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Chebotarev, Alexander Mikhailovich

Total publications: 82 (80)
in MathSciNet: 71 (70)
in zbMATH: 46 (45)
in Web of Science: 37 (35)
in Scopus: 10 (10)
Cited articles: 51
Citations in Math-Net.Ru: 144
Citations in Web of Science: 182
Citations in Scopus: 19
Presentations: 3

Number of views:
This page:3504
Abstract pages:11568
Full texts:3301
References:857
Professor
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 14.12.1947
Phone: +7(495)939-11-90
Fax: +7(495)932-88-20
E-mail:
Website: http://cheb.newmail.ru
Keywords: Irrevercible quantum evolution, regularity conditions, squeezed states, solvable problems.
UDC: 517, 517.248.21, 517.432, 517.5, 517.9, 517.948, 517.95, 517.98, 519.2, 519.6, 519.634, 518
MSC: 81S, 81V, 82S25

Subject:

Probabilistic Methods in Quantum Mechanics.

   
Main publications:
  1. A. M. Chebotarev, “What is a quantum stochastic equation from the point of view of functional analysis?”, Math. Notes, 71:3–4 (2002), 408–427  crossref  mathscinet
  2. A. M. Chebotarev, F. Fagnola, “Sufficient conditions for conservativity of quantum dynamical semigroups”, J. Funct. Anal., 118:1 (1993), 131–153  crossref  mathscinet
  3. A. M. Chebotarev, F. Fagnola, “Sufficient conditions for conservativity of minimal quantum dynamical semigroups”, J. Funct. Anal., 153:2 (1998), 382–404  crossref  mathscinet
  4. A. M. Chebotarev, “On stable Pareto laws in a hierarchical model of economy”, Physica A, 373 (2007), 541–559  crossref
  5. A. M. Chebotarev, T. V. Tlyachev, “Normal Forms, Inner Products, and Maslov Indices of General Multimode Squeezing”, Mathematical Notes, 395:5 (2014), 721–737  crossref  mathscinet

http://www.mathnet.ru/eng/person17642
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/191582
http://elibrary.ru/author_items.asp?spin=2601-8700
http://orcid.org/0000-0002-4968-6694
http://www.researcherid.com/rid/D-4891-2014
http://www.scopus.com/authid/detail.url?authorId=7102-7747-04
https://www.researchgate.net/profile/Alexander_Chebotarev2

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



   2018
1. G. G. Amosov, Al. V. Bulinski, An. V. Bulinski, V. M. Buchstaber, I. A. Ibragimov, V. P. Maslov, A. Ya. Helemskii, A. M. Chebotarev, M. E. Shirokov, A. N. Shiryaev, “Alexander Semenovich Holevo (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1131–1136  mathnet  crossref  crossref  isi  elib

   2014
2. T. V. Tlyachev, A. M. Chebotarev, A. S. Chirkin, “Canonical transformations and multipartite coupled parametric processes”, PHYSICA SCRIPTA T, 160 (2014), 014041  crossref  isi (cited: 4)  scopus (cited: 4)
3. Math. Notes, 95:5 (2014), 721–737  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
4. A. M. Chebotarev, A. E. Teretenkov, “Singular value decomposition for the Takagi factorization of symmetric matrices”, Applied Mathematics and Computation (New York), 234 (2014), 380–384 , Netherlands, Netherlands  crossref  mathscinet  isi (cited: 2)  scopus (cited: 1)

   2013
5. T. V. Tlyachev, A. M. Chebotarev, A. S. Chirkin, “A new approach to quantum theory of multimode coupled parametric processes”, PHYSICA SCRIPTA T, 153 (2013), 014060  crossref  isi (cited: 3)
6. A. S. Chirkin, A. M. Chebotarev, T. V. Tlyachev, International Conference on Coherent and Nonlinear Optics (ICONO 2013). Technical digest, ICONO-03 Quantum and Atom Optics, ICONO/LAT 2013 Moskva, Rossiya, 2013
7. A. S. Chirkin, A. M. Chebotarev, T. V. Tlyachev, ASMDA 2013, Book of Abstracts, ISAST (International Society for the Advancement of Science and Technology, 2013, 43–43

   2012
8. A. M. Chebotarev, A. E. Teretenkov, “Operator-Valued ODEs and Feynman's Formula”, Math. Notes, 92:6 (2012), 837–842  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib  elib  scopus
9. A. M. Chebotarev, T. V. Tlyachev, A. A. Radionov, “Generalized Squeezed States and Multimode Factorization Formula”, Math. Notes, 92:5 (2012), 700–713  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

