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Arsen'ev Aleksei Alekseevich

Publications in Math-Net.Ru

  1. Tunneling through a quantum dot in a quantum waveguide

    Zh. Vychisl. Mat. Mat. Fiz., 50:7 (2010),  1222–1232
  2. Representation of the Green's function of Schrödinger's equation with almost periodic potential by a path integral over coherent states

    Mat. Sb., 197:11 (2006),  3–12
  3. Resonances and tunneling in a quantum wire

    TMF, 147:1 (2006),  92–102
  4. Approximation to the solution of the Cauchy problem for a smoothed Schrödinger–Poisson equation in a magnetic field

    Differ. Uravn., 41:1 (2005),  116–120
  5. Resonances and trapped modes in a quantum waveguide

    Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005),  1630–1638
  6. Complex Scaling for a Waveguide Scattering Problem

    Differ. Uravn., 40:2 (2004),  191–197
  7. On the asymptotics of energy transmitted by an almost periodic source of oscillations to an open resonator over a long time

    Mat. Sb., 195:3 (2004),  3–14
  8. Resonances and Tunneling in the Tight-Binding Approximation to Scattering in a Quantum Billiard

    TMF, 141:1 (2004),  100–112
  9. Relation Between a Pole of the Scattering Matrix and the Transmission and Reflection Coefficients in Scattering in a Quantum Waveguide

    TMF, 140:2 (2004),  303–309
  10. Approximation of the solution of the Cauchy problem for the Neumann–Liouville equation

    Zh. Vychisl. Mat. Mat. Fiz., 44:10 (2004),  1845–1849
  11. Resonance scattering in quantum wave guides

    Mat. Sb., 194:1 (2003),  3–22
  12. Mathematical Model of Resonances and Tunneling in a System with a Bound State

    TMF, 136:3 (2003),  507–516
  13. Fermi Rule and Scattering Amplitude Resonances

    TMF, 134:3 (2003),  341–352
  14. Combined scaling for the waveguide trapped modes and resonances

    Zh. Vychisl. Mat. Mat. Fiz., 43:8 (2003),  1223–1227
  15. A remark on the numerical solution of a scattering problem for the Schrödinger equation on the whole line

    Zh. Vychisl. Mat. Mat. Fiz., 43:3 (2003),  433–434
  16. Resonance scattering in a waveguide with filling

    Zh. Vychisl. Mat. Mat. Fiz., 42:12 (2002),  1804–1809
  17. Resonance scattering in quantum waveguides

    Zh. Vychisl. Mat. Mat. Fiz., 42:3 (2002),  417–424
  18. A Mathematical Model of Resonance Scattering

    Mat. Zametki, 70:4 (2001),  491–502
  19. Behaviour of the scattering amplitude of the Helmholtz resonator near a resonance

    Mat. Sb., 192:9 (2001),  3–16
  20. Resonance Scattering by Infinite Sheets

    TMF, 127:1 (2001),  21–33
  21. Resonances in the scattering problem for a Sturm–Liouville operator

    Mat. Sb., 191:3 (2000),  3–12
  22. An approximation of the Green function for the Schrödinger equation

    Differ. Uravn., 35:3 (1999),  319–324
  23. Example of resonance scattering for the one-dimensional wave equation

    Mat. Sb., 190:6 (1999),  3–10
  24. Resonance solutions to a scattering problem for the Sturm–Liouville equation on semiaxis

    Zh. Vychisl. Mat. Mat. Fiz., 39:8 (1999),  1317–1327
  25. Estimation of the Schrödinger operator Green's function

    TMF, 115:1 (1998),  85–92
  26. Estimation of the imaginary part of the scattering matrix pole for the three-dimensional Schrödinger equation with a trap potential

    TMF, 114:2 (1998),  271–276
  27. Approximate propagator for the Schrödinger equation

    Zh. Vychisl. Mat. Mat. Fiz., 38:7 (1998),  1186–1189
  28. Scattering problem for the Neumann-Liouville equation

    Zh. Vychisl. Mat. Mat. Fiz., 38:4 (1998),  635–637
  29. Estimate of the solution of the scattering problem for a one-dimensional trapping potential

    Mat. Sb., 188:12 (1997),  3–10
  30. Resonance properties of the scattering matrix for the one-dimensional Schrödinger operator with a trapping potential

    Mat. Sb., 187:6 (1996),  3–20
  31. Resonances of the scattering matrix and quasilevels

