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Transmission properties of random point scatterers for waves with two-band dispersion law

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Abstract

The scattering problem is considered for the one-dimensional Dirac equation whose potential is a system of randomly distributed point scatterers. Types of such scatterers are described. The probability densities for the transmission and transformation disbalance coefficients are determined in the high-energy region and various averaged characteristic are calculated.

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References

  1. I. M. Lifschitz, S. A. Gredeskul, and L. A. Pastur,Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

    Google Scholar 

  2. E. N. Bratus, S. A. Gredeskul, L. A. Pastur, and V. S. Shumejko, Quantum dynamics of quasiparticles in a stochastic field and nonlinear dissipation of wave packets,Phys. Lett. A 131:449 (1988).

    Google Scholar 

  3. E. N. Bratus, S. A. Gredeskul, L. A. Pastur, and V. S. Shumejko, Dynamics of quasiparticles in nonstationary random field,Teor. Mat. Fiz. 76:401 (1988).

    Google Scholar 

  4. V. I. Perel and D. G. Poljiakov,Zh. Eksp. Teor. Fiz., to appear.

  5. H. Bateman and A. Erdelyi,Higher Transcendental Functions, Vol. 1 (McGraw-Hill, New York, 1953).

    Google Scholar 

  6. F. Gesztesy and P. Seba, New analytically solvable model of relativistic point interaction,Lett. Math. Phys. 13:345 (1987).

    Google Scholar 

  7. V. A. Marchenko,Spectral Theory for Sturm-Liouville Operators (Naukova Dumka, Kiev, 1988).

    Google Scholar 

  8. S. Albeverio, F. Gesztesy, and H. Holden,Solvable Models in Quantum Mechanics (Springer-Verlag, Berlin, 1988).

    Google Scholar 

  9. N. Dunford and J. T. Schwartz,Linear Operators (Interscience, New York, 1963).

    Google Scholar 

  10. M. S. Birman and M. Z. Solomjak, The spectral asymptotic of integral operators,Izv. Akad. Nauk SSSR 34:1142 (1970).

    Google Scholar 

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Gredeskul, S.A., Pastur, L.A. & Seba, P. Transmission properties of random point scatterers for waves with two-band dispersion law. J Stat Phys 58, 795–816 (1990). https://doi.org/10.1007/BF01026551

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  • DOI: https://doi.org/10.1007/BF01026551

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