   2011
10. A. M. Chebotarev, T. V. Tlyachev, A. A. Radionov, “Squeezed States and Their Applications to Quantum Evolution”, Math. Notes, 89:4 (2011), 577–595  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)

   2010
11. A. M. Chebotarev, Trudy 53-i nauchnoi konferentsii MFTI, Sovremennye problemy fundamentalnykh i prikladnykh nauk, 10, Izdatelskii sektor operativnoi poligrafii 141700, Moskovskaya obl., g. Dolgoprudnyi, Institutskii per., d. 9 Moskva, Dolgoprudnyi, 2010, 6–7  mathscinet
12. A. A. Radionov, T. V. Tlyachev, A. M. Chebotarev, Vtoraya mezhdunarodnaya konferentsiya Matematicheskaya fizika i ee prilozheniya, Samarskii gosuniversitet i Matematicheskii in-t im.V.A.Steklova, Kniga publishers Samara, 2010, 274–276

   2009
13. A. M. Chebotarev, Vvedenie v teoriyu veroyatnostei i matematicheskuyu statistiku dlya fizikov, 250c. Moskva, FIZTEKh-POLIGRAF 141700 Moskovskaya obl., g. Dolgoprudnyi, Instritutskii per. 9, 2009 , 247 pp.
14. V. I. Bogachev, V. S. Vladimirov, I. V. Volovich, B. S. Kashin, A. I. Kirillov, V. V. Kozlov, V. P. Maslov, V. A. Sadovnichii, A. M. Stepin, V. M. Tikhomirov, A. V. Uglanov, A. Yu. Khrennikov, A. M. Chebotarev, E. T. Shavgulidze, “Oleg Georgievich Smolyanov (on his 70th birthday)”, Russian Math. Surveys, 64:1 (2009), 183–185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

   2007
15. A. M. Chebotarev, “On stable Pareto laws in a hierarchical model of economy”, Physica A: Statistical Mechanics and its Applications, 373 (2007), 541–559 , Netherlands, Netherlands  crossref  isi (cited: 5)

   2006
16. A. M. Chebotarev, Ekonofizika, Cb. statei pod red. V.V.Kharitonova i A.A.Ezhova,, Sovremennaya fizika v poiskakh ekonomicheskoi teorii, TROVANT Moskva, 2006, 434–470
17. Yu. G. Kondrat'ev, A. M. Chebotarev, “Bernstein theorems and transformations of correlation measures in statistical physics”, Math. Notes, 79:5 (2006), 649–663  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus

   2005
18. V. N. Baturin, V. P. Maslov, B. I. Sadovnikov, A. M. Chebotarev, “Gipoteza o zakone racpredeleniya vysokikh dokhodov i ego interpretatsiya”, Ekonomicheskaya nauka v sovremennoi Rossii, 31:4 (2005), 57–62

   2004
19. A. V. Polyakov, A. M. Chebotarëv, “Monte-Carlo method for the Schrödinger equation with a periodic asymmetric potential”, Comput. Math. Math. Phys., 44:10 (2004), 1807–1817  mathnet  mathscinet  zmath  elib
20. A. M. Chebotarev, A. V. Polyakov, “Deviation Estimates for Random Walks and Stochastic Methods for Solving the Schrödinger Equation”, Math. Notes, 76:4 (2004), 564–577  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  scopus (cited: 1)

   2003
21. A. M. Chebotarev, A. V. Tchourkin, G. V. Ryzhakov, A. M. Sinev, “A solvable model of gravitational wave detector and the standard quantum limit”, Russian Journal of Mathematical Physics, 10:2 (2003), 134–141 , Russian Federation, Russian Federation  mathscinet  isi
22. A. M. Chebotarev, “A Priori Estimates for Quantum Dynamical Semigroups”, Theoret. and Math. Phys., 134:2 (2003), 160–165  mathnet  crossref  crossref  mathscinet  zmath  isi
23. A. M. Chebotarev, G. V. Ryzhakov, “On the Strong Resolvent Convergence of the Schrödinger Evolution to Quantum Stochastics”, Math. Notes, 74:5 (2003), 717–733  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)

   2002
24. A. M. Chebotarev, S. Yu. Shustikov, “Conditions Sufficient for the Conservativity of a Minimal Quantum Dynamical Semigroup”, Math. Notes, 71:5 (2002), 692–710  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 5)
25. A. M. Chebotarev, “What Is a Quantum Stochastic Differential Equation from the Point of View of Functional Analysis?”, Math. Notes, 71:3 (2002), 408–427  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 3)

