Abstract
We theoretically study the evolution of longitudinal-transverse acoustic pulses propagating parallel to an external magnetic field in a system of resonant paramagnetic impurities with an effective spin S=1/2. For equal group velocities of the longitudinal and transverse waves, the pulse dynamics is shown to be described by evolution equations. In limiting cases, these equations reduce to equations integrable in terms of the inverse scattering transform method (ISTM). For the most general integrable system of equations that describes the dynamics of acoustic pulses outside the scope of the slow-envelope approximation, we derive the corresponding ISTM equations. These equations are used to find a soliton solution and a self-similar solution. The latter describes the leading edge of the packet of acoustic pulses generated when the initial unstable state of a spin system decays. Analysis of our solutions and models indicates that the presence of a longitudinal acoustic wave leads not only to a change in the amplitude and phase of the transverse wave but also to a qualitatively new dynamics of sound in such a medium.
Similar content being viewed by others
References
A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves (Kluwer, Dordrecht, 1999).
A. I. Maimistov, Kvantovaya Élektron. (Moscow) 30, 287 (2000).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: the Inverse Scattering Method (Nauka, Moscow, 1980; Consultants Bureau, New York, 1984).
H.-Y. Hao and H. J. Maris, Phys. Rev. B 64, 064302 (2001).
G. A. Denisenko, Zh. Éksp. Teor. Fiz. 60, 2269 (1971) [Sov. Phys. JETP 33, 1220 (1971)].
S. V. Voronkov and S. V. Sazonov, Fiz. Tverd. Tela (St. Petersburg) 43, 1969 (2001) [Phys. Solid State 43, 2051 (2001)].
S. V. Voronkov and S. V. Sazonov, Zh. Éksp. Teor. Fiz. 120, 269 (2001) [JETP 93, 236 (2001)].
V. A. Golenishchev-Kutuzov, V. V. Samartsev, N. K. Solovarov, and B. M. Khabibulin, Magnetic Quantum Acoustics (Nauka, Moscow, 1997).
N. S. Shiren, Phys. Rev. B 2, 2471 (1970).
V. V. Samartsev, B. P. Smolyakov, and R. Z. Sharipov, Pis’ma Zh. Éksp. Teor. Fiz. 20, 644 (1974) [JETP Lett. 20, 296 (1974)].
C. Kittel, Introduction to Solid State Physics, 5th ed. (Wiley, New York, 1976; Nauka, Moscow, 1974).
A. A. Zabolotskii, Phys. Lett. A 127, 83 (1988).
A. A. Zabolotskii, Physica D (Amsterdam) 40, 283 (1989).
A. A. Zabolotskii, Phys. Lett. A 124, 500 (1987).
A. A. Zabolotskii, Phys. Rev. A 57, 2958 (1998).
J. W. Tucker and V. W. Rampton, Microwave Ultrasonics in Solid State Physics (North-Holland, Amsterdam, 1972; Mir, Moscow, 1975).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7: Theory of Elasticity, 4th ed. (Nauka, Moscow, 1987; Pergamon, New York, 1986).
S. A. Al’tshuller and B. M. Kozyrev, Electron Paramagnetic Resonance in Compounds of Transition Elements (Nauka, Moscow, 1981; Halsted, New York, 1975).
Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984; Nauka, Moscow, 1989).
J. D. Gibbon, P. J. Coudrey, J. K. Eilbeck, and R. K. Bullough, J. Phys. A 6, 1237 (1973).
A. E. Borovik and S. I. Kulinich, Pis’ma Zh. Éksp. Teor. Fiz. 39, 320 (1984) [JETP Lett. 39, 384 (1984)].
L. A. Takhtadzhyan and L. A. Faddeev, Hamiltonian Methods in the Theory of Solitons (Nauka, Moscow, 1986; Springer, Berlin, 1987).
A. A. Zabolotskii, Zh. Éksp. Teor. Fiz. 107, 1100 (1995) [JETP 80, 614 (1995)].
A. A. Zabolotskii, Zh. Éksp. Teor. Fiz. 115, 1158 (1999) [JETP 88, 642 (1999)].
S. A. Akhmanov and V. É. Gusev, Usp. Fiz. Nauk 162, 3 (1992) [Sov. Phys. Usp. 35, 153 (1992)].
A. B. Matsko, V. V. Rostovstev, M. Flieschhauer, and M. O. Scully, Phys. Rev. Lett. 86, 2006 (2001); V. Kovalev, Phys. Rev. Lett. 88, 239301-1 (2002).
S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
S. E. Harris, Phys. Rev. Lett. 85, 4032 (2000).
A. B. Matsko, Yu. V. Rostovtsev, H. Z. Cummins, and M. O. Scully, Phys. Rev. Lett. 84, 5752 (2000).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 123, No. 3, 2003, pp. 560–574.
Original Russian Text Copyright © 2003 by Zabolotskii.
Rights and permissions
About this article
Cite this article
Zabolotskii, A.A. Integrable models for the dynamics of a longitudinal-transverse acoustic wave in a crystal with paramagnetic impurities. J. Exp. Theor. Phys. 96, 496–509 (2003). https://doi.org/10.1134/1.1567424
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1567424