Abstract
Tunneling effects for a nonlinear barrier of a constant height is studied analytically by the small-amplitude method. Explicit formulas for the field inside and outside the barrier are derived. The special case of a low barrier nontransparent to a linear medium and transparent to a nonlinear one is studied. The amplitude range of the obtained results is extended on the basis of the numerical analysis performed.
Similar content being viewed by others
References
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (Nauka, Moscow, 1974; Pergamon, New York, 1977).
L. M. Brekhovskikh, Waves in Layered Media (Nauka, Moscow, 1973; Academic, New York, 1980).
G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974; Mir, Moscow, 1977).
A.-H. Nayfeh, Perturbation Methods (Wiley, New York, 1973; Mir, Moscow, 1976).
I. A. Molotkov and S. A. Vakulenko, Concentrated Nonlinear Waves (Leningr. Gos. Univ., Leningrad, 1988) [in Russian].
Metal-Polymer Nanocomposites, Ed. by L. Nicolais and G. Carotenuto (Wiley, Hoboken, 2005).
A. L. Stepanov, Zh. Tekh. Fiz. 74(2), 1 (2004) [Tech. Phys. 49, 143 (2004)].
O. P. Vinogradova, M. S. Marukhina, and A. I. Sidorov, Pis’ma Zh. Tekh. Fiz. 31(12), 79 (2005) [Tech. Phys. Lett. 31, 528 (2005)].
G. I. Pearce, T. D. Hedley, and D. M. Bird, Phys. Rev. B 7, 195108 (2005).
A. C. Newell, J. Math. Phys. 19, 1126 (1978).
P. S. Lomdahl, O. H. Soerensen, O. L. Christiansen, et al., Phys. Rev. B 24, 7460 (1981).
I. A. Molotkov, Analytical Approach in the Theory of Nonlinear Waves (Fizmatlit, Moscow, 2003) [in Russian].
T. Y. Na, Computational Methods in Engineering Boundary Value Problems (Academic, New York, 1979; Mir, Moscow, 1982).
V. S. Ryaben’kii, Introduction to Computational Mathematics (Nauka, Moscow, 1994) [in Russian].
Modern Numerical Methods for Ordinary Differential Equations Ed. by G. Hall and J. M. Watt (Clarendon Press, Oxford, 1976; Mir, Moscow, 1979).
D. Kahaner, C. Moler, and S. Nash, Numerical Methods and Software (Prentice Hall, Englewood Cliffs, N. J., 1988; Mir, Moscow, 1998).
Additional information
Original Russian Text © I.A. Molotkov, A.B. Manenkov, 2007, published in Radiotekhnika i Elektronika, 2007, Vol. 52, No. 7, pp. 799–806.