   2000
26. A. M. Chebotarev, Lectures on quantum probability. Aportaciones Matematicas: Textos [Mathematical Contributions: Texts], 14, Sociedad Matematica Mexicana Mexico, 2000 , 292 pp.  mathscinet
27. A. M. Chebotarev, J. C. Garcia, R. Quezada, Stochastic analysis and mathematical physics, Santiago, 1998, Trends in Mathematics, 23, Trends Math., Birkhauser Santiago, Boston, Boston, MA, 2000, 23–31  mathscinet
28. V. P. Maslov, A. M. Chebotarev, “Limit theorems in new probability spaces associated with quantum statistics”, Dokl. Akad. Nauk SSSR (Russian), 373:2000 (2000), 311–315  mathscinet  zmath

   1999
29. V. P. Maslov, A. M. Chebotarev, “Markov evolution equations in quotient probability spaces”, Dokl. Akad. Nauk SSSR (Russian), 365:6 (1999), 745–749  mathscinet  zmath
30. A. M. Chebotarev, V. P. Maslov, Stochastic processes, physics and geometry: New interpays, Leipzig, January 18-22, 1999, CMS Conf. Proc, 28, American Mathematical Society [Providence, R.I., etc.], United States, 1999, 65–83  mathscinet
31. A. M. Chebotarev, V. P. Maslov, “On nonlinear evolution equations for occupancies”, Journal of Mathematical Sciences (New York), 105:2001 (1999), 2519–2533  mathscinet
32. A. Chebotarev, V. Liebscher, “On relative boundedness in operator spaces”, Reports of Math.Phys, 44:3 (1999), 339–344  crossref  mathscinet  zmath  isi
33. A. M. Chebotarev, “Maslov probability spaces associated with the Bose–Einstein and Fermi–Dirac statistics”, Math. Notes, 65:5 (1999), 627–637  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)

   2000
34. V. P. Maslov, A. M. Chebotarev, “An equation of the Kolmogorov–Feller type in a factorized probability space”, Theory Probab. Appl., 44:2 (2000), 309–318  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)

   1999
35. A. M. Chebotarev, A. V. Churkin, “The quantum gravitational wave detector”, Matem. Mod., 11:8 (1999), 32–44  mathnet

   1998
36. A. M. Chebotarev, Stochastic analysis and mathematical physics, Villa del Mar, 1996, World Sci. Publ River Edge, NJ, 1998, 42–54  mathscinet  zmath
37. A. M. Chebotarev, F. Fagnola, “Sufficient conditions for conservativity of minimal quantum dynamical semigroups”, Journal of Functional Analysis, 153:2 (1998), 382–404 , United States, United States  crossref  mathscinet  isi (cited: 74)
38. V. P. Maslov, A. M. Chebotarev, “Logarithmic asymptotics of solutions of the large deviation problem for the Boltzmann equation with small transfer of momentum”, Math. Notes, 64:1 (1998), 63–81  mathnet  crossref  crossref  mathscinet  zmath  isi

   1997
39. A.M. Chebotarev, J.C. Garcia, R. Quezada, Recent Trends in Infinite Dimensional Non-Commutative Analysis, RIMS Kokyuroku, 1035, 1997, 44–65  mathscinet
40. A. M. Chebotarev, J. C. Garcia, R. B. Quezada, “On the Lindblad equation with unbounded time-dependent coefficients”, Math. Notes, 61:1 (1997), 105–117  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)
41. A. M. Chebotarev, “The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation”, Math. Notes, 61:4 (1997), 510–518  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 22)

   1996
42. A. M. Chebotarev, “Symmetric form of the Hudson-Parthasarathy stochastic equation”, Math. Notes, 60:5 (1996), 544–561  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)

   1995
43. A. M. Chebotarev, “Logarithmic asymptotics for a solution of the Boltzmann evolution equation”, Matem. Mod., 7:12 (1995), 97–106  mathnet  mathscinet  zmath

   1994
44. A.M. Chebotarev, “Applications of quantum probability to classical stochastics. Third Symposium on Probability Theory and Stochastic Processes”, Aportaciones Mat. Notas Investigacion, 11 (1994), 61–79  mathscinet  zmath

   1995
45. V. P. Maslov, A. M. Chebotarev, “Cluster expansions and second quantization”, Proc. Steklov Inst. Math., 203 (1995), 123–136  mathnet  mathscinet  zmath

   1994
46. A. M. Chebotarev, “On the maximal $C^*$-algebra of zeros of completely positive mapping and on the boundary of a dynamic semigroup”, Math. Notes, 56:6 (1994), 1271–1282  mathnet  crossref  mathscinet  zmath  isi