    TMF, 106:1 (1996),  16–23
  32. Some questions of the spectral theory for the Schrödinger equation describing the tunnel diode

    Mat. Model., 7:9 (1995),  79–116
  33. On resonance properties of scattering amplitude for Schrödinger equation with trapping potential

    TMF, 104:2 (1995),  214–232
  34. Resonance properties of the solution of the problem of scattering by a one-dimensional potential trap

    Dokl. Akad. Nauk, 338:2 (1994),  171–172
  35. On the behavior of reflection and transmission coefficients near resonance at the quasi-level

    Dokl. Akad. Nauk, 336:3 (1994),  307–308
  36. The resonance properties of the scattering amplitude of the Helmholtz resonator

    Mat. Model., 6:6 (1994),  47–66
  37. On the resonant properties of the scattering time operator

    Mat. Model., 5:7 (1993),  49–58
  38. Initial-boundary problem for quantum Liouville equation

    Mat. Model., 4:3 (1992),  119–124
  39. A note on the particle method for the quantum Liouville equation

    Mat. Model., 3:2 (1991),  151–156
  40. On the connection between the solutions of the Boltzman and the Landau–Fokker–Planck equations

    Mat. Sb., 181:4 (1990),  435–446
  41. On a connection between the Boltzmann equation and the Landau–Fokker–Planck equations

    Dokl. Akad. Nauk SSSR, 305:2 (1989),  322–324
  42. The justification of direct statistical modelling in a problem from kinetic theory of gases

    Mat. Model., 1:11 (1989),  92–95
  43. On two mathematical models for description of a beam of charged particles in gas

    Mat. Model., 1:9 (1989),  101–106
  44. On the accuracy of macroparticle method for statistical modelling of kinetic equations

    Mat. Model., 1:4 (1989),  134–139
  45. The justification of direct statistic modelling in a problem from the kinetic theory of gases

    Mat. Model., 1:3 (1989),  135–145
  46. Mathematical foundation of particle method and modelling of semiconductor plasma

    Mat. Model., 1:1 (1989),  108–119
  47. Approximation of the Boltzmann equation by stochastic equations

    Zh. Vychisl. Mat. Mat. Fiz., 28:4 (1988),  560–567
  48. On the approximation of the Boltzmann equation by Ito stochastic equations

    Dokl. Akad. Nauk SSSR, 293:3 (1987),  584–586
  49. Vlasov limit of correlation functions of the grand canonical ensemble

    TMF, 72:3 (1987),  477–480
  50. Estimates for the rate of convergence of the particle method for the Vlasov equation

    Zh. Vychisl. Mat. Mat. Fiz., 27:4 (1987),  557–563
  51. On the approximation of the solution of the Boltzmann equation by solutions of the Ito stochastic differential equations

    Zh. Vychisl. Mat. Mat. Fiz., 27:3 (1987),  400–410
  52. Estimates for the rate of convergence of the particle method for the Vlasov equation

    Dokl. Akad. Nauk SSSR, 291:6 (1986),  1340–1342
  53. Vlasov limit of the correlation functions of the grand canonical ensemble

    TMF, 68:1 (1986),  151–154
  54. Some estimates for the solution of the Vlasov equation

    Zh. Vychisl. Mat. Mat. Fiz., 25:1 (1985),  80–87
  55. On invariant measures for classical dynamical systems with infinite-dimensional phase space

    Mat. Sb. (N.S.), 121(163):3(7) (1983),  297–309
  56. Estimate of the critical density of Bose-Einstein condensation in a periodic potential

    TMF, 55:1 (1983),  156–160
  57. Kubo-Martin-Schwinger states for dynamical systems that are described by equations of hyperbolic type

    Differ. Uravn., 17:10 (1981),  1759–1764
  58. An example of a Kubo–Martin–Schwinger state for a nonlinear classical poisson system with infinite-dimensional phase space

    Mat. Sb. (N.S.), 115(157):1(5) (1981),  116–129
  59. Uniqueness of Kubo–Martin–Schwinger states for classical dynamical systems with infinite-dimensional phase space

    TMF, 44:2 (1980),  209–216
  60. The existence of generalized and stationary statistical solutions of a system of Vlasov equations in a bounded domain

    Differ. Uravn., 15:7 (1979),  1253–1266
  61. Statistical solutions of a nonlinear wave equation

    Differ. Uravn., 15:7 (1979),  1239–1252
  62. On statistical solutions of the Navier–Stokes system of equations

