel, was constructed. A special model analogous to the known model in classical cryptography was constructed, a theorem about its security was proved. The problem of specification of quantum key distribution systems was considered. A fundamental characteristics, i.e., average time of key generation, and other numerical and functional characteristics of such systems' operation were introduced. A new procedure for statistical processing of quantum decoy state in quantum key distribution protocol was proposed.

Biography

Graduated from Moscow Engineering Physics Institute (MEPhI) with honour in 2006 (faculty of cybernetics, depertment of system analysis). Post-graduate education in the Steklov Mathematical Institute of the Russian Academy of Sciences (Department of Mathematical Physics, supervisor: Prof. I.V. Volovich). Ph.D. (2009). Now I am a senior scientific researcher in the Steklov Mathematical Institute of the Russian Academy of Sciences (Department of Mathematical Physics) and an assistent professor of MEPHI (faculty of cybernetics).

   
Main publications:
  1. 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  mathnet  crossref  isi  elib  scopus
  2. A. Pechen, A. Trushechkin, “Measurement-assisted Landau-Zener transitions”, Phys. Rev. A, 91:5 (2015), 052316 , 15 pp., arXiv: 1506.08323  mathnet  crossref  isi  elib  scopus
  3. A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274  mathnet  crossref  crossref  isi  elib  elib  scopus
  4. 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  mathnet  crossref  mathscinet  zmath  isi  elib  scopus

http://www.mathnet.ru/eng/person31114
http://scholar.google.com/citations?user=GUuqZH4AAAAJ&hl=en
http://zbmath.org/authors/?q=ai:trushechkin.anton-s
http://www.ams.org/mathscinet/search/author.html?return=viewitems&mrauthid=782023
http://elibrary.ru/author_items.asp?authorid=155153
http://orcid.org/0000-0002-9541-0752
http://www.researcherid.com/rid/K-1744-2013
http://www.scopus.com/authid/detail.url?authorId=15133086100
https://www.researchgate.net/profile/Anton_Trushechkin
http://arxiv.org/a/trushechkin_a_1

Full list of publications:
| by years | by types | by times cited | scientific publications | common list |



   2017
1. A. S. Trushechkin, “On general production of entropy in open Markov quantum systems”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 82–98  mathnet
2. E. A. Markevich, A. S. Trushechkin, “Quantum branch-and-bound algorithm and its application to the travelling salesman problem”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 60–75  mathnet
3. Anton 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  mathnet  crossref  mathscinet  isi  scopus
4. A. S. Trushechkin, P. A. Tregubov, E. O. Kiktenko, Y. V. Kurochkin, A. K. Fedorov, Quantum key distribution protocol with pseudorandom bases, 2017 , 16 pp., arXiv: 1706.00611
5. E. O. Kiktenko, N. O. Pozhar, M. N. Anufriev, A. S. Trushechkin, R. R. Yunusov, Y. V. Kurochkin, A. I. Lvovsky, A. K. Fedorov, Quantum-secured blockchain, 2017 , 8 pp., arXiv: 1705.09258
6. 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, Y. V. Kurochkin, A. K. Fedorov, Demonstration of a quantum key distribution network across urban fiber channels, 2017 , 5 pp., arXiv: 1705.07154
7. E. O. Kiktenko, A. S. Trushechkin, A. K. Fedorov, Symmetric blind information reconciliation and hash-function-based verification for quantum key distribution, 2017 , 4 pp., arXiv: 1705.06664
8. 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) , 7 pp., arXiv: 1702.08531  mathnet  crossref  isi

   2016
9. 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  mathnet (cited: 5)  crossref  isi (cited: 5)  elib  scopus (cited: 5)
10. Evgeny Kiktenko, Anton Trushechkin, Yury Kurochkin, Aleksey Fedorov, “Post-processing procedure for industrial quantum key distribution systems”, JPCS, 741:1 (2016), 12081 , 6 pp.  mathnet  crossref  isi (cited: 3)  elib  scopus (cited: 3)

   2015
11. A. Pechen, A. Trushechkin, “Measurement-assisted Landau-Zener transitions”, Phys. Rev. A, 91:5 (2015), 052316 , 15 pp., arXiv: 1506.08323  mathnet  crossref  isi (cited: 4)  elib (cited: 2)  scopus (cited: 4)

   2014
12. A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274  mathnet  crossref  crossref  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
13. 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  mathnet  crossref  mathscinet  zmath  isi  elib  scopus

   2013
14. 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  mathnet  crossref  rsci
15. 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  crossref  isi (cited: 1)

   2012
16. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib  elib  scopus (cited: 1)
17. 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  mathnet  crossref  mathscinet (cited: 1)  zmath  adsnasa  scopus (cited: 1)

   2011
18. 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  mathnet  crossref  rsci  elib
19. 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  crossref  mathscinet  adsnasa

   2010
20. 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  mathnet  crossref  crossref  adsnasa  isi (cited: 4)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 3)

   2009
21. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 3)
22. 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  crossref  mathscinet (cited: 3)  adsnasa
23. 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
24. 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  crossref  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  scopus (cited: 1)
25. A. S. Trushechkin, “Kvantovye kogerentnye sostoyaniya i sootnosheniya neopredelënnostei dlya nanoskopicheskikh sistem”, Vestnik Samarskogo gosudarstvennogo universiteta, 2008, no. 8/1(67), 254–273

   2006
26. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus

   2005
27. 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  mathnet  mathscinet  zmath  adsnasa  isi  elib  elib  scopus