   1993
47. A. M. Chebotarev, F. Fagnola, “Sufficient conditions for conservativity of quantum dynamical semigroups”, Journal of Functional Analysis, 118:1 (1993), 131–153 , United States, United States  crossref  mathscinet  isi (cited: 24)
48. A.M. Chebotarev, S.Yu. Dobrokhotov, A.I. Shafarevich, “An example of the diffusion approximation method as applied to the density function of a one-dimensional oscillator”, Russian Journal of Mathematical Physics, 1:3 (1993), 391–396 , Russian Federation, Russian Federation  mathscinet

   1992
49. A. M. Chebotarev, Quantum Probability and Related Topics, 7, World Sci. Publ River Edge, NJ, 1992, 79–91  crossref  mathscinet
50. A. M. Chebotarev, “Sufficient conditions of the conservatism of a minimal dynamical semigroup”, Math. Notes, 52:4 (1992), 1067–1077  mathnet  crossref  mathscinet  zmath  isi (cited: 2)

   1990
51. A. A. Konstantinov, V. P. Maslov, A. M. Chebotarev, “Probability representations of solutions of the Cauchy problem for quantum mechanical equations”, Russian Math. Surveys, 45:5 (1990), 1–26  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)

   1989
52. A. M. Chebotarev, Probability theory and mathematical statistics, 1, Mokslas, Vilnius Mokslas, Vilnius, 1989, 217–227  mathscinet
53. A. M. Chebotarev, Stochastic methods in experimental sciences, Szklarska Poremba, World Sci. Publ River Edge, NJ, 1989, 79–95  mathscinet
54. A. M. Chebotarev, “Sufficient conditions for dissipative dynamical semigroups to be conservative”, Theoret. and Math. Phys., 80:2 (1989), 804–818  mathnet  crossref  mathscinet  zmath  isi (cited: 6)

   1991
55. A. M. Chebotarev, “Necessary and sufficient conditions for the conservativity of dynamical semigroups”, J. Soviet Math., 56:5 (1991), 2697–2719  mathnet  crossref  mathscinet  zmath

   1988
56. A. M. Chebotarev, “Approximately complete sets of the generalized Feynman measure”, Dokl. Akad. Nauk SSSR (Russian), 298:1 (1988), 46–51  mathscinet  zmath
57. A. M. Chebotarev, Stochastic methods in mathematics and physics, Karpacz, World Sci. Publ Teaneck, NJ, 1988, 96–106  mathscinet
58. A. M. Chebotarev, “The fast Fourier transform in a problem with multiple grid-points”, U.S.S.R. Comput. Math. Math. Phys., 28:1 (1988), 180–183  mathnet  crossref  mathscinet  zmath
59. A. M. Chebotarev, “Asymptotic of nonclassical rapidly oscillating integrals”, Math. Notes, 44:2 (1988), 616–619  mathnet  crossref  mathscinet  zmath  isi
60. A. M. Chebotarev, “Sufficient Conditions of Regularity of Jump Markov Processes”, Theory Probab. Appl., 33:1 (1988), 22–35  mathnet  crossref  mathscinet  zmath  isi (cited: 1)
61. A. A. Konstantinov, V. P. Maslov, A. M. Chebotarev, “Shift of the boundary conditions for partial differential equations”, U.S.S.R. Comput. Math. Math. Phys., 28:6 (1988), 111–121  mathnet  crossref  mathscinet  zmath

   1986
62. V. P. Maslov, A. M. Chebotarev, “Drift of boundary conditions and uniqueness theorems for nonlinear boundary value problems”, Dokl. Akad. Nauk SSSR, 289:1 (1986), 47–51  mathnet  mathscinet  isi (cited: 1)

   1985
63. V. R. Struletskaya, V. Yu. Subochev, A. M. Chebotarev, “A series of invariant characteristics of extremum and the logarithmic asymptotic of Laplace integrals”, Math. Notes, 37:4 (1985), 303–307  mathnet  crossref  mathscinet  zmath  isi

   1983
64. V. P. Maslov, A. M. Chebotarev, “On random fields corresponding to the BBGKY, Vlasov, and Boltzmann hierarchies”, Theoret. and Math. Phys., 54:1 (1983), 48–55  mathnet  crossref  mathscinet  isi
65. A. M. Chebotarev, “Formula for the second term of the logarithmic asymptotic of Laplace integrals”, Math. Notes, 34:2 (1983), 620–625  mathnet  crossref  mathscinet  zmath  isi
66. V. P. Maslov, A. M. Chebotarev, “Second term of the logarithmic asymptotics of path integrals”, J. Soviet Math., 23:5 (1983), 2580–2598  mathnet  crossref  mathscinet  zmath