    Mat. Sb. (N.S.), 110(152):1(9) (1979),  35–50
  63. Kubo—Martin–Schwinger states of classical dynamical systems with infinite phase space

    TMF, 38:3 (1979),  306–312
  64. On the existence of generalized and stationary statistical solutions of Vlasov’s system of equations in a bounded domain

    Dokl. Akad. Nauk SSSR, 239:4 (1978),  761–763
  65. On the existence of invariant measures on the solution space of an evolution equation

    Dokl. Akad. Nauk SSSR, 233:2 (1977),  269–271
  66. Construction of a turbulent measure for Vlasov's system of equations

    Mat. Sb. (N.S.), 102(144):1 (1977),  13–32
  67. On the existence of a generalized solution of Landau's equation

    Zh. Vychisl. Mat. Mat. Fiz., 17:4 (1977),  1063–1068
  68. Construction of a turbulence measure for the system of Navier–Stokes equations

    Mat. Sb. (N.S.), 101(143):2(10) (1976),  204–211
  69. The existence of resonance poles and scattering resonances in the case of boundary conditions of the second and third kind

    Zh. Vychisl. Mat. Mat. Fiz., 16:3 (1976),  718–724
  70. Construction of a turbulent measure for the system of Navier–Stokes equations

    Dokl. Akad. Nauk SSSR, 225:1 (1975),  18–20
  71. On the existence of statistical solutions of the Vlasov system of equations

    Dokl. Akad. Nauk SSSR, 220:6 (1975),  1249–1250
  72. The existence of statistical solutions of Vlasov's system of equations

    Differ. Uravn., 11:7 (1975),  1256–1268
  73. Note on estimating the width of lower energy bands in a periodic potential

    TMF, 23:3 (1975),  418–420
  74. Existence and uniqueness of the classical solution of Vlasov's system of equations

    Zh. Vychisl. Mat. Mat. Fiz., 15:5 (1975),  1344–1349
  75. Asymptotic behaviour of the energy emitted by an almost periodic source of oscillations

    Zh. Vychisl. Mat. Mat. Fiz., 15:4 (1975),  1062–1066
  76. Existence in the large of a weak solution of Vlasov's system of equations

    Zh. Vychisl. Mat. Mat. Fiz., 15:1 (1975),  136–147
  77. On the existence of resonance poles and resonances in scattering in the case of boundary conditions of the second and third kind

    Dokl. Akad. Nauk SSSR, 219:5 (1974),  1033–1035
  78. Local uniqueness and existence of a classical solution of Vlasov's system of equations

    Dokl. Akad. Nauk SSSR, 218:1 (1974),  11–12
  79. Global existence of a weak solution of Vlasov's system of equations

    Dokl. Akad. Nauk SSSR, 213:4 (1973),  761–763
  80. On phase shift behavior near resonance

    TMF, 15:2 (1973),  259–265
  81. Èîíèçàòîð ïàðîâ ùåëî÷íûõ ìåòàëëîâ

    TVT, 10:1 (1972),  182–183
  82. A method for the asymptotic estimation of integrals

    Zh. Vychisl. Mat. Mat. Fiz., 12:4 (1972),  1005–1012
  83. The singularities of the analytic continuation and resonance properties of the solution of the scattering problem for the Helmholtz equation

    Zh. Vychisl. Mat. Mat. Fiz., 12:1 (1972),  112–138
  84. On the singularities of the analytic continuation and the resonance properties of a solution of the dispersion problem for the Helmholtz equation

    Dokl. Akad. Nauk SSSR, 197:3 (1971),  511–512
  85. The behavior of the energy of a solution of the wave equation in an unbounded region, for large values of the time

    Dokl. Akad. Nauk SSSR, 193:6 (1970),  1215–1217
  86. mean value formula for the fundamental functions of the Beltrami operator, and a precise estimate of the sum of the squares of the fundamental functions

    Dokl. Akad. Nauk SSSR, 190:6 (1970),  1263–1266
  87. Estimate of the energy width of a quasistationary level

    TMF, 5:1 (1970),  94–97
  88. Resonance scattering by a “potential trap” and the Breit–Wigner formula

    TMF, 2:3 (1970),  361–366
  89. The behavior of the energy of a solution of the wave equation at large values of the time

    Zh. Vychisl. Mat. Mat. Fiz., 10:4 (1970),  1037–1041
  90. The asymptotic behavior of the wave function for a quasi-stationary state

    Dokl. Akad. Nauk SSSR, 188:3 (1969),  545–547
  91. The behavior of a generalized solution of a mixed problem for the wave equation in a region which is nearly closed

