Chebotarev, Alexander Mikhailovich

Total publications: 83 (81)
in MathSciNet: 72 (70)
in zbMATH: 49 (47)
in Web of Science: 37 (35)
in Scopus: 45 (45)
Cited articles: 52
Citations in Math-Net.Ru: 152
Citations in Web of Science: 218
Citations in Scopus: 212
Presentations: 3

Number of views:
This page:3921
Abstract pages:14150
Full texts:4897
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 14.12.1947
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


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
List of publications on Google Scholar
List of publications on ZentralBlatt

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

1. 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: 6)  scopus (cited: 5)
2. Math. Notes, 95:5 (2014), 721–737  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
3. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 4)  scopus (cited: 4)

4. 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: 6)  scopus (cited: 6)
5. 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
6. 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

7. 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: 4)  elib  elib  elib  elib  scopus (cited: 1)  scopus (cited: 1)
8. 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: 4)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)  scopus (cited: 2)

9. 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: 6)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 3)  scopus (cited: 3)

10. 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
11. 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

12. 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.

13. 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)  scopus (cited: 5)

14. 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
15. 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  elib  scopus  scopus

16. 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

17. 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  elib
18. 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)  elib (cited: 1)  scopus (cited: 1)  scopus (cited: 1)

19. 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
20. 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  scopus
21. 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: 4)

22. 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)  scopus (cited: 5)
23. 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: 4)  scopus (cited: 3)  scopus (cited: 3)

24. A. M. Chebotarev, Lectures on quantum probability. Aportaciones Matematicas: Textos [Mathematical Contributions: Texts], 14, Sociedad Matematica Mexicana Mexico, 2000 , 292 pp.  mathscinet
25. 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
26. 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

27. 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
28. 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
29. A. M. Chebotarev, V. P. Maslov, “On nonlinear evolution equations for occupancies”, Journal of Mathematical Sciences (New York), 105:2001 (1999), 2519–2533  mathscinet
30. A. Chebotarev, V. Liebscher, “On relative boundedness in operator spaces”, Reports of Math.Phys, 44:3 (1999), 339–344  crossref  mathscinet  zmath  isi
31. 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)  scopus (cited: 2)

32. 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)

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

34. A. M. Chebotarev, Stochastic analysis and mathematical physics, Villa del Mar, 1996, World Sci. Publ River Edge, NJ, 1998, 42–54  mathscinet  zmath
35. 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: 84)  scopus (cited: 77)
36. 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  scopus

37. A.M. Chebotarev, J.C. Garcia, R. Quezada, Recent Trends in Infinite Dimensional Non-Commutative Analysis, RIMS Kokyuroku, 1035, 1997, 44–65  mathscinet
38. 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: 7)  scopus (cited: 7)
39. 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)

40. 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)  scopus (cited: 5)

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

42. 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

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

44. 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 (cited: 1)  scopus

45. 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: 27)  scopus (cited: 26)
46. 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

47. A. M. Chebotarev, Quantum Probability and Related Topics, 7, World Sci. Publ River Edge, NJ, 1992, 79–91  crossref  mathscinet
48. 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: 3)  scopus (cited: 7)

49. 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: 2)  scopus (cited: 4)

50. A. M. Chebotarev, Probability theory and mathematical statistics, 1, Mokslas, Vilnius Mokslas, Vilnius, 1989, 217–227  mathscinet
51. A. M. Chebotarev, Stochastic methods in experimental sciences, Szklarska Poremba, World Sci. Publ River Edge, NJ, 1989, 79–95  mathscinet
52. 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: 9)  scopus (cited: 13)

53. 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  scopus (cited: 11)

54. A. M. Chebotarev, “Approximately complete sets of the generalized Feynman measure”, Dokl. Akad. Nauk SSSR (Russian), 298:1 (1988), 46–51  mathscinet  zmath
55. A. M. Chebotarev, Stochastic methods in mathematics and physics, Karpacz, World Sci. Publ Teaneck, NJ, 1988, 96–106  mathscinet
56. 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  scopus
57. A. M. Chebotarev, “Asymptotic of nonclassical rapidly oscillating integrals”, Math. Notes, 44:2 (1988), 616–619  mathnet  crossref  mathscinet  zmath  isi  scopus
58. 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)
59. 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  scopus (cited: 4)
60. A. M. Chebotarev, “Approximately complete sets of the generalized Feynman measure”, Dokl. Math., 37:1 (1988), 46–51  mathnet  mathscinet  zmath

61. 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  zmath  isi (cited: 1)

62. 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  scopus

63. 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  scopus
64. 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  scopus
65. 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  scopus

66. 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)  scopus (cited: 1)
67. V. P. Maslov, A. M. Chebotarev, “Kontinualnyi integral po vetvyaschimsya traektoriyam”, Teoreticheskaya i matematicheskaya fizika, 34:2 (1980), 273–282  mathnet

68. A. M. Chebotarev, V. P. Maslov, Lecture Notes in Phys, 106, Springer Marseille, Berlin-New York, 1978, 58–72  crossref  mathscinet
69. 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  scopus (cited: 4)

70. 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  scopus (cited: 6)

71. 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
72. A. M. Chebotarev, “$T$-maps connected with Hartree's equation”, Math. Notes, 21:5 (1977), 340–345  mathnet  crossref  mathscinet  zmath  scopus

73. 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
74. 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  scopus (cited: 6)

75. 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
76. A. M. Chebotarev, “T-mappings and continual integrals”, Dokl. Akad. Nauk SSSR (Russian), 225:4 (1975), 763–766  mathscinet  zmath
77. 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
78. A. M. Chebotarev, “$T$-mappings and functional integrals”, Dokl. Akad. Nauk SSSR, 225:4 (1975), 763–766  mathnet  mathscinet  zmath

79. A. M. Chebotarev, Trudy MIEM, Asimpt. Metody v Teorii Uravn. s Tchastn. Proizvodnymi, 38, Moskov. Inst. Elektron. Mashinostroenija, 1974, 141–151  mathscinet
80. 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  scopus
81. 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

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