   1980
67. V. P. Maslov, A. M. Chebotarev, “Path integral over branching paths”, Theoret. and Math. Phys., 45:3 (1980), 1058–1069  mathnet  crossref  mathscinet  isi (cited: 1)
68. V. P. Maslov, A. M. Chebotarev, “Kontinualnyi integral po vetvyaschimsya traektoriyam”, Teoreticheskaya i matematicheskaya fizika, 34:2 (1980), 273–282  mathnet

   1978
69. A. M. Chebotarev, V. P. Maslov, Lecture Notes in Phys, 106, Springer Marseille, Berlin-New York, 1978, 58–72  crossref  mathscinet
70. A. M. Chebotarev, “Representation of solution of the Schrödinger equation in the form of mathematical expectation of a functional of a transition process”, Math. Notes, 24:5 (1978), 873–877  mathnet  crossref  mathscinet  zmath

   1980
71. V. P. Maslov, A. M. Chebotarev, “Jump-type processes and their applications in quantum mechanics”, J. Soviet Math., 13:3 (1980), 315–358  mathnet  crossref  mathscinet  zmath

   1977
72. V. P. Maslov, A. M. Chebotarev, Proc. Second IMACS Internat. Sympos., Lehigh Univ, Advances in computer methods for partial differential equations, Bethlehem, Pa., IMACS, New Brunswick, N.J, 1977, 349–353  mathscinet
73. A. M. Chebotarev, “$T$-maps connected with Hartree's equation”, Math. Notes, 21:5 (1977), 340–345  mathnet  crossref  mathscinet  zmath

   1976
74. V. P. Maslov, A. M. Chebotarev, “Dfinition of the Feynman path integral in the $P$-representation”, Doklady Akademii nauk SSSR, 229:1 (1976), 37–38 , Russian Federation, Russian Federation  mathnet (cited: 3)  mathscinet  mathscinet  zmath
75. V. P. Maslov, A. M. Chebotarev, “Generalized measure in Feynman path integrals”, Theoret. and Math. Phys., 28:3 (1976), 793–805  mathnet  crossref  mathscinet  zmath

   1975
76. V. P. Maslov, A. M. Chebotarev, “A representation of the solution of an equation of Hartree type in the form of a $T$-mapping”, Dokl. Akad. Nauk SSSR (Russian), 222:5 (1975), 1037–1040  mathscinet  zmath
77. A. M. Chebotarev, “T-mappings and continual integrals”, Dokl. Akad. Nauk SSSR (Russian), 225:4 (1975), 763–766  mathscinet  zmath
78. V. P. Maslov, A. M. Chebotarev, “Representation of the solution of an equation of Hartree type in the form of a $T$-mapping”, Dokl. Akad. Nauk SSSR, 222:5 (1975), 1037–1040  mathnet  mathscinet  zmath
79. A. M. Chebotarev, “$T$-mappings and functional integrals”, Dokl. Akad. Nauk SSSR, 225:4 (1975), 763–766  mathnet  mathscinet  zmath

   1974
80. A. M. Chebotarev, Trudy MIEM, Asimpt. Metody v Teorii Uravn. s Tchastn. Proizvodnymi, 38, Moskov. Inst. Elektron. Mashinostroenija, 1974, 141–151  mathscinet
81. A. M. Chebotarev, “The stationary phase method for nondifferentiable functions”, U.S.S.R. Comput. Math. Math. Phys., 14:1 (1974), 210–214  mathnet  crossref  mathscinet  zmath
82. A. M. Chebotarev, “The extension of a non-Wiener quasi-measure to a complex measure on nonsmooth functionals”, Uspekhi Mat. Nauk, 29:3(177) (1974), 235–236  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. On the normal form of multimode squeezings
A. M. Chebotarev, T. V. Tlyachev, A. E. Teretenkov, V. V. Belokurov
International conference "QP 34 – Quantum Probability and Related Topics"
September 17, 2013 12:00   
2. Свойства многомерных сжатых состояний и их применения
A. M. Chebotarev
Seminar on Quantum Probability, Statistics, Information
April 19, 2010 15:30
3. Об оценке энтропии в конструкции Хастингса
A. M. Chebotarev
Seminar on Quantum Probability, Statistics, Information
April 27, 2009 14:00

Organisations
 
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