    Dokl. Akad. Nauk SSSR, 185:3 (1969),  495–498
  92. Scattering of a plane wave by a “trap-like” region

    Differ. Uravn., 5:10 (1969),  1854–1860
  93. Asymptotics of the wave function of the quasistationary state

    TMF, 1:1 (1969),  120–136
  94. Behaviour of an S. L. Sobolev generalized solution of a mixed problem for a wave equation in almost closed domains

    Zh. Vychisl. Mat. Mat. Fiz., 9:5 (1969),  1094–1101
  95. Equivalent regularizations of the problem of scattering at a singular potential

    Zh. Vychisl. Mat. Mat. Fiz., 9:4 (1969),  959–960
  96. The expansion in eigenfunctions of the Schrödinger operator with a strongly singular potential

    Zh. Vychisl. Mat. Mat. Fiz., 9:1 (1969),  137–163
  97. The eigenfunction expansion of a Schrödinger operator with strongly singular potential

    Dokl. Akad. Nauk SSSR, 182:1 (1968),  13–15
  98. Scattering of a plane wave on a singular potential

    Dokl. Akad. Nauk SSSR, 178:6 (1968),  1231–1233
  99. The spectral function of a Schrödinger operator with strongly singular potential wave operators

    Zh. Vychisl. Mat. Mat. Fiz., 8:6 (1968),  1232–1241
  100. Scattering of a plane wave on a singular potential

    Zh. Vychisl. Mat. Mat. Fiz., 8:3 (1968),  544–572
  101. The asymptotics of the spectral function of Schrödinger's operator

    Dokl. Akad. Nauk SSSR, 176:4 (1967),  751–753
  102. The asymptotic spectral function of the Schrödinger equation

    Zh. Vychisl. Mat. Mat. Fiz., 7:6 (1967),  1298–1319
  103. Asymptotic behavior of the spectral function of the Schrödinger operator in an unbounded region

    Uspekhi Mat. Nauk, 21:5(131) (1966),  254–255
  104. On solution of the dispersion equation for the linearized Boltzmann equation in the kinetic theory of rarefied gases

    Zh. Vychisl. Mat. Mat. Fiz., 6:2 (1966),  375–380
  105. Cauchy problem for Boltzmann's linearized equation

    Dokl. Akad. Nauk SSSR, 163:5 (1965),  1104–1106
  106. The Cauchy problem for the linearized Boltzmann equation

    Zh. Vychisl. Mat. Mat. Fiz., 5:5 (1965),  864–882
  107. Asymptotic properties of the trace of the spectral function of a self-adjoint elliptic differential operator of second order

    Dokl. Akad. Nauk SSSR, 157:4 (1964),  761–763
  108. On the Fourier transform of a slowly decreasing function

    Dokl. Akad. Nauk SSSR, 154:2 (1964),  251–253

  109. Aleksandr Andreevich Samarskiǐ (on the occasion of his eightieth birthday)

    Differ. Uravn., 35:2 (1999),  147–151
  110. Corrigenda: Teor. Mat. Fiz. 1996. V. 106. № 1. P. 16–23

    TMF, 111:1 (1997),  159
  111. Aleksandr Andreevich Samarskiǐ (on the occasion of his seventy-fifth birthday)

    Differ. Uravn., 30:7 (1994),  1107–1110
  112. Aleksandr Andreevich Samarskiǐ (on the occasion of his seventieth birthday)

    Differ. Uravn., 25:12 (1989),  2027–2043
  113. Aleksandr Andreevich Samarskii (on his sixtieth birthday)

    Uspekhi Mat. Nauk, 35:1(211) (1980),  223–232
  114. Aleksandr Andreevič Samarskiǐ (on the occasion of his 60th birthday)

    Differ. Uravn., 15:7 (1979),  1155–1163
  115. Letter to the editors: “The existence of statistical solutions of a system of Vlasov equations” (Differencial'nye Uravnenija 11 (1975), no. 7, 1256–1268)

    Differ. Uravn., 12:11 (1976),  2105
  116. Aleksandr Andreevič Samarskiǐ on his fiftieth birthday

    Differ. Uravn., 5:10 (1969),  1909–1914
  117. Errata

    Zh. Vychisl. Mat. Mat. Fiz., 9:6 (1969),  1234
  118. Letter to the editors

    Zh. Vychisl. Mat. Mat. Fiz., 9:5 (1969),  1223

© Steklov Math. Inst. of RAS, 2026