Geodesic
Metastable states of a composite system tunneling through repulsive barriers
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 27-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a method for solving the problem of quantum tunneling through repulsive potential barriers for a composite system consisting of several identical particles coupled via pair oscillator-type potentials in the oscillator symmetrized-coordinate representation. We confirm the efficiency of the proposed approach by calculating complex energy values and analyzing metastable states of composite systems of three, four, and five identical particles on a line, which leads to the effect of quantum transparency of the repulsive barriers.
Keywords: quantum tunneling, system of identical particles, symmetrized-coordinate representation, harmonic oscillator basis, complex energy value, metastable state, quantum transparency. 
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     title = {Metastable states of a~composite system tunneling through repulsive barriers},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. A. Gusev; S. I. Vinitsky; O. Chuluunbaatar; V. L. Derbov; A. Gozdz; P. M. Krasovitskii. Metastable states of a composite system tunneling through repulsive barriers. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 27-50. http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a1/

[1] S. P. Merkurev, L. D. Faddeev, Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985 | MR | Zbl

[2] V. I. Kukulin, V. M. Krasnopolsky, J. Horáček, Theory of Resonances. Principles and Applications, Reidel Texts in the Mathematical Sciences, 3, Springer, Netherlands, 1989 | DOI | MR | Zbl

[3] S. N. Ershov, B. V. Danilin, J. S. Vaagen, Phys. Rev. C, 64:6 (2001), 064609, 23 pp. | DOI

[4] F. M. Penkov, ZhETF, 118:4 (2000), 806–815 | DOI

[5] P. M. Krassovitskiy, F. M. Pen'kov, J. Phys. B, 47:22 (2014), 225210, 5 pp., arXiv: 1412.3905 | DOI

[6] I. V. Puzynin, T. L. Boyadzhiev, S. I. Vinitskii, E. V. Zemlyanaya, T. P. Puzynina, O. Chuluunbaatar, EChAYa, 38:1 (2007), 144–232 | DOI

[7] A. A. Gusev, S. I. Vinitsky, O. Chuluunbaatar, V. P. Gerdt, V. A. Rostovtsev, “Symbolic-numerical algorithms to solve the quantum tunneling problem for a coupled pair of ions”, Computer Algebra in Scientific Computing (Kassel, Germany, September 5–9, 2011), Lecture Notes in Computer Science, 6885, eds. V. P. Gerdt, W. Koepf, E. W. Mayr, E. V. Vorozhtsov, Springer, Berlin, Heidelberg, 2011, 175–191 | DOI | MR | Zbl

[8] J. G. Muga, J. P. Palao, B. Navarro, I. L. Egusquiza, Phys. Rep., 395:6 (2004), 357–426 | DOI | MR

[9] V. A. Fok, UFN, 93:2 (1967), 342–361 | DOI | MR

[10] A. A. Gusev, S. I. Vinitsky, O. Chuluunbaatar, L. L. Hai, V. L. Derbov, A. Góźdź, P. M. Krassovitskiy, YaF, 77:3 (2014), 414–438 | DOI | DOI

[11] P. Kramer, M. Moshinsky, Nucl. Phys., 82:2 (1966), 241–274 | DOI | MR | Zbl

[12] M. Moshinsky, Yu. F. Smirnov, The Harmonic Oscillator in Modern Physics, Contemporary Concepts in Physics, 9, Harwood, Amsterdam, 1996 | Zbl

[13] K. Vildermut, Ya. Tan, Edinaya teoriya yadra, Mir, M., 1980

[14] A. Novoselsky, J. Katriel, Ann. Phys., 196:1 (1989), 135–149 | DOI | MR | Zbl

[15] P. Kramer, T. Kramer, Phys. Scr., 90:7 (2015), 074014, arXiv: 1410.4768 | DOI

[16] A. Gusev, S. Vinitsky, O. Chuluunbaatar, V. A. Rostovtsev, L. L. Hai, V. Derbov, A. Gozdz, E. Klimov, “Symbolic-numerical algorithm for generating cluster eigenfunctions: identical particles with pair oscillator interactions”, Computer Algebra in Scientific Computing (Berlin, Germany, September 9–13, 2013), Lecture Notes in Computer Science, 8136, eds. V. P. Gerdt, W. Koepf, E. W. Mayr, E. V. Vorozhtsov, Springer, 2013, 155–168 | DOI | MR | Zbl

[17] A. A. Gusev, Vestn. RUDN. Ser. Matematika. Informatika. Fizika, 2014, no. 1, 52–70

[18] A. A. Gusev, O. Chuluunbaatar, S. I. Vinitsky, A. G. Abrashkevich, Comput. Phys. Commun., 185:12 (2014), 3341–3343 | DOI | Zbl

[19] O. Chuluunbaatar, A. A. Gusev, V. L. Derbov, P. M. Krassovitskiy, S. I. Vinitsky, YaF, 72:5 (2009), 811–821 | DOI

[20] A. J. F. Siegert, Phys. Rev., 56:8 (1939), 750–752 | DOI

[21] C. W. McCurdy, C. K. Stroud, Comput. Phys. Commun., 63:1–3 (1991), 323–330 | DOI | Zbl

[22] A. Dobrowolski, A. Góźdź, K. Mazurek, J. Dudek, Internat. J. Modern Phys. E, 20:2 (2011), 500–506 | DOI

[23] V. G. Neudachin, Yu. F. Smirnov, Nuklonnye assotsiatsii v legkikh yadrakh, 1969, Nauka, M.

[24] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR | MR | Zbl | Zbl

[25] G. A. Baker, Jr., Phys. Rev., 103:4 (1956), 1119–1120 | DOI | MR | Zbl

[26] A. A. Gusev, S. I. Vinitsky, O. Chuluunbaatar, A. Góźdź, V. L. Derbov, Phys. Scr., 89:5 (2014), 054011, 7 pp. | DOI

[27] O. Chuluunbaatar, A. A. Gusev, A. G. Abrashkevich, A. Amaya-Tapia, M. S. Kaschiev, S. Y. Larsen, S. I. Vinitsky, Comput. Phys. Commun., 177:6 (2007), 649–675 | DOI | MR | Zbl

[28] Yu. N. Demkov, Variatsionnye printsipy v teorii stolknovenii, GIFML, M., 1958 | MR

[29] O. A. Ladyzhenskaya, Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | DOI | MR | MR | Zbl

[30] G. Streng, G. Fiks, Teoriya metoda konechnykh elementov, Mir, M., 1977 | MR | MR | Zbl

[31] T. Zhanlav, R. Mizhiddorzh, O. Chuluunbaatar, Vestn. Tversk. gos. un-ta. Ser. Prikladnaya matematika, 2:9 (2008), 27–37

[32] T. Zhanlav, O. Chuluunbaatar, V. Ulziibayar, Appl. Math. Comput., 236 (2014), 239–246 | DOI | MR | Zbl

[33] Dzh. Uilkinson, Ts. Rainsh, Spravochik algoritmov na yazyke ALGOL. Lineinaya algebra, Mashinostroenie, M., 1976 | MR