Presentations in Math-Net.Ru
1. О производстве энтропии в марковских открытых квантовых системах
International youth workshop «Mathematical methods in the problems of quantum technologies»
October 9, 2017 15:50
2. Квазиклассическая эволюция квантовых волновых пакетов на торе за пределами времени Эренфеста
Differential operators on singular spaces, algebraically integrable systems and quantization
October 2, 2017 18:40
3. Квантовая криптография. Лекция 27

May 26, 2017 18:00   
4. Квантовая криптография. Лекция 26

May 19, 2017 18:00   
5. Квантовая криптография. Лекция 25

May 12, 2017 18:00   
6. Как компьютер научили играть в го?
Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences
May 11, 2017 16:00   
7. Квантовая криптография. Лекция 24

May 5, 2017 18:00   
8. Квантовая криптография. Лекция 23

April 28, 2017 18:00   
9. Квантовая криптография. Лекция 22

April 21, 2017 18:00   
10. Квантовая криптография. Лекция 21

April 14, 2017 18:00   
11. Квантовая криптография. Лекция 20

April 7, 2017 18:00   
12. Квантовая криптография. Лекция 19

March 31, 2017 18:00   
13. Квантовая криптография. Лекция 18

March 24, 2017 18:00   
14. Квантовая криптография. Лекция 17

March 17, 2017 18:00   
15. Квантовая криптография. Лекция 16

March 10, 2017 18:00   
16. Квантовая криптография. Лекция 15

March 3, 2017 18:00   
17. Квантовая криптография. Лекция 14

February 17, 2017 18:00   
18. Квантовая криптография. Лекция 13

December 16, 2016 18:00   
19. Квантовая криптография. Лекция 12

December 9, 2016 18:00   
20. Квантовая криптография. Лекция 11

December 2, 2016 18:00   
21. Квантовая криптография. Лекция 10

November 25, 2016 18:00   
22. Квантовая криптография. Лекция 9

November 18, 2016 18:00   
23. Квантовая криптография. Лекция 8

November 11, 2016 18:00   
24. Об общем определении производства энтропии в марковских открытых квантовых системах
Seminar on Quantum Probability, Statistics, Information
November 7, 2016 16:30
25. Квантовая криптография. Лекция 7

October 28, 2016 18:00   
26. Квантовая криптография. Лекция 6

October 21, 2016 18:00   
27. Квантовая криптография. Лекция 5

October 14, 2016 18:00   
28. Квантовая криптография. Лекция 4

October 7, 2016 18:00   
29. On the definition of entropy production in Markovian open quantum systems
New Trends in Mathematical and Theoretical Physics
October 6, 2016 12:00   
30. Квантовая криптография. Лекция 3

September 30, 2016 18:00   
31. Квантовая криптография. Лекция 2

September 23, 2016 18:00   
32. Квантовая криптография. Лекция 1

September 16, 2016 18:00   
33. Perturbative treatment of inter-site couplings in the local description of open quantum networks
The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
May 11, 2016 17:50   
34. Квантовое оптимальное управление посредством неселективных измерений в модели Ландау–Зинера (продолжение)
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
December 24, 2015 11:00
35. Квантовое оптимальное управление посредством неселективных измерений в модели Ландау–Зинера
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
December 17, 2015 11:00
36. Динамика в открытых квантовых сетях: локальное приближение и поправки к нему
Mathematical problems of quantum theory of nanosystems and photosynthesis
September 17, 2015 12:30
37. Optimal control of a nonadiabatic quantum transition in the Landau-Zener model
International Conference on Mathematical Control Theory and Mechanics
July 6, 2015 10:40
38. Квантовое оптимальное управление посредством неселективных измерений в модели Ландау–Зинера
Seminar on Quantum Probability, Statistics, Information
December 29, 2014 16:30
39. Optimal control in the Landau–Zener model by non-selective measurements
Quantum physics and quantum information
December 16, 2014 11:00
40. Quantum Poincare model with a random geometric parameter
Random geometry and physics
September 9, 2014 16:40   
41. Optimal Quantum Control of the Landau–Zener System by Measurements
International youth conference "Geometry & Control"
April 15, 2014 17:00
42. Исследование динамики классических и квантовых волновых пакетов в ограниченных областях
Scientific session of the Steklov Mathematical Institute dedicated to the results of 2013
November 20, 2013 13:40   
43. Semiclassical description of collapses and revivals of quantum wave packets in bounded domains
International conference "QP 34 – Quantum Probability and Related Topics"
September 19, 2013 12:00   
44. Mathematics of quantum mechanics
Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences
May 23, 2013 16:15   
45. Микроскопические решения уравнения Больцмана–Энскога и обобщённые функции
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
February 7, 2013 11:00
46. О микроскопических решениях уравнения Больцмана–Энскога
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
April 5, 2012 11:00
47. On derivarion of the kinetic Boltzmann equation from the Focker–Planck equatuion
International Conference "Irreversibility Problem in Classical and Quantum Dynamical Systems"
December 8, 2011 16:50   
48. Исследование асимптотических свойств некоторых квантовомеханических моделей в ограниченных областях
Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
November 25, 2009 14:00
49. Асимптотическое исследование некоторых квантовомеханических моделей в ограниченных областях
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 22, 2009 11:00
50. Квантовые сжатые состояния на отрезке и асимптотическая минимизация соотношений неопределённостей для наноскопических систем
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
June 25, 2009 11:00

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